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 table The atomic mass of hydrogen is about 1.008 amu, that of helium is about 4.003 amu, etc. The formula mass of a substance is simply the sum of the atomic masses of the atoms represented in the chemical formula What is the formula mass of CO 2? H 2 O? Introducing the Mole The dozen is a unit of quanity If I have a dozen atoms, I have 12 atoms by definition. The mole (mol) is a very important unit of quantity in chemistry. It is used to count large numbers of atoms, molecules, and other submicroscopic pieces of matter. If you have 1 mole of something, you have 6.02 10 23 of it. The number 6.02 10 23 is commonly called Avogadro s Number Examples How many eggs are in 5.5 dozen eggs? How many atoms are in 5.5 mole of atoms? How many hydrogen atoms are in one molecule of water? How many oxygen atoms? Page 1
How many hydrogen atoms are in one mole of water? How many oxygen atoms? How many atoms total? Practice If you have 18.45 mol of oxygen gas, how many individual molecules do you have? How many individual atoms? If a sample of methane contains 7.35 10 25 atoms, how many moles of methane do you have? Page 2
Atomic Weights and The Mole The atomic weights provided on the periodic table can be used in much more convenient units than amu. The values on the periodic table can be interpreted as grams per mole of the atom. For example, 1 mol of calcium atoms has a mass of 40.08 g; 1 mol of neon atoms has a mass of 20.18 g. The molar mass of a substance (be it an element or compound) is the mass of one mole of that substance Molar Mass The mass of molecules can be calculated by adding up the atomic weights of the individual atoms making up the molecule. For example, suppose we wanted to know the molar mass of CO 2. Every 1 mol of CO 2 contains mole of C atoms and moles of O atoms. Calculate the total mass of all of these atoms and add them up to get the molecular weight of CO 2. Aside: what is the mass of a single molecule of CO 2 in amu? Note that the term formula weight is applied for those compounds which do not form true molecules (ionic compounds like NaCl and CaO). Example Determine the molar mass of glucose (C 6 H 12 O 6 ) Mass-Mole Relationships Given the formula of a substance, we can use the molar mass to relate the mass of a substance to the number of moles present Examples What is the mass of 3.55 mols of CO 2? Page 3
How many moles of glucose are in 985 grams of glucose? How many grams of carbon are there in 50.0 grams of CO 2? An Introduction to Chemical Reactions and Equations A chemical reaction involves the conversion of one or more substances into one or more different substances. The chemical equation is a symbolic way of representing what occurs in a chemical reaction The substance(s) which we begin with are called the reactant(s) The substance(s) which we end with are called the product(s) We will examine chemical reactions in greater depth in Chapter Eight Writing Chemical Equations Chemical equations are written with the reactants to the left, the products to the right, and an arrow between them to indicate the change. Occasionally symbols or values may be written over or under the arrow to indicate the reaction conditions. An Example: H 2 + O 2 H 2 O Balancing Chemical Equations Consider the last reaction: H 2 + O 2 H 2 O There is a problem with this equation! It indicates that we started with two oxygen atoms, but ended with one. What does this contradict? Page 4
We must balance chemical equations, which is to say that there must be equal numbers of each type of atom on either side of a chemical reaction. To accomplish this, we put coefficients in front of the chemical formulas whose atom numbers we wish to increase. Note that you may never change the subscripts already in place in a chemical formula! Why? To balance chemical equations first count the number of each type of atom you have on both sides of the reaction. Identify any lone elements (as opposed to compounds) in the formulas; you will balance these last. From here, each equation requires its own logic; by trial and error, you should be able to balance the equation. The only other real tip I can give you on this subject is that practice makes perfect! Examples Balance each of the following chemical reactions: Mg + O 2 MgO HgO Hg + O 2 Na + MgCl 2 Mg + NaCl Na 3 PO 4 + BaCl 2 Ba 3 (PO 4 ) 2 + NaCl C 6 H 12 O 6 + O 2 CO 2 + H 2 O Page 5
Examples Write the balanced equation that corresponds to each statement When methane reacts with oxygen gas, carbon dioxide and water vapor are produced. Calcium metal reacts with iron (III) oxide, giving calcium oxide and iron metal. Treatment of carbon monoxide gas with oxygen gas produces carbon dioxide. Chemical Equations and the Mole The coefficients in chemical equations tell us how many moles of reactants are required to produce a certain number of moles of products. Consider the following reaction: 4 Fe + 3 O 2 2 Fe 2 O 3 We can say that four moles of iron reacts with three moles of oxygen gas, producing 2 moles of iron (III) oxide. The three are equivalent for the purpose of this reaction. 4 mol Fe 3 mol O 2 2 mol Fe 2 O 3 Coefficients of Reactions We can convert between moles of reactants and products using dimensional analysis, the same technique we used for unit conversions. To convert between moles of iron and moles of iron (III) oxide, we use the following ratio: What other ratios can be derived from this chemical equation? Page 6
Basic Problems Let s consider the following reaction: 2H 2(g) + O 2(g) 2H 2 O (l) To produce 2 mol of water we need to combine mol H 2 with mol O 2. How many moles of each reactant are required to produce 10 moles of water? How many moles of water can be produced at most from 13 moles of hydrogen? How many moles of oxygen would I need to accomplish this? Balance the reaction below, then answer questions a. and b. HCl + Ba(OH) 2 H 2 O + BaCl 2 a. How many moles of each reactant do you need to produce 5.75 mol water? Page 7
b. What is the maximum number of moles of water you can produce with 18.0 mol HCl? How many moles of barium hydroxide would you need to accomplish this? Using the Mass-Mole Relationship Recall that the molar mass relates the mass of a compound (or element) to the number of moles. Therefore, if we know the mass of a given reactant, we can easily determine the number of moles of the reactant, and from there the number of moles of product produced. Remember, you must use the mole-mole relationship to carry out a conversion; the mass alone is not sufficient! Mass-Mole Problems Balance the chemical equation below, then use it to answer questions a.-c. Na + Cl 2 NaCl a. How many moles of sodium are contained in 15.50 g of sodium? b. Assuming we have excess (that is, more than enough) chlorine, how many moles of sodium chloride could be produced? c. How many grams of sodium chloride is this? Page 8
When 39.75 g of sodium is reacted with excess chlorine, how many grams of sodium chloride can be produced? When 146.7 g of chlorine is reacted with excess sodium, how many grams of sodium chloride can be produced? How many grams of each reactant do you need to produce 100.00 g of sodium chloride? Page 9
Balance the chemical equation below, then use it to answer questions a and b. C 2 H 6 O + O 2 CO 2 + H 2 O a.how many grams of carbon dioxide and water can be produced if 55.0 ml of C 2 H 6 O is reacted? Note: The density of C 2 H 6 O is 0.789 g/ml. b. How many oxygen molecules are required to react with this amount of C 2 H 6 O? Page 10