# Calculations with Chemical Reactions

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1 Calculations with Chemical Reactions Calculations with chemical reactions require some background knowledge in basic chemistry concepts. Please, see the definitions from chemistry listed below: Atomic mass the total mass of protons, neutrons and electrons in a single atom. (Note that atomic mass has no units. It is a relative measure). Molecular mass the mass of one molecule. Molecular mass is equal to the total mass of all the elements making up a molecule. Mole a unit of measurement widely used in chemistry to measure an amount of a particular substance. One mole has approximately x elementary entities (atoms, molecules, ions, etc.) of a substance. The Avogadro constant, x 10 23, is equal to the amount of atoms in 12 grams of pure carbon-12. Molar mass the mass of e of a substance (molecule or atom). (Molar mass for an atom can be determined from the Periodic Table. For MATH 1096 and 1097 problems, the molar mass is usually given in the question). Balanced chemical reactions a chemical reaction consists of reactants (written on the left) and products (written on the right). A chemical reaction is balanced when there is an equal amount of each element on the reactants and the products sides of the equation (this is consistent with the Law of Conservation of Mass). e.g. 2H 2 + O 2 2H 2 O There are 4 H atoms and 2 O atoms on the reactants and on the products sides of the equation. NOTE: Coefficients provide mole-to-mole ratio of the different substances involved in the reaction! Heat the amount of energy (in the form of heat) released or absorbed during a chemical reaction. Heat is usually measured in kilojoules (kj). e.g. Combustion of of ethanol produces 1368 kj of energy. C 2 H 5 O 6 + 3O 2 2CO 2 + 3H 2 O kj Acid solution a mixture of water and pure acid. The strength of an acid solution is usually given as a percentage of pure acid in water. For example, in 100 ml of 25% hydrochloric acid (HCl) solution, there is 25 ml of HCl and 75 ml of water.

2 Problem Solving Techniques in MATH 1096: First, list the unknown quantity name (uqn), unknown quantity symbol (uqs), unknown unit name (uun) and unknown unit symbol (uus). uqn: uqs: uun: uus: Step-by-Step Technique - Number the steps (e.g. Step 1). 1. In sentence form, say what is the purpose of the step (What are you calculating?). 2. Write out and perform the mathematical operation. 3. In sentence form, write the answer that you got. - Repeat points 1-3 for every different step. 4. Write your final answer in sentence form. Algebraic Technique 1. Define the unknown variable. 2. Interpret the problem and write an algebraic statement that leads to the solution. 3. Solve the algebraic statement. 4. Write your final answer in sentence form. Sample Problem: What mass (g) of iron (Fe) will be produced from g of carbon monoxide and an excess of iron (III) oxide? The molar mass of carbon monoxide is g/mol and the molar mass of iron is g/mol. Fe 2 O 3 (s) + 3 CO(g) 2 Fe(s) + 3 CO 2 (g) Solution 1: Using the Step-by-Step Proportion Technique uqn: mass uqs: m uun: gram uus: g Step 1: Convert g of carbon monoxide (CO) to moles. Important note: We need to convert the quantity of carbon monoxide given in the question into moles because the ratio of iron (Fe) to carbon monoxide (CO) is in moles. From the balanced chemical reaction we can see that the ratio of iron to carbon monoxide is 2 mol Fe : 3 mol CO 2.

3 In order to convert the quantity of carbon monoxide from grams to amount of moles, n, we use the molar mass of CO, which is given in the question as g/mol. Set up a proportion for converting the mass of CO to moles. This information is the given mass of CO, g, and the unknown amount of moles, n, that we are trying to find g n g This information comes from the molar mass of CO, which grams per mole Solve the proportion for n using cross-multiplication g n g 28.01n (1) n 152.6(1) n Tip: Use the units to set up proportion correctly! After, you can drop the units to make the calculation easier. Tip: Keep all decimals places in intermediate calculations. Round your final answer at the end. Therefore, mol of CO reacts with excess Fe. Step 2: Calculate the amount of Fe, n, produced from mol of CO. Set up a proportion relating the amount of Fe that is produced for a given amount of CO. Important note: When setting up the proportion, amounts of the same substance should go together (i.e. both on top; both on the bottom or on the same side of the proportion) mol CO n mol Fe 3 mol CO 2 mol Fe This side of the proportion includes the given amount of CO and the unknown amount of Fe produced from this amount of CO. This information comes from the balanced chemical equation, which states that for every 3 mol of CO, 2 mol of Fe are produced. Solve the proportion for n using cross-multiplication.

4 mol CO n mol Fe 3 mol CO 2 mol Fe Tip: You can now drop the units to make the calculation easier. 3n (2) n (2) 3 n Therefore, mol of Fe are produced. Step 3: Convert mol of Fe into grams. Since the question is asking for mass (g) of iron produced, we need to convert the amount of Fe in moles into grams. The molar mass of Fe, g/mol, given in the question allows us to convert from moles of Fe to grams of Fe. Set up a proportion for converting the amount of Fe into grams mol m g This side of the proportion includes the amount of Fe found in Step 2 and the unknown mass of Fe. This information comes from the molar mass of Fe, which grams per mole. Solve the proportion for m using cross-multiplication mol m g 1m 55.85( ) m 55.85( ) 1 m Since this is the final step, round the answer to the correct number of significant digits.

5 The given quantities in the question all had 4 significant digits. Since the operations of multiplication and division were used throughout the calculations, we round the final answer to the least number of significant digits in the given quantities, which is 4. m Therefore, g of Fe will be produced from g of carbon monoxide and an excess of iron (III) oxide. Solution 2: Using the Algebraic Technique uqn: mass uqs: m uun: gram uus: g Let m represent the unknown mass of Fe (in grams) produced from g of carbon monoxide. m g CO x CO 2 mol Fe g Fe g CO x 3 mol CO x Fe given mass of CO, g. molar mass of CO, which grams per mole. ratio of Fe to CO as stated in the balanced chemical equation. molar mass of Fe, which grams per mole. Important note: When building the algebraic statement, use the units to guide which quantity goes where (top or bottom). The goal is for the units to cancel out so that you are left with your desired unit. m g CO x CO g CO x 2 mol Fe 3 mol CO x g Fe Fe m 152.6(1)(2)(55.85) 28.01(3)(1) g Fe m g Fe

6 Round the final answer to 4 significant digits. m g Fe Therefore, g of Fe will be produced from g of carbon monoxide and an excess of iron (III) oxide. Practice Questions: 1. How many grams of CO 2 are produced in the combustion of 50.0 g of propane, C 3 H 8? The molar mass of CO 2 is g/mol and the molar mass of propane is g/mol. C 3 H 8 (g) + 5 O 2 (g) 3 CO 2 (g) + 4 H 2 O(l) 2. Determine the amount of oxygen produced when g of KClO 3 decomposes. The molar mass of O 2 is 32.0 g/mol and the molar mass of KClO 3 is g/mol. 2 KClO 3 (s) 2 KCl(s) + 3 O 2 (g) 3. How many grams of C 6 H 12 O 6 are needed to form g of C 2 H 5 OH? The molar mass of C 6 H 12 O 6 is g/mol and the molar mass of C 2 H 5 OH is g/mol. C 6 H 12 O 6 (aq) 2 C 2 H 5 OH(aq) + 2 CO 2 (g) 4. How much energy (kj) is produced from the combustion of 53.8 g of methane, CH 4? The molar mass of methane is g/mol. CH 4 + 2O 2 CO 2 + 2H 2 O kj Answers: g CO g O g C 6 H 12 O kj

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