2.9 The Mole and Chemical Equations:

Transcription

1 2.9 The Mole and Chemical Equations: Stoichiometry Whether you are making omelettes in a kitchen or soap in a factory, you need to know the quantities of ingredients required to produce a certain quantity of product. For example, a manufacturing company needs to know how much raw material to buy to make the quantities of products ordered by its customers. By applying the mole concept (section 2.1) to balanced chemical equations, you can make quantitative predictions such as these. To predict the masses of reactants and products, you always begin with a balanced equation for the reaction. A balanced equation tells you the ratio of the amounts of reactants and products that take part in a chemical reaction. Determining Ratios from Balanced Chemical Equations Consider the reaction between nitrogen gas and hydrogen gas to produce ammonia, NH 3(g). A balanced equation for the production of ammonia is given below: N 2(g) 3 H 2(g) 2NH 3(g) The coefficients in the balanced equation may be analyzed in terms of numbers of entities or amounts (number of moles) of entities. The equation indicates that two molecules of ammonia are produced for every molecule of nitrogen that reacts with three molecules of hydrogen according to the molecule ratio 1 molecule N 2(g) : 3 molecules H 2(g) : 2 molecules NH 3(g) mole ratio the ratio of the amount, in moles, of reactants and products in a chemical reaction Considering amounts of reactants and products, the equation tells you that two moles of ammonia molecules are produced for every mole of nitrogen molecules that react with three moles of hydrogen molecules. The ratio of moles in a balanced chemical equation is called the mole ratio. The mole ratio for the reaction between nitrogen and hydrogen is or simply 1 : 3 : 2. To summarize, 1 mol N 2(g) : 3 mol H 2(g) : 2 mol NH 3(g) N 2(g) 3 H 2(g) 2NH 3(g) molecule ratio 1 molecule : 3 molecules : 2 molecules mole ratio 1 mol : 3 mol : 2 mol stoichiometry mathematical procedures for calculating the quantities of reactants and products involved in chemical reactions Calculations Involving Mole Ratios The procedure for calculating quantities of reactants and products in chemical reactions is called stoichiometry. In stoichiometry, you use mole ratios in balanced equations to calculate the quantities of reactants used or products formed. 144 Unit 2 NEL

2 Section 2.9 SAMPLE problem 1 Calculations Involving Mass of Reactants Propane, C 3 (g), is a gas that is commonly used in barbecues. Calculate the mass of oxygen that is needed to burn 15 g of propane. Step 1: Write Unbalanced Equation Remember that in the complete combustion of a hydrocarbon, carbon dioxide gas and water vapour are the only products. C 3 (g) O 2(g) CO 2(g) H 2 O (g) Step 2: Balance Equation, List Given Values and Molar Masses To organize the information, list the given values and calculated molar masses below their corresponding entities: Balanced equation C 3 (g) 5 O 2(g) 3 CO 2(g) 4 H 2 O (g) Given mass 15 g Molar mass g/mol g/mol Step 3: Convert Mass of Given Substance to Amount of Given Substance In this problem, the given substance is propane. Using the molar mass of propane, convert the mass of propane (given) to an amount (in moles). n C3 15 g C 3 n C mol C 3 Step 4: Convert Amount of Given Substance to Amount of Required Substance To perform the conversion, first determine which mole ratio you need to use. The mole ratio can be expressed as or. Since you are 5 mol O2 1 mol C3 converting amount of propane to amount of oxygen, use the form. 1 mol C mol C mol O 2 Step 5: Convert Amount of Required Substance to Required Value In this case, the required value is the mass of oxygen. To find the mass of oxygen, you must multiply the amount of oxygen by the molar mass of oxygen. 1.7 mol O 2 54 g O g C3 1 mol C g O 2 1 mol O2 Therefore, 54 g of oxygen is needed to burn 15 g of propane. NEL Quantities in Chemistry 145

3 The calculations in steps 3, 4, and 5 can be combined as follows: 15 g C g C3 1 mol C g O 2 1 mol O2 54 g O 2 The stoichiometric calculation can be extended to determine the number of entities (N) that have reacted or are produced. The next Sample Problem involves this type of calculation. SAMPLE problem 2 Calculations Involving Numbers of Entities and Mass of Reactants How many molecules of oxygen are produced from the decomposition of 12 g of water into its elements? Step 1: Write Unbalanced Equation H 2 O (l) H 2(g) O 2(g) Step 2: Balance Equation, List Given Values and Molar Masses Balanced equation 2H 2 O (l) 2H 2(g) O 2(g) Given mass Step 3: Convert Mass of Given Substance to Amount of Given Substance Use the molar mass of the measured n H2 O 12 g H 2 O O g H2 O n H2 O 0.67 mol H 2 O Step 4: Convert Amount of Given Substance to Amount of Required Substance First determine which mole ratio to use. The mole ratio for oxygen and water in the balanced equation is 2 mol H 2 O :. This ratio can be expressed as 2 mol H 2 O or. Use the form to convert the amount of 1 mol O2 2 mol H2 O 2 mol H2 O water into the amount of oxygen mol H 2 O 0.34 mol O 2 12 g Molar mass g/mol g/mol 2 mol H2 O 146 Unit 2 NEL

4 Section 2.9 Step 5: Convert Amount of Required Substance to Required Value In this case, the required value is the number of molecules of oxygen. Use the equation molecules O 2 to form a suitable conversion factor mol O molecules O molecules O 2 When 10.0 g of water decomposes into its elements, molecules of oxygen are formed. The combined calculation is given below: O 12 g H 2 O g H2 O 2 mol H2 O molecules O molecules O 2 Example Magnesium metal reacts with hydrochloric acid to produce aqueous magnesium chloride and hydrogen gas. How many hydrogen molecules are produced when 60.0 g of magnesium reacts with excess hydrochloric acid? Solution Balanced equation Mg (s) 2HCl (aq) MgCl 2(aq) H 2(g) Given mass 60.0 g Molar mass g/mol 2.02 g/mol n Mg 60.0 g Mg n Mg 2.47 mol Mg n H mol Mg n H mol H mol H 2 1 mol Mg g Mg 1 mol Mg molecules H molecules H 2 1 mol H2 When 60.0 g of magnesium reacts with hydrochloric acid, hydrogen molecules are produced. The combined calculation is given below: 1 mol Mg 60.0 g Mg g Mg 1 mol Mg molecules H molecules H 2 1 mol H2 NEL Quantities in Chemistry 147

5 Figure 1 summarizes the steps in a stoichiometric calculation. Start Step 1 Step 2 Step 3 Step 4 Step 5 Read question carefully. Write unbalanced chemical equation. Balance chemical equation, list given values and molar masses. Convert mass of given substance to amount of given Convert amount of given substance to amount of required Convert amount of required substance to required value. Figure 1 Use molar mass of given Use mole ratio from balanced chemical equation. Required value may be mass or number of entities. Answers g g formula units Practice Understanding Concepts 1. Bauxite ore contains aluminum oxide, Al 2 O 3(s), which is decomposed using electricity to produce aluminum metal (Figure 2) and oxygen. What mass of aluminum metal can be produced from 125 g of aluminum oxide? 2. Potassium metal, K (s), reacts with hydrochloric acid to produce aqueous potassium chloride and hydrogen gas. How many grams of potassium are required to produce 5.00 g of hydrogen gas? 3. Potassium chlorate, KClO 3(s), decomposes when heated to form solid potassium chloride and oxygen gas. How many formula units of potassium chlorate must decompose to produce 0.96 g of oxygen? Figure 2 An aluminum refinery Section 2.9 Questions Understanding Concepts 1. What is a mole ratio? 2. In a balanced equation, the total number of atoms in the reactants equals the total number of atoms in the products. Does the equality of atoms mean that the total amount (in moles) before and after a chemical reaction is the same? Give an example to illustrate your answer. 3. Write a balanced equation for the reaction between nitrogen dioxide gas and water to produce nitric acid and nitrogen monoxide gas. State the mole ratios of the reactants and the products. 4. What does the term stoichiometry mean? 5. How many molecules of hydrogen are produced from the decomposition of 12.0 g of water into its elements? 148 Unit 2 NEL