Chemical Reactions and Chemical Quantities: Balancing, Stoichiometry, and Yield

Chapter 4: Chemical Reactions and Chemical Quantities

Introduction

This chapter covers the fundamental concepts of chemical reactions, including how to write and balance chemical equations, the principles of reaction stoichiometry, and calculations involving limiting reactants and percent yield. These skills are essential for understanding the quantitative relationships in chemical processes.

Climate Change and the Combustion of Fossil Fuels

Combustion and CO2 Emissions

• Combustion of fossil fuels is a major source of atmospheric carbon dioxide (CO2).

• CO2 is a greenhouse gas that contributes to global warming by trapping heat in the Earth's atmosphere.

• To quantify CO2 emissions, chemical equations for combustion reactions are used to calculate the amount of CO2 produced.

Example: Combustion of octane (a component of gasoline):

$2\,\mathrm{C}_8\mathrm{H}_{18}(l) + 25\,\mathrm{O}_2(g) \rightarrow 16\,\mathrm{CO}_2(g) + 18\,\mathrm{H}_2\mathrm{O}(g)$

Writing and Balancing Chemical Equations

Fundamentals of Chemical Equations

• A chemical equation represents a chemical reaction, showing reactants (left side) and products (right side).

• States of matter are indicated: (s) solid, (l) liquid, (g) gas, (aq) aqueous.

• Coefficients are used to balance the equation, ensuring the same number of each atom on both sides.

Example:

$\mathrm{CH}_4(g) + 2\,\mathrm{O}_2(g) \rightarrow \mathrm{CO}_2(g) + 2\,\mathrm{H}_2\mathrm{O}(g)$

Guidelines for Balancing Chemical Equations

• Matter cannot be lost in any chemical reaction; all atoms must be accounted for.

• Balance elements that appear in only one compound first.

• Adjust coefficients to ensure equal numbers of each atom on both sides.

• Do not change subscripts; only coefficients can be changed.

Practice Problems: Balancing Equations

• Balance the following equations:

• $\mathrm{CH}_4(g) + \mathrm{O}_2(g) \rightarrow \mathrm{CO}_2(g) + \mathrm{H}_2\mathrm{O}(g)$

• $\mathrm{Na}(s) + \mathrm{H}_2\mathrm{O}(l) \rightarrow \mathrm{NaOH}(aq) + \mathrm{H}_2(g)$

Example Multiple Choice: What is the coefficient of ammonia gas (NH3) after balancing the equation $\mathrm{N}_2(g) + \mathrm{H}_2(g) \rightarrow \mathrm{NH}_3(g)$?

Reaction Stoichiometry

Stoichiometric Relationships

• Stoichiometry is the calculation of reactants and products in chemical reactions using balanced equations.

• Coefficients indicate the relative number of moles of each substance.

• Allows conversion between moles of reactants and products.

Example: For the combustion of octane:

$2\,\mathrm{C}_8\mathrm{H}_{18}(l) + 25\,\mathrm{O}_2(g) \rightarrow 16\,\mathrm{CO}_2(g) + 18\,\mathrm{H}_2\mathrm{O}(g)$

If 22.0 moles of C8H18 are burned, how many moles of CO2 are formed?

Mass-to-Mass Conversions

Using Moles to Relate Masses

• Balanced equations relate moles, not masses, of reactants and products.

• To convert mass to mass, use molar mass and mole ratios from the equation.

General Steps:

1. Convert mass of reactant to moles using molar mass.

2. Use mole ratio from balanced equation to find moles of product.

3. Convert moles of product to mass using molar mass.

Example: For C8H18 to CO2:

$\text{molar mass of C}_8\text{H}_{18} = 114.22\,\text{g/mol}$ $\text{molar mass of CO}_2 = 44.01\,\text{g/mol}$

Limiting Reactant and Excess Reactant

Definitions and Calculations

• The limiting reactant is the reactant that is completely consumed first, limiting the amount of product formed.

• The excess reactant is the reactant that remains after the reaction is complete.

• To identify the limiting reactant, compare the mole ratios of reactants used to those required by the balanced equation.

Example: For the reaction $\mathrm{CH}_4(g) + 2\,\mathrm{O}_2(g) \rightarrow \mathrm{CO}_2(g) + 2\,\mathrm{H}_2\mathrm{O}(g)$, if you start with 1 mole CH4 and 2 moles O2, both are consumed completely.

Theoretical Yield and Percent Yield

Calculating Yield

• Theoretical yield is the maximum amount of product that can be formed from given amounts of reactants.

• Actual yield is the amount of product actually obtained from a reaction.

• Percent yield is calculated as:

$\text{percent yield} = \frac{\text{actual yield}}{\text{theoretical yield}} \times 100\%$

Example: If the theoretical yield is 50.0 g and the actual yield is 37.5 g, then:

$\text{percent yield} = \frac{37.5}{50.0} \times 100\% = 75\%$

Summary Table: Key Concepts in Chemical Reactions

Concept	Definition	Example
Balanced Equation	Equal number of each atom on both sides	$\mathrm{CH}_4 + 2\,\mathrm{O}_2 \rightarrow \mathrm{CO}_2 + 2\,\mathrm{H}_2\mathrm{O}$
Stoichiometry	Quantitative relationships in reactions	2 mol C8H18 : 16 mol CO2
Limiting Reactant	Reactant used up first	1 mol CH4 + 2 mol O2
Theoretical Yield	Maximum possible product	Calculated from balanced equation
Percent Yield	Actual yield as % of theoretical	$\frac{\text{actual}}{\text{theoretical}} \times 100\%$

Additional info:

• Practice problems throughout the notes reinforce key concepts and provide opportunities for self-assessment.

• Real-world applications, such as climate change and fuel combustion, illustrate the importance of chemical reaction calculations.