# Stoichiometry. Unit Outline

Size: px
Start display at page:

Transcription

1 3 Stoichiometry Unit Outline 3.1 The Mole and Molar Mass 3.2 Stoichiometry and Compound Formulas 3.3 Stoichiometry and Chemical Reactions 3.4 Stoichiometry and Limiting Reactants 3.5 Chemical Analysis In This Unit As you have learned in Units 1 and 2, much of chemistry involves using macroscopic measurements to deduce what happens between atoms and molecules. We now explore the chemical counting unit that links the atomic and macroscopic scales, the mole. The mole allows us to study in greater detail chemical formulas and chemical reactions. Specifically, in this Unit we investigate stoichiometry, the relationship between quantities of materials in chemical reactions. In Unit 4 (Chemical Reactions and Solution Stoichiometry), we will expand our study of stoichiometry to include different types of chemical reactions and focus on reactions that take place in water. Vladmir Fedorchuk/Fotolia.com

2 3.1 The Mole and Molar Mass 3.1a Avogadro s Number As you learned in Unit 1, atoms are so small and have such small masses that any amount of atoms we would work with would be very hard to count. For example, a piece of aluminum about the size of a pencil eraser contains approximately aluminum atoms! The mole (abbreviated mol) is the unit chemists use when counting numbers of atoms or molecules in a sample. The number of particles (atoms, molecules, or other objects) in one mole is equal to the number of atoms in exactly 12 g of carbon-12. This number of particles is called Avogadro s number (N A ) and has a value of In most cases we will use or for Avogadro s number. One mole of any element contains atoms of that element, and one mole of a molecular compound contains molecules of that compound. Avogadro s number is an extremely large number, as it must be to connect tiny atoms to the macroscopic world. Using the mole counting unit to measure something on the macroscopic scale demonstrates just how big Avogadro s number is. For example, one mole of pencil erasers would cover the Earth s surface to a depth of about 500 meters. Interactive Figure shows one mole quantities of some elements and compounds. Avogadro s number can be used to convert between moles and the number of particles in a sample, as shown in the following example. Interactive Figure Recognize how the mole connects macroscopic and atomic scales. Example Problem Convert between moles and numbers of atoms. A sample of titanium contains Ti atoms. What amount of Ti, in moles, does this represent? You are asked to calculate the amount (moles) of Ti in a given sample of the metal. You are given the number of atoms of Ti in the sample. Use the equality 1 mol = atoms to create a conversion factor that converts from units of atoms to units of moles. c One mole quantities of (from left to right) the elements copper, aluminum, sulfur and the compounds potassium dichromate, water, and copper(ii) chloride dihydrate. Charles D. Winters Unit 3 Stoichiometry 56

3 b Example Problem (continued) Ti atoms 3 1 mol Ti mol Ti Ti atoms Is your answer reasonable? The sample contains more than Avogadro s number of Ti atoms and therefore contains more than 1 mol of Ti atoms. Problem b Molar Mass Molar mass is the mass, in grams, of one mole of a substance. The molar mass of an element is the mass in grams of one mole of atoms of the element. It is related to the atomic weight of an element, as shown here: 1 12 C atom = 12 u (1 mole) 12 C atoms = 12 grams Thus, one mole of an element has a mass in grams equal to its atomic weight in atomic mass units (u). For example, according to the periodic table, the element magnesium has an atomic weight of u, and one mole of magnesium atoms has a mass of g. Just as Avogadro s number can be used to convert between moles and the number of particles in a sample, molar mass can be used to convert between moles and the mass in grams of a sample, as shown in the following example. Note that the number of significant figures in molar mass and Avogadro s number can vary. In calculations, include one more significant figure than the data given in the problem so that they do not limit the number of significant figures in the answer. Example Problem Convert between mass and moles of an element. What amount of oxygen, in moles, does 124 g O represent? You are asked to calculate the amount (in moles) of oxygen atoms in a given sample. You are given the mass of the oxygen sample. Use the molar mass of oxygen (1 mol O = g) to create a conversion factor that converts mass (in grams) to amount (in mol) of oxygen. 124 g O 3 1 mol O mol O g c Unit 3 Stoichiometry 57

5 molar mass H 2 O 5 12 mol H2 a 1.01 g g b 1 11 mol O2 a 1 mol H 1 mol O b molar mass H 2 O = g/mol We will generally report the molar mass of an element or compound to two decimal places, unless more significant figures are required in a calculation. Example Problem Determine the molar mass of a compound. Calculate the molar mass for each of the following compounds: a. 2-Propanol, CH 3 CH(OH)CH 3 b. Iron(II) phosphate, Fe 3 (PO 4 ) 2 You are asked to calculate the molar mass of a compound. You are given the compound s formula. Add the molar masses for the constituent elements, taking into account the number of each element present in the compound. a. One mole of 2-propanol, CH 3 CH(OH)CH 3, contains three moles of C, eight moles of H, and one mole of O. C: 3 mol C g 1 mol C g C H: 8 mol H g 1 mol H g H O: 1 mol O g 1 mol O g O molar mass 2-propanol = g C g H g O = g/mol b. One mole of iron(ii) phosphate, Fe 3 (PO 4 ) 2, contains three moles of Fe, two moles of P, and eight moles of O. Fe: 3 mol Fe g g Fe 1 mol Fe P: 2 mol P g 1 mol P g P O: 8 mol O g 1 mol O g O molar mass iron(ii) phosphate = g Fe g P g O = g/mol Problem Unit 3 Stoichiometry 59

6 The molar mass of a compound can be used to convert between moles and the mass in grams of a sample, as shown in the following example. Example Problem Convert between mass and moles of a compound. Use the molar mass of 2-propanol, g/mol, to calculate the amount of 2-propanol present in a 10.0-g sample of the alcohol. You are asked to calculate the amount (mol) of compound present in a given sample. You are given the mass of the sample and the molar mass of the compound. Use the molar mass of 2-propanol to create a conversion factor that converts mass (in grams) to amount (in mol) of 2-propanol g CH 3 CH1OH2CH mol CH 3CH1OH2CH g mol CH 3 CH1OH2CH 3 Note that the molar mass used in the calculation has four significant figures, one more than the data given in the problem. Is your answer reasonable? The mass of the sample is less than the molar mass of the compound, so the amount of compound present is less than 1 mole. Problem Section 3.1 Mastery 3.2 Stoichiometry and Compound Formulas 3.2a Element Composition Stoichiometry is the study of the relationship between relative amounts of substances. The formula of a compound provides information about the relative amount of each element present in either one molecule of the compound or one mole of the compound. For example, one molecule of acetic acid, CH 3 CO 2 H, contains two atoms of oxygen and one mole of acetic acid and contains 2 mol of oxygen atoms. When working with ionic and other types of nonmolecular compounds, the compound formula is still used to describe the stoichiometry of a compound. For example, the ionic compound calcium chloride, CaCl 2, is not made up of CaCl 2 molecules but rather one mole of CaCl 2 contains 1 mol Ca 2+ ions and 2 mol Cl 2 ions. Unit 3 Stoichiometry 60

7 The compound formula can be used to determine the amount of an element present in a sample of compound, as shown in the following example. Example Problem Use compound formulas to determine element composition. A sample of acetic acid, CH 3 CO 2 H, contains 2.50 mol of the compound. Determine the amount (in mol) of each element present and the number of atoms of each element present in the sample. You are asked to calculate the amount (mol) and number of atoms of each element present in a given sample of a compound. You are given the amount of sample (mol) and the chemical formula of the compound. Use the compound formula to create conversion factors that relate the amount (in mol) of each element to one mole of the compound mol CH 3 CO 2 H mol CH 3 CO 2 H mol CH 3 CO 2 H 3 2 mol C 1 mol CH 3 CO 2 H 4 mol H 1 mol CH 3 CO 2 H 2 mol O 1 mol CH 3 CO 2 H mol C mol H mol O Use Avogadro s number and the amount of each element present to determine the number of atoms of each element present in the 2.50-mol sample of acetic acid mol C C atoms 1 mol C 10.0 mol H H atoms 1 mol H C atoms H atoms 5.00 mol O O atoms 1 mol O O atoms Is your answer reasonable? The sample contains more than one mole of the compound, so it also contains more than one mole of each element and more than Avogadro s number of atoms of each element in the compound. Problem Unit 3 Stoichiometry 61

8 3.2b Percent Composition The mole-to-mole relationships in a chemical formula can also be used to determine the percent composition of an element in a compound. The percent composition of an element in a compound is the mass of an element present in exactly 100 g of a compound and is calculated using the following equation: % element 5 1number of atoms of element in formula2 1molar mass of element % (3.1) mass of 1 mol of compound For example, the percent composition of hydrogen in water, H 2 O, is calculated as follows: 2 mol Ha 1.01 g 1 mol H b % H in H 2 O 5 1 mol H 2 Oa g 3 100% % H 1 mol H 2 O b Notice that percent composition is calculated by using the mole-to-mole ratio in the chemical formula of water (2 mol H in 1 mol H 2 O) and converting it to a mass ratio using molar mass. Because water is made up of only two elements and the sum of all the percent composition values must equal 100%, the percent composition of oxygen in water is % O in H 2 O = 100% 2 % H = 100% % = 88.8% O Example Problem Calculate percent composition from a compound formula. Determine the percent composition of each element in potassium permanganate, KMnO 4, a compound used as an antiseptic in some countries. You are asked to calculate the percent composition of each element in a compound. You are given the compound formula. First calculate the molar mass of KMnO 4, then use it along with the chemical formula to calculate the percent composition of each element. molar mass KMnO mol K2 a g 1 mol K b 1 11 mol Mn2 a g g b 1 14 mol O2 a 1 mol Mn 1 mol O b molar mass KMnO 4 = g/mol c Unit 3 Stoichiometry 62

9 b Example Problem (continued) % K in KMnO 4 5 % Mn in KMnO 4 5 % O in KMnO mol K a g 1 mol K b g KMnO % % K 1 mol Mn a g 1 mol Mn b g KMnO % % Mn 4 mol O a g 1 mol O b g KMnO % % O Is your answer reasonable? Each percentage should be less than 100%, and the sum of the percent composition values for the constituent elements must be equal to 100%. Notice that the oxygen percent composition could have been calculated from the % K and % Mn values. % O in KMnO 4 = 100% 2 % K 2 % Mn = 100% % % = 40.48% O The slight difference between the values is due to rounding during the calculation steps. Problem c Empirical Formulas from Percent Composition A common practice in the chemical laboratory is to determine the percent composition of each element in a compound and use that information to determine the formula that shows the simplest whole-number ratio of elements present in the compound, the empirical formula (b Flashback to Section 2.3 Covalent Compounds) of the compound. In a sense, this is the reverse of the process that is used to determine percent composition. The first step in the process is to understand that the percent composition of any element is equal to the mass of that element in exactly 100 g of compound. For example, a compound containing only phosphorus and chlorine is analyzed and found to contain 22.55% P and 77.45% Cl by mass. The percent composition of phosphorus can be written as 22.55% P g P 100 g compound Thus, if we assume that we are working with a sample that has a mass of exactly 100 g, the mass of each element present is equal to the percent composition. For the compound containing only phosphorus and chlorine, 22.55% P = g P in 100 g compound 77.45% Cl = g Cl in 100 g compound Unit 3 Stoichiometry 63

10 To determine the empirical formula of the compound, the mass of each element is converted to an amount in moles g P 3 1 mol P g 1 mol Cl g Cl g mol P mol Cl Thus, this compound contains phosphorus and chlorine in a mole ratio of P Cl The empirical formula, however, shows the simplest whole-number ratio of elements. Dividing each amount by the smallest amount present produces integer subscripts without changing the relative amounts of each element present in the compound mol Cl mol Cl < 3 mol Cl mol P mol P 5 1 mol P Notice that the amount of Cl can be rounded to the nearest whole number. The empirical formula of the compound, therefore, contains 3 mol of Cl and 1 mol of P, or PCl 3. Example Problem Use percent composition to determine an empirical formula. A solid compound is found to contain K, S, and O with the following percent composition: K: 41.09% S: 33.70% O: 25.22% What is the empirical formula of this compound? You are asked to determine the empirical formula for a compound. You are given the percent composition of each element in the compound. First, assume that you are given a 100-g sample, which would mean that the mass of each element in grams is equal to the percent composition value. Calculate the amount (in mol) of each element present, and then use the relative amounts to determine the empirical formula of the compound g K 3 1 mol K g mol K c Unit 3 Stoichiometry 64

11 b Example Problem (continued) g S 3 1 mol S mol S g g O 3 1 mol O mol O g To determine the simplest whole-number ratio of elements, divide each by the smallest value mol K mol S mol O mol K 5 1 mol K mol S 5 1 mol S mol O mol O Recall that the value 1.5 is the same as the fraction 3 / 2. Multiply all three amounts by 2, the fraction denominator, to express the ratio of elements as whole numbers. 1 mol K mol K The empirical formula is therefore K 2 S 2 O 3. 1 mol S mol S 1.5 mol O mol O Problem d Determining Molecular Formulas The empirical formula of a compound gives the simplest whole-number ratio of atoms of each element H H H H present in a compound, but it may not be representative of the molecular formula of a compound. For C H C C H example, the hydrocarbons cyclopropane and cyclobutane have the same empirical formula (CH 2 ) H C C H H C C H but different molecular formulas (C 3 H 6 and C 4 H 8, H H H H respectively). Ionic compounds and other compounds that do not exist as individual molecules are Cyclopropane Cyclobutane always represented using empirical formulas. For molecular compounds, additional information is needed to determine the molecular formula from an empirical formula. Unit 3 Stoichiometry 65

12 The molecular formula of a compound is a whole-number multiple of its empirical formula. For cyclobutane, the empirical formula (CH 2 ) has a molar mass of g/mol and the molecular formula has a molar mass of g/mol. molar mass of compound molar mass of empirical formula g/mol g/mol 5 whole number < 4 The whole-number multiple is equal to the number of empirical formula units in one molecule of the compound. For cyclobutane, there are four empirical formula units per molecule, and the molecular formula is (CH 2 ) 4 or C 4 H 8. The molar mass of a compound must be determined, usually through additional experiments, in order to determine the molecular formula of a compound. Example Problem Use percent composition and molar mass to determine molecular formula. Resorcinol is a compound used in the manufacture of fluorescent and leather dyes as well as to treat acne and other greasy skin conditions. Analysis of the compound showed that it is 65.45% C and 5.493% H, with oxygen accounting for the remainder. In a separate experiment, the molar mass of the compound was found to be g/mol. Determine the molecular formula of resorcinol. You are asked to determine the molecular formula of a compound. You are given the percent composition of all but one element in the compound and the compound s molar mass. First, determine the percent composition of oxygen. % O = % 2 % C 2 % H = % % C % H = 29.06% O Next, assume a 100-g sample and calculate the amount (in mol) of each element present g C 3 1 mol C g g H 3 1 mol H g mol C mol H g O 3 1 mol O g mol O c Unit 3 Stoichiometry 66

13 b Example Problem (continued) To determine the simplest whole-number ratio of elements, divide each by the smallest value mol C mol C < 3 mol C mol H mol H < 3 mol H mol O mol O 5 1 mol O The empirical formula is C 3 H 3 O. Use the molar mass of the empirical formula and the molar mass of the compound to determine the whole-number multiple that relates the empirical and molecular formulas. molar mass of compound molar mass of empirical formula g /mol g/mol 5 2 There are two empirical formula units in the molecular formula. The molecular formula of resorcinol is (C 3 H 3 O) 2 or C 6 H 6 O 2. Is your answer reasonable? The molar mass of the compound should be a whole-number multiple of the empirical formula s molar mass. In this case, it is twice the empirical formula s molar mass, which suggests that the empirical formula was determined correctly. Problem e Hydrated Compounds A hydrated ionic compound is an ionic compound that has a well-defined amount of water trapped within the crystalline solid. The water associated with the compound is called the water of hydration. A hydrated compound formula includes the term nh 2 O, where n is the number of moles of water incorporated into the solid per mole of ionic compound. Prefixes are used in naming hydrated compounds to indicate the number of waters of hydration. Many solids used in the laboratory are hydrated. For example, reagent-grade copper(ii) sulfate is usually provided as the hydrated compound CuSO 4 5H 2 O, copper(ii) sulfate pentahydrate. Some common hydrated compounds and their uses are shown in Table Notice that the molar mass of a hydrated compound includes the mass of the water of hydration. Unit 3 Stoichiometry 67

14 Table Some Common Hydrated Ionic Compounds Molecular Formula Name Molar Mass (g/mol) Common Name Uses Na 2 CO 3 10H 2 O Na 2 S 2 O 3 5H 2 O MgSO 4 7H 2 O CaSO 4 2H 2 O CaSO 4 ½H 2 O CuSO 4 5H 2 O Sodium carbonate decahydrate Sodium thiosulfate pentahydrate Magnesium sulfate heptahydrate Calcium sulfate dihydrate Calcium sulfate hemihydrate Copper(II) sulfate pentahydrate Washing soda Water softener Hypo Photography Epsom salt Dyeing and tanning Gypsum Wallboard Plaster of Paris Casts, molds Blue vitriol Algicide, root killer Heating a hydrated compound releases the water in the crystalline solid. For example, heating the compound CuCl 2 2H 2 O releases two moles of water (in the form of water vapor) per mole of hydrated compound. As shown in the following example problem, we can determine the formula of a hydrated compound by performing this experiment in the laboratory. Example Problem Determine the formula of a hydrated compound. A g sample of a hydrate of CoCl 2 was heated thoroughly in a porcelain crucible until its weight remained constant. After heating, g of the dehydrated compound remained in the crucible. What is the formula of the hydrate? You are asked to determine the formula of an ionic hydrated compound. You are given the mass of the hydrated compound and the mass of the compound when it has been dehydrated. First, determine the mass of water lost when the hydrated compound was heated g g = g H 2 O c Unit 3 Stoichiometry 68

15 b Example Problem (continued) Next, calculate moles of water and moles of the dehydrated compound g H 2 O 3 1 mol H 2 O g mol H 2O g CoCl mol CoCl g mol CoCl 2 Finally, determine the simplest whole-number ratio of water to dehydrated compound mol H 2 O mol H 2O < 6 mol H 2O mol CoCl 2 1 mol CoCl 2 1 mol CoCl 2 The chemical formula for the hydrated compound is CoCl 2 6H 2 O. Problem Section 3.2 Mastery 3.3 Stoichiometry and Chemical Reactions 3.3a Chemical Reactions and Chemical Equations Stoichiometry is used not only to determine the chemical formula of a compound but also to study the relative amounts of compounds involved in chemical reactions. Chemical reactions are represented by chemical equations, in which the reacting species (reactants) are shown to the left of a reaction arrow and the species produced during the reaction (products) appear to the right of the reaction arrow. In addition, the physical state of each reactant and product is often indicated using the symbols (g), (l), (s), and (aq) for gas, liquid, solid, and aqueous (dissolved in water) solution, respectively. For example, the reaction of gaseous methane (CH 4 ) with gaseous molecular oxygen to produce gaseous carbon dioxide and water vapor is written as CH 4 (g) 1 2 O 2 (g) CO 2 (g) 1 2 H 2 O(g) reactants products Reading the equation, we say that one CH 4 molecule and two O 2 molecules react to form one CO 2 molecule and two H 2 O molecules. The number that appears to the left of a compound formula in a balanced equation is called a stoichiometric coefficient; it indicates the relative number of molecules of that reactant or product in the reaction. (A stoichiometric coefficient of 1 is not written in a chemical equation.) Recall that the subscript to the right of each element symbol indicates the relative number of atoms of that element in the compound. Therefore, multiplying the stoichiometric coefficient of a compound by the subscript for each element in the compound formula gives the total number of atoms of each element that the compound contributes to the reactants or products. Unit 3 Stoichiometry 69

16 The word equation, which means equal on both sides, reflects the fact that when a chemical reaction takes place, matter is neither created nor destroyed, in accordance with the Law of Conservation of Matter. This means that the products of a chemical reaction are made up of the same type and number of atoms found in the reactants but rearranged into new compounds. In the reaction of methane with oxygen, for example, both the reactants and the products contain one carbon atom, four hydrogen atoms, and four oxygen atoms Cengage Learning H H C H H Reactants O O O O O C O Products H H O O H H The reactants in this reaction are a CH 4 molecule and two O 2 molecules. When the re action occurs, the chemical bonds between elements in the reactants are broken and new bonds are formed to make products. The same atoms are present both before and after the reaction, but the linkages between them have changed. When an equation meets the conditions of the Law of Conservation of Matter by having the same num-ber of atoms of each element on both sides of the reaction arrow, the equation is balanced. Example Problem Identify the components of a chemical equation. Consider the following chemical equation: MgCO 3 (s) + 2 HCl(aq) S CO 2 (g) + MgCl 2 (aq) + H 2 O(l) a. Is CO 2 a reactant or a product in the reaction? b. How many chlorine atoms are there in the reactants? c. What is the physical state of H 2 O in this reaction? You are asked to answer questions about a chemical equation. You are given a chemical equation. a. Product. Chemical products are shown to the right of a reaction arrow. b. Two. There is one chlorine atom in an HCl molecule. The stoichiometric coefficient to the left of HCl indicates that there are two HCl molecules, and thus two Cl atoms, in the reactants. c. Liquid. The liquid physical state is indicated by the symbol (l). Problem Unit 3 Stoichiometry 70

17 3.3b Balancing Chemical Equations Very often we know what elements and compounds are involved in a reaction but not the relative amounts. To correctly describe the reaction, we must determine the relative amounts of the reactants and products involved in the reaction by balancing the equation (Interactive Figure 3.3.1). For example, consider the reaction that occurs in a gas grill when propane (C 3 H 8 ) reacts with oxygen to form carbon dioxide and water. The unbalanced equation and the number of each element present in the reactants and product are C 3 H 8 + O 2 S CO 2 + H 2 O 3 C 1 C 8 H 2 H 2 O 3 O The equation is not balanced because the number of atoms of each element present in the reactants is not equal to the number present in the products. The equation can be balanced by changing the coefficients to the left of each chemical species from 1 to a whole number that results in equal numbers of atoms of each element on both sides of the reaction arrow. It is important to note that the subscripts in a chemical formula are never changed when balancing an equation. A change in the subscript in a formula changes the chemical identity of the compound, not the amount of compound present in the reaction. Although balancing chemical equations is usually done by trial and error, it is helpful to follow some general guidelines. Interactive Figure Relate conservation of mass to balanced equations CH 4 2 O 2 1 CO 2 2 H 2 O Reactants Products REACTANTS C: 1 H: 4 O: 4 PRODUCTS C: 1 H: 4 O: 4 Number of Atoms The mass of reactants equals the mass of the products 2013 Cengage Learning 1. If an element appears in more than one compound in the reactants or products, it is usually best to balance that element last. In this case, we will begin by balancing carbon and hydrogen, balancing oxygen last because it appears in two compounds in the products. 2. As stated earlier, only coefficients are changed when balancing equations, never the subscripts within a chemical formula. For example, we cannot balance carbon by changing the formula of CO 2 to C 3 O 2. Although this balances the number of carbon atoms, this change alters the chemical identity of the compound and makes the chemical equation invalid. 3. Balanced chemical equations are written so that the coefficients are the lowest possible whole numbers. Balance Carbon In the unbalanced equation, there are three carbon atoms in the reactants and only one carbon atom in the products. Changing the coefficient in front of CO 2 from 1 to 3 balances Unit 3 Stoichiometry 71

18 the carbon atoms in the equation and also increases the number of oxygen atoms in the products from 3 to 7. C 3 H 8 + O 2 S 3 CO 2 + H 2 O 3 C 3 C 8 H 2 H 2 O 7 O Balance Hydrogen There are eight hydrogen atoms in the reactants and only two hydrogen atoms in the products. Each increase in the H 2 O coefficient increases the number of hydrogen atoms by a factor of 2. Changing the coefficient in front of H 2 O from 1 to 4 balances the number of hydrogen atoms in the equation and also increases the number of oxygen atoms in the products from 7 to 10. C 3 H 8 + O 2 S 3 CO H 2 O 3 C 3 C 8 H 8 H 2 O 10 O Balance Oxygen There are 10 oxygen atoms in the products (6 in the three CO 2 molecules and 4 in the four H 2 O molecules) and only 2 in the reactants. Each increase in the O 2 coefficient increases the number of oxygen atoms by a factor of 2, so changing the coefficient in front of O 2 from 1 to 5 balances the oxygen atoms in the equation. C 3 H O 2 S 3 CO H 2 O 3 C 3 C 8 H 8 H 10 O 10 O 2013 Cengage Learning 1 1 The number of atoms of each element in the reactants and products is the same, so the equation is balanced. Finally, note that this equation can be balanced using a multiple of the coefficients above. Unit 3 Stoichiometry 72

19 2 C 3 H O 2 S 6 CO H 2 O 6 C 6 C 16 H 16 H 20 O 20 O However, this is incorrect because it is possible to balance the equation using simpler coefficients. Example Problem Balance equations. Balance the chemical equation for the neutralization of phosphoric acid by calcium hydroxide to form calcium phosphate and water. The unbalanced equation is H 3 PO 4 + Ca(OH) 2 S Ca 3 (PO 4 ) 2 + H 2 O. You are asked to balance a chemical equation. You are given an unbalanced equation. Notice that both hydrogen and oxygen appear in more than one compound in the reactants. Begin by balancing the other elements, phosphorus and calcium, before balancing hydrogen and oxygen. H 3 PO 4 + Ca(OH) 2 S Ca 3 (PO 4 ) 2 + H 2 O 5 H 2 H 1 P 2 P 6 O 9 O 1 Ca 3 Ca Balance phosphorus. Change the coefficient in front of H 3 PO 4 from 1 to 2 and note the change in H and O. 2 H 3 PO 4 + Ca(OH) 2 S Ca 3 (PO 4 ) 2 + H 2 O 8 H 2 H 2 P 2 P 10 O 9 O 1 Ca 3 Ca Balance calcium. Change the coefficient in front of Ca(OH) 2 from 1 to 3 and note the change in H and O. 2 H 3 PO Ca(OH) 2 S Ca 3 (PO 4 ) 2 + H 2 O 12 H 2 H 2 P 2 P 14 O 9 O 3 Ca 3 Ca c Unit 3 Stoichiometry 73

20 b Example Problem (continued) Balance hydrogen and oxygen. Changing the coefficient in front of H 2 O from 1 to 6 (each increase in the H 2 O coefficient adds two H atoms) balances both hydrogen and oxygen. The equation is balanced. 2 H 3 PO Ca(OH) 2 S Ca 3 (PO 4 ) H 2 O 12 H 12 H 2 P 2 P 14 O 14 O 3 Ca 3 Ca Is your answer reasonable? When balancing equations, it is a good idea to check the atom balance for all elements in the equation when you are finished. In this case, there are equal numbers of elements in both reactants and products, so the equation is balanced. Problem c Reaction Stoichiometry A balanced chemical equation shows the relative amounts of reactants and products involved in a chemical reaction on both the molecular and macroscopic scale. For example, the balanced equation for the reaction of methane with oxygen to form carbon dioxide and water describes the reaction at the atomic level and at the macroscopic level. CH O 2 S CO H 2 O 1 CH 4 molecule + 2 O 2 molecules S 1 CO 2 molecule + 2 H 2 O molecules 1 mol CH mol O 2 S 1 mol CO mol H 2 O g CH g O 2 S g CO g H 2 O On the molecular level, one molecule of CH 4 reacts with two molecules of O 2 to produce one molecule of CO 2 and two molecules of H 2 O. Scaling up to macroscopic amounts, the equation also represents the reaction of one mole of CH 4 (16.04 g) with two moles of O 2 (64.00 g) to form one mole of CO 2 (44.01 g) and two moles of H 2 O (36.03 g). Reaction stoichiometry is the study of the relationships between the amount of reactants and products on the macroscopic scale, and balanced chemical equations are the key to understanding these relationships. Consider the reaction between butane and oxygen to form carbon dioxide and water. The balanced equation is 2 C 4 H O 2 S 8 CO H 2 O Unit 3 Stoichiometry 74

21 According to the balanced equation, 8 mol of CO 2 are produced for every 2 mol of C 4 H 10 that react with oxygen. A typical reaction, however, might involve more or fewer than 2 mol of butane. The balanced equation gives us the information needed to determine the amount of CO 2 produced from any amount of C 4 H 10. The mole-to-mole relationships in a balanced chemical equation are used in the form of conversion factors to relate amounts of materials reacting or forming during a chemical reaction. For example, consider a butane lighter that contains 0.24 mol of C 4 H 10. We can use the coefficients in the balanced equation to determine the amount of carbon dioxide produced in the reaction of this amount of butane with oxygen. 2 C 4 H O 2 S 8 CO H 2 O 0.24 mol C 4 H mol CO 2 2 mol C 4 H mol CO 2 The ratio of coefficients from the balanced equation, called the stoichiometric factor (or stoichiometric ratio), relates the amount of one species to another. In this case, the stoichiometric factor relates the amount of carbon dioxide formed from the reaction of butane with oxygen. It is important to note that stoichiometric factors are always created from coefficients in a balanced chemical equation. The amount of water produced in the reaction can also be determined. Again, a stoichiometric factor is created using the coefficients in the balanced equation that relate moles of H 2 O and C 4 H C 4 H O 2 S 8 CO H 2 O 0.24 mol C 4 H mol H 2O 2 mol C 4 H mol H 2 O Stoichiometric relationships exist between all species in a balanced equation, not just between reactants and products. For example, if the reaction of a sample of butane with oxygen produces 2.8 mol of CO 2, it is possible to determine the amount of H 2 O produced using a stoichiometric factor. 2.8 mol CO mol H 2O 8 mol CO mol H 2 O Unit 3 Stoichiometry 75

22 Example Problem Use balanced chemical equations to relate amounts of reactants and products. The unbalanced equation for the reaction between magnesium nitride and sulfuric acid is shown here. Mg 3 N 2 (s) + H 2 SO 4 (aq) S MgSO 4 (aq) + (NH 4 ) 2 SO 4 (aq) Balance the equation and determine the amount of H 2 SO 4 consumed and the amounts of MgSO 4 and (NH 4 ) 2 SO 4 produced when 3.5 mol of Mg 3 N 2 reacts. You are asked to balance a chemical equation and determine the amount of reactant consumed and products formed by a given amount of reactant. You are given an unbalanced equation and the amount of one reactant consumed in the reaction. Step 1. Write a balanced chemical equation. Mg 3 N 2 (s) + 4 H 2 SO 4 (aq) S 3 MgSO 4 (aq) + (NH 4 ) 2 SO 4 (aq) Step 2. Use the coefficients in the balanced equation to create a stoichiometric factor that will convert moles of Mg 3 N 2 to moles of H 2 SO 4 consumed. 3.5 mol Mg 3 N mol H 2SO mol H 2 SO 4 consumed 1 mol Mg 3 N 2 Step 3. Use the coefficients in the balanced equation to create a stoichiometric factor that will convert moles of Mg 3 N 2 to moles of MgSO 4 produced. 3.5 mol Mg 3 N mol MgSO mol MgSO 4 1 mol Mg 3 N 2 Step 4. Use the coefficients in the balanced equation to create a stoichiometric factor that will convert moles of Mg 3 N 2 to moles of (NH 4 ) 2 SO 4 produced. 3.5 mol Mg 3 N mol 1NH 4 2 2SO 4 1 mol Mg 3 N mol 1NH SO 4 Is your answer reasonable? According to the balanced equation, one mole of Mg 3 N 2 reacts with four moles of H 2 SO 4, producing three moles of MgSO 4 and one mole of (NH 4 ) 2 SO 4. Here, more than one mole of Mg 3 N 2 reacts, which means more than these amounts of reactants and products are consumed and produced, respectively. Problem Unit 3 Stoichiometry 76

23 Molar mass is combined with stoichiometric factors in order to determine the mass of each species consumed or produced in the reaction. In these types of calculations, it is very important to keep track of the units for each value calculated. For example, the mass of oxygen consumed by 7.8 g of C 4 H 10 is calculated as shown here. First, convert the mass of butane to an amount in units of moles. 7.8 g C 4 H mol C 4H mol C 58.1 g 4 H 10 Next, use the stoichiometric factor from the balanced equation to convert moles of C 4 H 10 to moles of O mol C 4 H mol O 2 2 mol C 4 H mol O 2 Finally, use the molar mass of oxygen to calculate the mass of O 2 consumed by 7.8 g of C 4 H mol O g 1 mol O g O 2 In the calculations above, values were rounded to the correct number of significant figures after each step. This introduces rounding errors that can be eliminated by carrying extra significant figures until the final calculation is performed or by combining the calculations into a single step. In general, stoichiometric calculations are performed in the following order: Grams of A Grams of B g A 3 mol A g A Multiply by 1/molar mass of A. Multiply by molar mass of B. mol B 3 g B mol B 2013 Cengage Learning Moles of A mol A 3 mol B mol A Multiply by the stoichiometric ratio. Moles of B Unit 3 Stoichiometry 77

24 Example Problem Use reaction stoichiometry to calculate amounts of reactants and products. Calcium carbonate reacts with hydrochloric acid to form calcium chloride, carbon dioxide, and water. Unbalanced equation: CaCO 3 + HCl S CaCl 2 + CO 2 + H 2 O In one reaction, 54.6 g of CO 2 is produced. What amount (in mol) of HCl was consumed? What mass (in grams) of calcium chloride is produced? You are asked to calculate the amount (in mol) of a reactant consumed and the mass (in grams) of a product formed in a reaction. You are given the unbalanced equation and the mass of one of the products of the reaction. Step 1. Write a balanced chemical equation. CaCO HCl S CaCl 2 + CO 2 + H 2 O Step 2. Calculate moles of CO 2 produced g CO mol CO mol CO g Step 3. Calculate moles of HCl consumed and moles of CaCl 2 produced using stoichiometric factors derived from the balanced chemical equation. 2 mol HCl 1.24 mol CO mol HCl 1 mol CO mol CO mol CaCl mol CaCl 1 mol CO 2 2 Step 4. Calculate mass (in grams) of CaCl 2 produced mol CaCl g g CaCl 1 mol CaCl 2 2 Notice that it is possible to set up both calculations as a single step g CO 2 a 1 mol CO 2 2 mol HCl b a b mol HCl g 1 mol CO g CO 2 a 1 mol CO g b a1 mol CaCl g b a b g CaCl 1 mol CO 2 1 mol CaCl 2 2 Is your answer reasonable? More than one mole of CO 2 is produced in the reaction, so the amounts of HCl consumed and CaCl 2 produced are greater than one mole. Problem Section 3.3 Mastery Unit 3 Stoichiometry 78

25 3.4 Stoichiometry and Limiting Reactants 3.4a Limiting Reactants A balanced equation represents a situation in which a reaction proceeds to completion and all of the reactants are converted into products. Under nonstoichiometric conditions, the reaction continues only until one of the reactants is entirely consumed, and at this point the reaction stops. Under these conditions, it is important to know which reactant will be consumed first and how much product can be produced. When a butane lighter is lit, for example, only a small amount of butane is released from the lighter and combined with a much larger amount of oxygen present in air. 2 C 4 H O 2 S 8 CO H 2 O Under these conditions, the oxygen is considered an excess reactant because more is available than is required for reaction with butane. The butane is the limiting reactant, which means that it controls the amount of products produced in the reaction. When a nonstoichiometric reaction is complete, the limiting reactant is completely consumed and some amount of the excess reactant remains unreacted (Interactive Figure 3.4.1). Consider a situation where 12 mol of butane is combined with 120 mol of oxygen. Under stoichiometric conditions, butane and oxygen react in a 2:13 mole ratio. The amount of oxygen needed to react with 12 mol of butane is Interactive Figure Determine how much Zn remains after reaction with HCl. mol O 2 needed 5 12 mol C 4 H mol O 2 2 mol C 4 H mol O 2 Because more oxygen is available than is needed to react with all of the available butane (120 mol available versus 78 mol needed), oxygen is the excess reactant. The amount of butane that would be needed to react with 120 mol of O 2 is mol C 4 H 10 needed mol O mol C 4H mol O mol C 4 H 10 Less butane is available than is needed to react with all of the oxygen available (12 mol available versus 18 mol needed), so butane is the limiting reactant. The amount of products that can be produced in the reaction is determined by the amount of limiting reactant present. For water, mol H 2 O produced 5 12 mol C 4 H mol H 2O 2 mol C 4 H mol H 2 O Reaction of Zn with HCl Charles D. Winters Unit 3 Stoichiometry 79

26 The limiting reactant concept can be illustrated in the laboratory. For example, consider the reaction of iron(iii) chloride with sodium hydroxide. FeCl 3 (aq) + 3 NaOH(aq) S Fe(OH) 3 (s) + 3 NaCl(aq) If a student starts with 50.0 g of FeCl 3 and adds NaOH in 1-gram increments, the mass of Fe(OH) 3 produced in each experiment can be measured. Plotting mass of Fe(OH) 3 as a function of mass of NaOH added results in the graph shown in Interactive Figure As expected, as more NaOH is added to the FeCl 3, increasing amounts of Fe(OH) 3 are produced. But when more than 37.0 g of NaOH are added, the mass of Fe(OH) 3 no longer changes. When 37.0 g (0.925 mol) of NaOH are added to 50.0 g (0.308 mol) of FeCl 3, the stoichiometric ratio is equal to 3:1 and all reactants are consumed completely. When more than 37.0 g of NaOH are added to 50.0 g FeCl 3, there is excess NaOH available (FeCl 3 is limiting) and no additional Fe(OH) 3 is produced. Example Problem Identify limiting reactants (mole ratio method). Identify the limiting reactant in the reaction of hydrogen and oxygen to form water if 61.0 g of O 2 and 8.40 g of H 2 are combined. Determine the amount (in grams) of excess reactant that remains after the reaction is complete. You are asked to identify the limiting reactant and mass (in grams) of the excess reactant remaining after the reaction is complete. You are given the mass of the reactants. Step 1. Write a balanced chemical equation. 2 H 2 + O 2 S 2 H 2 O Step 2. Determine the limiting reactant by comparing the relative amounts of reactants available. Calculate the amount (in mol) of one of the reactants needed and compare that value to the amount available. Interactive Figure Analyze reaction stoichiometry in the laboratory. Mass Fe(OH) 3 produced, g Mass NaOH added, g Mass of Fe(OH) 3 as a function of mass of NaOH Cengage Learning amount of O 2 needed: 8.40 g H 2 a 1 mol H g b a1 mol O 2 2 mol H 2 b mol O 2 amount of O 2 available: 61.0 g O mol O g mol O 2 More O 2 is needed (2.08 mol) than is available (1.91 mol), so O 2 is the limiting reactant. c Unit 3 Stoichiometry 80

27 b Example Problem (continued) Alternatively, the amounts of reactants available can be compared to the stoichiometric ratio in the balanced equation in order to determine the limiting reactant mol H mol H 2. 2 mol H mol O 2 1 mol O 2 1 mol O 2 ratio of reactants ratio of reactants (available) (balanced equation) Here, the mole ratio of H 2 to O 2 available is greater than the mole ratio from the balanced chemical equation. Thus, hydrogen is in excess and oxygen is the limiting reactant. Step 3. Use the amount of limiting reactant (O 2 ) available to calculate the amount of excess reactant (H 2 ) needed for complete reaction mol O 2 a 2 mol H 2 b a g b g H 1 mol O 2 1 mol H 2 2 Step 4. Calculate the mass of excess reactant that remains when all the limiting reactant is consumed g H 2 available g H 2 consumed = 0.70 g H 2 remains Is your answer reasonable? More O 2 is needed than is available, so it is the limiting reactant. There is H 2 remaining after the reaction is complete because it is the excess reactant in the reaction. Problem An alternative method of performing stoichiometry calculations that involve limiting reactants is to simply calculate the maximum amount of product that could be produced from each reactant. (This method works particularly well for reactions with more than two reactants.) In this method, the reactant that produces the least amount of product is the limiting reactant. Example Problem Identify limiting reactants (maximum product method). Consider the reaction of gold with nitric acid and hydrochloric acid. Au + 3 HNO HCl S HAuCl NO H 2 O Determine the limiting reactant in a mixture containing 125 g of each reactant and calculate the maximum mass (in grams) of HAuCl 4 that can be produced in the reaction. c Unit 3 Stoichiometry 81

28 b Example Problem (continued) You are asked to calculate the maximum mass of a product that can be formed in a reaction. You are given the balanced equation and the mass of each reactant available. In this case there are three reactants, so it is most efficient to calculate the maximum amount of product (HAuCl 4 ) that can be produced by each one. The reactant that produces the least amount of HAuCl 4 is the limiting reactant. Step 1. Write the balanced chemical equation. Au + 3 HNO HCl S HAuCl NO H 2 O Step 2. Use the molar 1 mass mol Au 125 g Aua of each reactant and the stoichiometric factors derived from the balanced equation to calculate g the b a1 mol HAuCl 4 amount 1 mol Au of HAuCl b a g b g HAuCl 1 mol 4 that HAuCl 4 can be 4 produced by each reactant. 1 mol Au 125 g Aua g b a1 mol HAuCl 4 1 mol Au b a g b g HAuCl 1 mol HAuCl g HNO 3 a 1 mol HNO 3 b a 1 mol HAuCl g b a b g HAuCl g 3 mol HNO 3 1 mol HAuCl mol HCl 125 g HCla g b a1 mol HAuCl g b a b g HAuCl 4 mol HCl 1 mol HAuCl 4 4 Gold is the limiting reagent. The maximum amount of HAuCl 4 that can be produced is 216 g. Problem b Percent Yield When chemists perform experiments to make a compound, it is rare that the amount of materials produced is equal to that predicted based on stoichiometric calculations. The reasons for this are numerous. For example, side reactions may occur, using some of the reactants to make other, undesired products. Sometimes, the reaction does not go to completion and some reactants remain unreacted. In other cases, some of the product cannot be physically isolated (for example, because it is embedded in filter paper, it does not completely precipitate from solution or is lost via evaporation). Because laboratory results rarely match calculations exactly, we make a distinction between the predicted amount of product, called the theoretical yield, and the actual amount of product produced in the experiment, called the experimental yield (or actual yield). Unit 3 Stoichiometry 82

29 When reporting the success of a chemical synthesis, the ratio of product mass obtained (the experimental yield) to the maximum mass that could have been produced based on the amounts of reactants used (the theoretical yield) is calculated. This ratio is reported in the form of a percent, called the percent yield of a reaction. experimental yield percent yield % (3.2) theoretical yield All the calculations we have done to this point allow us to determine the theoretical yield for a reaction. An experimental yield value is never calculated but is instead measured in the chemical laboratory after a reaction is complete. Example Problem Calculate percent yield. Consider the reaction of Pb(NO 3 ) 2 with NaCl to form PbCl 2 and NaNO 3. If 24.2 g Pb(NO 3 ) 2 is reacted with excess NaCl and 17.3 g of PbCl 2 is ultimately isolated, what is the percent yield for the reaction? You are asked to calculate the percent yield for a reaction. You are given the mass of the limiting reactant and the experimental yield for one of the products in the reaction. Step 1. Write a balanced chemical equation for the reaction. Pb(NO 3 ) NaCl S PbCl NaNO 3 Step 2. Use the amount of limiting reactant to calculate the theoretical yield of PbCl g Pb1NO a 1 mol Pb1NO b a 1 mol PbCl g b a b g PbCl g 1 mol Pb1NO mol PbCl 2 2 Step 3. Use the experimental yield (17.3 g PbCl 2 ) and the theoretical yield (20.3 g PbCl 2 ) to calculate the percent yield for the reaction g PbCl % % 20.3 g PbCl 2 Is your answer reasonable? The theoretical yield is greater than the experimental yield, so the percent yield is less than 100%. Problem Section 3.4 Mastery Unit 3 Stoichiometry 83

### Chapter 3 Stoichiometry

Chapter 3 Stoichiometry 3-1 Chapter 3 Stoichiometry In This Chapter As you have learned in previous chapters, much of chemistry involves using macroscopic measurements to deduce what happens between atoms

### Calculating Atoms, Ions, or Molecules Using Moles

TEKS REVIEW 8B Calculating Atoms, Ions, or Molecules Using Moles TEKS 8B READINESS Use the mole concept to calculate the number of atoms, ions, or molecules in a sample TEKS_TXT of material. Vocabulary

### Formulas, Equations and Moles

Chapter 3 Formulas, Equations and Moles Interpreting Chemical Equations You can interpret a balanced chemical equation in many ways. On a microscopic level, two molecules of H 2 react with one molecule

### Moles. Balanced chemical equations Molar ratios Mass Composition Empirical and Molecular Mass Predicting Quantities Equations

Moles Balanced chemical equations Molar ratios Mass Composition Empirical and Molecular Mass Predicting Quantities Equations Micro World atoms & molecules Macro World grams Atomic mass is the mass of an

### Balance the following equation: KClO 3 + C 12 H 22 O 11 KCl + CO 2 + H 2 O

Balance the following equation: KClO 3 + C 12 H 22 O 11 KCl + CO 2 + H 2 O Ans: 8 KClO 3 + C 12 H 22 O 11 8 KCl + 12 CO 2 + 11 H 2 O 3.2 Chemical Symbols at Different levels Chemical symbols represent

### IB Chemistry. DP Chemistry Review

DP Chemistry Review Topic 1: Quantitative chemistry 1.1 The mole concept and Avogadro s constant Assessment statement Apply the mole concept to substances. Determine the number of particles and the amount

### The Mole Concept. The Mole. Masses of molecules

The Mole Concept Ron Robertson r2 c:\files\courses\1110-20\2010 final slides for web\mole concept.docx The Mole The mole is a unit of measurement equal to 6.022 x 10 23 things (to 4 sf) just like there

### Chapter 1: Moles and equations. Learning outcomes. you should be able to:

Chapter 1: Moles and equations 1 Learning outcomes you should be able to: define and use the terms: relative atomic mass, isotopic mass and formula mass based on the 12 C scale perform calculations, including

### 1. What is the molecular formula of a compound with the empirical formula PO and a gram-molecular mass of 284 grams?

Name: Tuesday, May 20, 2008 1. What is the molecular formula of a compound with the empirical formula PO and a gram-molecular mass of 284 grams? 2 5 1. P2O 5 3. P10O4 2. P5O 2 4. P4O10 2. Which substance

### Calculation of Molar Masses. Molar Mass. Solutions. Solutions

Molar Mass Molar mass = Mass in grams of one mole of any element, numerically equal to its atomic weight Molar mass of molecules can be determined from the chemical formula and molar masses of elements

### Chapter 3: Stoichiometry

Chapter 3: Stoichiometry Key Skills: Balance chemical equations Predict the products of simple combination, decomposition, and combustion reactions. Calculate formula weights Convert grams to moles and

### Chapter 5, Calculations and the Chemical Equation

1. How many iron atoms are present in one mole of iron? Ans. 6.02 1023 atoms 2. How many grams of sulfur are found in 0.150 mol of sulfur? [Use atomic weight: S, 32.06 amu] Ans. 4.81 g 3. How many moles

### Chapter 3. Chemical Reactions and Reaction Stoichiometry. Lecture Presentation. James F. Kirby Quinnipiac University Hamden, CT

Lecture Presentation Chapter 3 Chemical Reactions and Reaction James F. Kirby Quinnipiac University Hamden, CT The study of the mass relationships in chemistry Based on the Law of Conservation of Mass

### Study Guide For Chapter 7

Name: Class: Date: ID: A Study Guide For Chapter 7 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. The number of atoms in a mole of any pure substance

### W1 WORKSHOP ON STOICHIOMETRY

INTRODUCTION W1 WORKSHOP ON STOICHIOMETRY These notes and exercises are designed to introduce you to the basic concepts required to understand a chemical formula or equation. Relative atomic masses of

### Formulae, stoichiometry and the mole concept

3 Formulae, stoichiometry and the mole concept Content 3.1 Symbols, Formulae and Chemical equations 3.2 Concept of Relative Mass 3.3 Mole Concept and Stoichiometry Learning Outcomes Candidates should be

### Sample Exercise 3.1 Interpreting and Balancing Chemical Equations

Sample Exercise 3.1 Interpreting and Balancing Chemical Equations The following diagram represents a chemical reaction in which the red spheres are oxygen atoms and the blue spheres are nitrogen atoms.

### The Mole Concept and Atoms

Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Chapter 4 24 September 2013 Calculations and the Chemical Equation The Mole Concept and Atoms Atoms are exceedingly

### Chapter 1 The Atomic Nature of Matter

Chapter 1 The Atomic Nature of Matter 6. Substances that cannot be decomposed into two or more simpler substances by chemical means are called a. pure substances. b. compounds. c. molecules. d. elements.

### stoichiometry = the numerical relationships between chemical amounts in a reaction.

1 REACTIONS AND YIELD ANSWERS stoichiometry = the numerical relationships between chemical amounts in a reaction. 2C 8 H 18 (l) + 25O 2 16CO 2 (g) + 18H 2 O(g) From the equation, 16 moles of CO 2 (a greenhouse

### Chem 1100 Chapter Three Study Guide Answers Outline I. Molar Mass and Moles A. Calculations of Molar Masses

Chem 1100 Chapter Three Study Guide Answers Outline I. Molar Mass and Moles A. Calculations of Molar Masses B. Calculations of moles C. Calculations of number of atoms from moles/molar masses 1. Avagadro

### Stoichiometry. Lecture Examples Answer Key

Stoichiometry Lecture Examples Answer Key Ex. 1 Balance the following chemical equations: 3 NaBr + 1 H 3 PO 4 3 HBr + 1 Na 3 PO 4 2 C 3 H 5 N 3 O 9 6 CO 2 + 3 N 2 + 5 H 2 O + 9 O 2 2 Ca(OH) 2 + 2 SO 2

### Moles. Moles. Moles. Moles. Balancing Eqns. Balancing. Balancing Eqns. Symbols Yields or Produces. Like a recipe:

Like a recipe: Balancing Eqns Reactants Products 2H 2 (g) + O 2 (g) 2H 2 O(l) coefficients subscripts Balancing Eqns Balancing Symbols (s) (l) (aq) (g) or Yields or Produces solid liquid (pure liquid)

### Chemical Equations & Stoichiometry

Chemical Equations & Stoichiometry Chapter Goals Balance equations for simple chemical reactions. Perform stoichiometry calculations using balanced chemical equations. Understand the meaning of the term

### Chapter 6 Chemical Calculations

Chapter 6 Chemical Calculations 1 Submicroscopic Macroscopic 2 Chapter Outline 1. Formula Masses (Ch 6.1) 2. Percent Composition (supplemental material) 3. The Mole & Avogadro s Number (Ch 6.2) 4. Molar

### YIELD YIELD REACTANTS PRODUCTS

Balancing Chemical Equations A Chemical Equation: is a representation of a chemical reaction in terms of chemical formulas Example: 1. Word Description of a Chemical Reaction When methane gas (CH 4 ) burns

### MOLES AND MOLE CALCULATIONS

35 MOLES ND MOLE CLCULTIONS INTRODUCTION The purpose of this section is to present some methods for calculating both how much of each reactant is used in a chemical reaction, and how much of each product

### Unit 2: Quantities in Chemistry

Mass, Moles, & Molar Mass Relative quantities of isotopes in a natural occurring element (%) E.g. Carbon has 2 isotopes C-12 and C-13. Of Carbon s two isotopes, there is 98.9% C-12 and 11.1% C-13. Find

### Name Date Class CHEMICAL QUANTITIES. SECTION 10.1 THE MOLE: A MEASUREMENT OF MATTER (pages 287 296)

10 CHEMICAL QUANTITIES SECTION 10.1 THE MOLE: A MEASUREMENT OF MATTER (pages 287 296) This section defines the mole and explains how the mole is used to measure matter. It also teaches you how to calculate

### SCH 4C1 Unit 2 Problem Set Questions taken from Frank Mustoe et all, "Chemistry 11", McGraw-Hill Ryerson, 2001

SCH 4C1 Unit 2 Problem Set Questions taken from Frank Mustoe et all, "Chemistry 11", McGraw-Hill Ryerson, 2001 1. A small pin contains 0.0178 mol of iron. How many atoms of iron are in the pin? 2. A sample

### Chemical Calculations: Formula Masses, Moles, and Chemical Equations

Chemical Calculations: Formula Masses, Moles, and Chemical Equations Atomic Mass & Formula Mass Recall from Chapter Three that the average mass of an atom of a given element can be found on the periodic

### Element of same atomic number, but different atomic mass o Example: Hydrogen

Atomic mass: p + = protons; e - = electrons; n 0 = neutrons p + + n 0 = atomic mass o For carbon-12, 6p + + 6n 0 = atomic mass of 12.0 o For chlorine-35, 17p + + 18n 0 = atomic mass of 35.0 atomic mass

### Chapter 3 Mass Relationships in Chemical Reactions

Chapter 3 Mass Relationships in Chemical Reactions Student: 1. An atom of bromine has a mass about four times greater than that of an atom of neon. Which choice makes the correct comparison of the relative

### Other Stoich Calculations A. mole mass (mass mole) calculations. GIVEN mol A x CE mol B. PT g A CE mol A MOLE MASS :

Chem. I Notes Ch. 12, part 2 Using Moles NOTE: Vocabulary terms are in boldface and underlined. Supporting details are in italics. 1 MOLE = 6.02 x 10 23 representative particles (representative particles

### Honors Chemistry: Unit 6 Test Stoichiometry PRACTICE TEST ANSWER KEY Page 1. A chemical equation. (C-4.4)

Honors Chemistry: Unit 6 Test Stoichiometry PRACTICE TEST ANSWER KEY Page 1 1. 2. 3. 4. 5. 6. Question What is a symbolic representation of a chemical reaction? What 3 things (values) is a mole of a chemical

### IB Chemistry 1 Mole. One atom of C-12 has a mass of 12 amu. One mole of C-12 has a mass of 12 g. Grams we can use more easily.

The Mole Atomic mass units and atoms are not convenient units to work with. The concept of the mole was invented. This was the number of atoms of carbon-12 that were needed to make 12 g of carbon. 1 mole

### Chemical Equations. Chemical Equations. Chemical reactions describe processes involving chemical change

Chemical Reactions Chemical Equations Chemical reactions describe processes involving chemical change The chemical change involves rearranging matter Converting one or more pure substances into new pure

### Stoichiometry. What is the atomic mass for carbon? For zinc?

Stoichiometry Atomic Mass (atomic weight) Atoms are so small, it is difficult to discuss how much they weigh in grams We use atomic mass units an atomic mass unit (AMU) is one twelfth the mass of the catbon-12

### Chemistry 65 Chapter 6 THE MOLE CONCEPT

THE MOLE CONCEPT Chemists find it more convenient to use mass relationships in the laboratory, while chemical reactions depend on the number of atoms present. In order to relate the mass and number of

### 1. How many hydrogen atoms are in 1.00 g of hydrogen?

MOLES AND CALCULATIONS USING THE MOLE CONCEPT INTRODUCTORY TERMS A. What is an amu? 1.66 x 10-24 g B. We need a conversion to the macroscopic world. 1. How many hydrogen atoms are in 1.00 g of hydrogen?

### Chapter 8: Chemical Equations and Reactions

Chapter 8: Chemical Equations and Reactions I. Describing Chemical Reactions A. A chemical reaction is the process by which one or more substances are changed into one or more different substances. A chemical

### Tutorial 4 SOLUTION STOICHIOMETRY. Solution stoichiometry calculations involve chemical reactions taking place in solution.

T-27 Tutorial 4 SOLUTION STOICHIOMETRY Solution stoichiometry calculations involve chemical reactions taking place in solution. Of the various methods of expressing solution concentration the most convenient

### Calculations and Chemical Equations. Example: Hydrogen atomic weight = 1.008 amu Carbon atomic weight = 12.001 amu

Calculations and Chemical Equations Atomic mass: Mass of an atom of an element, expressed in atomic mass units Atomic mass unit (amu): 1.661 x 10-24 g Atomic weight: Average mass of all isotopes of a given

### Concept 1. The meaning and usefulness of the mole. The mole (or mol) represents a certain number of objects.

Chapter 3. Stoichiometry: Mole-Mass Relationships in Chemical Reactions Concept 1. The meaning and usefulness of the mole The mole (or mol) represents a certain number of objects. SI def.: the amount of

### Chemistry B11 Chapter 4 Chemical reactions

Chemistry B11 Chapter 4 Chemical reactions Chemical reactions are classified into five groups: A + B AB Synthesis reactions (Combination) H + O H O AB A + B Decomposition reactions (Analysis) NaCl Na +Cl

### STOICHIOMETRY UNIT 1 LEARNING OUTCOMES. At the end of this unit students will be expected to:

STOICHIOMETRY LEARNING OUTCOMES At the end of this unit students will be expected to: UNIT 1 THE MOLE AND MOLAR MASS define molar mass and perform mole-mass inter-conversions for pure substances explain

### Experiment 5. Chemical Reactions A + X AX AX A + X A + BX AX + B AZ + BX AX + BZ

Experiment 5 Chemical Reactions OBJECTIVES 1. To observe the various criteria that are used to indicate that a chemical reaction has occurred. 2. To convert word equations into balanced inorganic chemical

### Chemistry Final Study Guide

Name: Class: Date: Chemistry Final Study Guide Multiple Choice Identify the choice that best completes the statement or answers the question. 1. The electrons involved in the formation of a covalent bond

### EXPERIMENT 7 Reaction Stoichiometry and Percent Yield

EXPERIMENT 7 Reaction Stoichiometry and Percent Yield INTRODUCTION Stoichiometry calculations are about calculating the amounts of substances that react and form in a chemical reaction. The word stoichiometry

### UNIT (4) CALCULATIONS AND CHEMICAL REACTIONS

UNIT (4) CALCULATIONS AND CHEMICAL REACTIONS 4.1 Formula Masses Recall that the decimal number written under the symbol of the element in the periodic table is the atomic mass of the element. 1 7 8 12

### EXPERIMENT 12: Empirical Formula of a Compound

EXPERIMENT 12: Empirical Formula of a Compound INTRODUCTION Chemical formulas indicate the composition of compounds. A formula that gives only the simplest ratio of the relative number of atoms in a compound

### Part One: Mass and Moles of Substance. Molecular Mass = sum of the Atomic Masses in a molecule

CHAPTER THREE: CALCULATIONS WITH CHEMICAL FORMULAS AND EQUATIONS Part One: Mass and Moles of Substance A. Molecular Mass and Formula Mass. (Section 3.1) 1. Just as we can talk about mass of one atom of

### Balancing Chemical Equations

Balancing Chemical Equations Academic Success Center Science Tutoring Area Science Tutoring Area Law of Conservation of Mass Matter cannot be created nor destroyed Therefore the number of each type of

### F321 MOLES. Example If 1 atom has a mass of 1.241 x 10-23 g 1 mole of atoms will have a mass of 1.241 x 10-23 g x 6.02 x 10 23 = 7.

Moles 1 MOLES The mole the standard unit of amount of a substance (mol) the number of particles in a mole is known as Avogadro s constant (N A ) Avogadro s constant has a value of 6.02 x 10 23 mol -1.

### Ch. 10 The Mole I. Molar Conversions

Ch. 10 The Mole I. Molar Conversions I II III IV A. What is the Mole? A counting number (like a dozen) Avogadro s number (N A ) 1 mole = 6.022 10 23 representative particles B. Mole/Particle Conversions

### 20.2 Chemical Equations

All of the chemical changes you observed in the last Investigation were the result of chemical reactions. A chemical reaction involves a rearrangement of atoms in one or more reactants to form one or more

### Moles, Molecules, and Grams Worksheet Answer Key

Moles, Molecules, and Grams Worksheet Answer Key 1) How many are there in 24 grams of FeF 3? 1.28 x 10 23 2) How many are there in 450 grams of Na 2 SO 4? 1.91 x 10 24 3) How many grams are there in 2.3

### CHEM 110: CHAPTER 3: STOICHIOMETRY: CALCULATIONS WITH CHEMICAL FORMULAS AND EQUATIONS

1 CHEM 110: CHAPTER 3: STOICHIOMETRY: CALCULATIONS WITH CHEMICAL FORMULAS AND EQUATIONS The Chemical Equation A chemical equation concisely shows the initial (reactants) and final (products) results of

### Chemical Calculations: The Mole Concept and Chemical Formulas. AW Atomic weight (mass of the atom of an element) was determined by relative weights.

1 Introduction to Chemistry Atomic Weights (Definitions) Chemical Calculations: The Mole Concept and Chemical Formulas AW Atomic weight (mass of the atom of an element) was determined by relative weights.

### PART I: MULTIPLE CHOICE (30 multiple choice questions. Each multiple choice question is worth 2 points)

CHEMISTRY 123-07 Midterm #1 Answer key October 14, 2010 Statistics: Average: 74 p (74%); Highest: 97 p (95%); Lowest: 33 p (33%) Number of students performing at or above average: 67 (57%) Number of students

### Chemical Equations and Chemical Reactions. Chapter 8.1

Chemical Equations and Chemical Reactions Chapter 8.1 Objectives List observations that suggest that a chemical reaction has taken place List the requirements for a correctly written chemical equation.

### Chemical Composition. Introductory Chemistry: A Foundation FOURTH EDITION. Atomic Masses. Atomic Masses. Atomic Masses. Chapter 8

Introductory Chemistry: A Foundation FOURTH EDITION by Steven S. Zumdahl University of Illinois Chemical Composition Chapter 8 1 2 Atomic Masses Balanced equation tells us the relative numbers of molecules

### Chemical Proportions in Compounds

Chapter 6 Chemical Proportions in Compounds Solutions for Practice Problems Student Textbook page 201 1. Problem A sample of a compound is analyzed and found to contain 0.90 g of calcium and 1.60 g of

### Chapter 3. Molecules, Compounds and Chemical Equations

3. Molecules, Compounds and Chemical Equations Stoichiometry Mole concept and Avogadro s Number Determining Chemical Formulas Name Compound Balancing Chemical Reactions Yields Solutions and Stoichiometry

### Stoichiometry Review

Stoichiometry Review There are 20 problems in this review set. Answers, including problem set-up, can be found in the second half of this document. 1. N 2 (g) + 3H 2 (g) --------> 2NH 3 (g) a. nitrogen

### How much does a single atom weigh? Different elements weigh different amounts related to what makes them unique.

How much does a single atom weigh? Different elements weigh different amounts related to what makes them unique. What units do we use to define the weight of an atom? amu units of atomic weight. (atomic

### Moles Lab mole. 1 mole = 6.02 x 1023. This is also known as Avagadro's number Demo amu amu amu

Moles I. Lab: Rice Counting II. Counting atoms and molecules I. When doing reactions chemists need to count atoms and molecules. The problem of actually counting individual atoms and molecules comes from

### Chapter 3! Stoichiometry: Calculations with Chemical Formulas and Equations. Stoichiometry

Chapter 3! : Calculations with Chemical Formulas and Equations Anatomy of a Chemical Equation CH 4 (g) + 2O 2 (g) CO 2 (g) + 2 H 2 O (g) Anatomy of a Chemical Equation CH 4 (g) + 2 O 2 (g) CO 2 (g) + 2

### Mole Notes.notebook. October 29, 2014

1 2 How do chemists count atoms/formula units/molecules? How do we go from the atomic scale to the scale of everyday measurements (macroscopic scale)? The gateway is the mole! But before we get to the

### Chem 115 POGIL Worksheet - Week 4 Moles & Stoichiometry

Chem 115 POGIL Worksheet - Week 4 Moles & Stoichiometry Why? Chemists are concerned with mass relationships in chemical reactions, usually run on a macroscopic scale (grams, kilograms, etc.). To deal with

### Topic 4 National Chemistry Summary Notes. Formulae, Equations, Balancing Equations and The Mole

Topic 4 National Chemistry Summary Notes Formulae, Equations, Balancing Equations and The Mole LI 1 The chemical formula of a covalent molecular compound tells us the number of atoms of each element present

### Chem 31 Fall 2002. Chapter 3. Stoichiometry: Calculations with Chemical Formulas and Equations. Writing and Balancing Chemical Equations

Chem 31 Fall 2002 Chapter 3 Stoichiometry: Calculations with Chemical Formulas and Equations Writing and Balancing Chemical Equations 1. Write Equation in Words -you cannot write an equation unless you

### Chapter 5. Chemical Reactions and Equations. Introduction. Chapter 5 Topics. 5.1 What is a Chemical Reaction

Introduction Chapter 5 Chemical Reactions and Equations Chemical reactions occur all around us. How do we make sense of these changes? What patterns can we find? 1 2 Copyright The McGraw-Hill Companies,

### Appendix D. Reaction Stoichiometry D.1 INTRODUCTION

Appendix D Reaction Stoichiometry D.1 INTRODUCTION In Appendix A, the stoichiometry of elements and compounds was presented. There, the relationships among grams, moles and number of atoms and molecules

### THE MOLE / COUNTING IN CHEMISTRY

1 THE MOLE / COUNTING IN CHEMISTRY ***A mole is 6.0 x 10 items.*** 1 mole = 6.0 x 10 items 1 mole = 60, 00, 000, 000, 000, 000, 000, 000 items Analogy #1 1 dozen = 1 items 18 eggs = 1.5 dz. - to convert

### = 16.00 amu. = 39.10 amu

Using Chemical Formulas Objective 1: Calculate the formula mass or molar mass of any given compound. The Formula Mass of any molecule, formula unit, or ion is the sum of the average atomic masses of all

### Aqueous Solutions. Water is the dissolving medium, or solvent. Some Properties of Water. A Solute. Types of Chemical Reactions.

Aqueous Solutions and Solution Stoichiometry Water is the dissolving medium, or solvent. Some Properties of Water Water is bent or V-shaped. The O-H bonds are covalent. Water is a polar molecule. Hydration

### AS1 MOLES. oxygen molecules have the formula O 2 the relative mass will be 2 x 16 = 32 so the molar mass will be 32g mol -1

Moles 1 MOLES The mole the standard unit of amount of a substance the number of particles in a mole is known as Avogadro s constant (L) Avogadro s constant has a value of 6.023 x 10 23 mol -1. Example

### Solution a homogeneous mixture = A solvent + solute(s) Aqueous solution water is the solvent

Solution a homogeneous mixture = A solvent + solute(s) Aqueous solution water is the solvent Water a polar solvent: dissolves most ionic compounds as well as many molecular compounds Aqueous solution:

### Chapter 5 Chemical Quantities and Reactions. Collection Terms. 5.1 The Mole. A Mole of a Compound. A Mole of Atoms.

Chapter 5 Chemical Quantities and Reactions 5.1 The Mole Collection Terms A collection term states a specific number of items. 1 dozen donuts = 12 donuts 1 ream of paper = 500 sheets 1 case = 24 cans 1

### Balancing Chemical Equations Worksheet

Balancing Chemical Equations Worksheet Student Instructions 1. Identify the reactants and products and write a word equation. 2. Write the correct chemical formula for each of the reactants and the products.

### CHAPTER 3 Calculations with Chemical Formulas and Equations. atoms in a FORMULA UNIT

CHAPTER 3 Calculations with Chemical Formulas and Equations MOLECULAR WEIGHT (M. W.) Sum of the Atomic Weights of all atoms in a MOLECULE of a substance. FORMULA WEIGHT (F. W.) Sum of the atomic Weights

### Chemistry: Chemical Equations

Chemistry: Chemical Equations Write a balanced chemical equation for each word equation. Include the phase of each substance in the equation. Classify the reaction as synthesis, decomposition, single replacement,

### Atomic Masses. Chapter 3. Stoichiometry. Chemical Stoichiometry. Mass and Moles of a Substance. Average Atomic Mass

Atomic Masses Chapter 3 Stoichiometry 1 atomic mass unit (amu) = 1/12 of the mass of a 12 C atom so one 12 C atom has a mass of 12 amu (exact number). From mass spectrometry: 13 C/ 12 C = 1.0836129 amu

### Unit 6 The Mole Concept

Chemistry Form 3 Page 62 Ms. R. Buttigieg Unit 6 The Mole Concept See Chemistry for You Chapter 28 pg. 352-363 See GCSE Chemistry Chapter 5 pg. 70-79 6.1 Relative atomic mass. The relative atomic mass

### CHEMICAL REACTIONS. Chemistry 51 Chapter 6

CHEMICAL REACTIONS A chemical reaction is a rearrangement of atoms in which some of the original bonds are broken and new bonds are formed to give different chemical structures. In a chemical reaction,

### Chapter 4. Chemical Composition. Chapter 4 Topics H 2 S. 4.1 Mole Quantities. The Mole Scale. Molar Mass The Mass of 1 Mole

Chapter 4 Chemical Composition Chapter 4 Topics 1. Mole Quantities 2. Moles, Masses, and Particles 3. Determining Empirical Formulas 4. Chemical Composition of Solutions Copyright The McGraw-Hill Companies,

### CONSERVATION OF MASS During a chemical reaction, matter is neither created nor destroyed. - i. e. the number of atoms of each element remains constant

1 CHEMICAL REACTINS Example: Hydrogen + xygen Water H + H + + - Note there is not enough hydrogen to react with oxygen - It is necessary to balance equation. reactants products + H + H (balanced equation)

### Name Date Class CHEMICAL QUANTITIES. SECTION 10.1 THE MOLE: A MEASUREMENT OF MATTER (pages 287 296)

Name Date Class 10 CHEMICAL QUANTITIES SECTION 10.1 THE MOLE: A MEASUREMENT OF MATTER (pages 287 296) This section defines the mole and explains how the mole is used to measure matter. It also teaches

### Atomic mass is the mass of an atom in atomic mass units (amu)

Micro World atoms & molecules Laboratory scale measurements Atomic mass is the mass of an atom in atomic mass units (amu) By definition: 1 atom 12 C weighs 12 amu On this scale 1 H = 1.008 amu 16 O = 16.00

### Chapter 8 How to Do Chemical Calculations

Chapter 8 How to Do Chemical Calculations Chemistry is both a qualitative and a quantitative science. In the laboratory, it is important to be able to measure quantities of chemical substances and, as

### Chemical Reactions 2 The Chemical Equation

Chemical Reactions 2 The Chemical Equation INFORMATION Chemical equations are symbolic devices used to represent actual chemical reactions. The left side of the equation, called the reactants, is separated

### ATOMS. Multiple Choice Questions

Chapter 3 ATOMS AND MOLECULES Multiple Choice Questions 1. Which of the following correctly represents 360 g of water? (i) 2 moles of H 2 0 (ii) 20 moles of water (iii) 6.022 10 23 molecules of water (iv)

### Solution. Practice Exercise. Concept Exercise

Example Exercise 9.1 Atomic Mass and Avogadro s Number Refer to the atomic masses in the periodic table inside the front cover of this textbook. State the mass of Avogadro s number of atoms for each of

### Problem Solving. Stoichiometry of Gases

Skills Worksheet Problem Solving Stoichiometry of Gases Now that you have worked with relationships among moles, mass, and volumes of gases, you can easily put these to work in stoichiometry calculations.

### Molar Mass Worksheet Answer Key

Molar Mass Worksheet Answer Key Calculate the molar masses of the following chemicals: 1) Cl 2 71 g/mol 2) KOH 56.1 g/mol 3) BeCl 2 80 g/mol 4) FeCl 3 162.3 g/mol 5) BF 3 67.8 g/mol 6) CCl 2 F 2 121 g/mol

### Writing and Balancing Chemical Equations

Name Writing and Balancing Chemical Equations Period When a substance undergoes a chemical reaction, chemical bonds are broken and new bonds are formed. This results in one or more new substances, often

### Unit 9 Stoichiometry Notes (The Mole Continues)

Unit 9 Stoichiometry Notes (The Mole Continues) is a big word for a process that chemist s use to calculate amounts in reactions. It makes use of the coefficient ratio set up by balanced reaction equations