Chapter 8: Quantities in Chemical Reactions – Stoichiometry, Limiting Reactants, and Enthalpy

Quantities in Chemical Reactions

Global Warming and Greenhouse Gases

The combustion of fossil fuels, such as octane, produces water and carbon dioxide. Carbon dioxide (CO2) is a major greenhouse gas implicated in global warming. Greenhouse gases trap heat in the Earth's atmosphere, causing the average global temperature to rise as their concentration increases.

• Greenhouse Effect: Sunlight enters the atmosphere, warms Earth's surface, and some heat is trapped by greenhouse gases, preventing it from escaping.

• Since 1880, atmospheric CO2 levels have risen by 38%, and Earth's average temperature has increased by about 1.9°F.

Stoichiometry: Relationships Between Chemical Quantities

Stoichiometry is the numerical relationship between chemical quantities in a balanced chemical equation. It allows prediction of product amounts based on reactant quantities and vice versa.

• Balanced equations provide ratios for reactants and products.

• Example: Combustion of octane (C8H18): $\mathrm{2\ C_8H_{18}\ (l) + 25\ O_2\ (g) \rightarrow 16\ CO_2\ (g) + 18\ H_2O\ (g)}$ 16 mol CO2 are produced for every 2 mol of octane burned.

Stoichiometry Analogy: Making Pancakes

Recipes illustrate stoichiometric relationships. For example, 1 cup flour + 2 eggs + 1/2 tsp baking powder yields 5 pancakes. If you have 2 eggs, you can make 5 pancakes; with 8 eggs, you can make 20 pancakes, assuming other ingredients are sufficient.

• Ratio: 2 eggs : 5 pancakes

• Calculation: $\mathrm{8\ eggs \times \frac{5\ pancakes}{2\ eggs} = 20\ pancakes}$

Mole-to-Mole Conversions

Balanced chemical equations act as recipes for reactants and products. For example, the synthesis of ammonia:

• Equation: $\mathrm{N_2\ (g) + 3\ H_2\ (g) \rightarrow 2\ NH_3\ (g)}$

• Ratio: 1 mol N2 : 3 mol H2 : 2 mol NH3

• Example: If you have 3 mol N2 and excess H2, you can make 6 mol NH3.

Mass-to-Mass Conversions

Often, stoichiometry problems require converting between masses of reactants and products. The general outline is:

• Convert mass of A to moles of A (using molar mass).

• Use the balanced equation to convert moles of A to moles of B.

• Convert moles of B to mass of B (using molar mass).

Limiting Reactant, Theoretical Yield, and Percent Yield

In reactions, the limiting reactant is the one that is completely consumed first, thus limiting the amount of product formed. The theoretical yield is the maximum amount of product possible based on the limiting reactant. The actual yield is the amount actually produced, and percent yield is calculated as:

• $\mathrm{Percent\ Yield = \frac{Actual\ Yield}{Theoretical\ Yield} \times 100\%}$

• Example: If you have enough flour for 15 pancakes, eggs for 25, and baking powder for 40, flour is the limiting reactant and 15 pancakes is the theoretical yield.

• If only 11 pancakes are made, percent yield is $\mathrm{\frac{11}{15} \times 100\% = 73\%}$

Limiting Reactant Problems: Moles and Mass

To determine the limiting reactant and theoretical yield, compare the amounts of product each reactant can produce. The smallest amount determines the limiting reactant.

• Example (moles): Ti + 2 Cl2 → TiCl4. Given 1.8 mol Ti and 3.2 mol Cl2, Cl2 is limiting, theoretical yield is 1.6 mol TiCl4.

• Example (mass): Na + Cl2 → 2 NaCl. Given 53.2 g Na and 65.8 g Cl2, Cl2 is limiting, theoretical yield is 108 g NaCl.

Limiting Reactant Problems: Percent Yield

Percent yield is calculated using actual and theoretical yields. For example, if actual yield is 86.4 g NaCl and theoretical yield is 108 g NaCl:

• $\mathrm{Percent\ Yield = \frac{86.4\ g}{108\ g} \times 100\% = 80.0\%}$

Limiting Reactant Problems: Complex Example

For the reaction Cu2O + C → 2 Cu + CO, given 11.5 g Cu2O and 114.5 g C, the limiting reactant and theoretical yield are determined by calculating the amount of Cu produced from each reactant.

Enthalpy: Heat Evolved or Absorbed in a Reaction

Enthalpy of reaction (ΔHrxn) quantifies the thermal energy emitted or absorbed under constant pressure. Reactions can be:

• Exothermic: Emit heat, ΔHrxn is negative.

• Endothermic: Absorb heat, ΔHrxn is positive.

Stoichiometry of Enthalpy (ΔHrxn)

The amount of heat exchanged depends on the amount of reactants. ΔHrxn is specified for the stoichiometric amounts in the balanced equation.

• Example: Combustion of propane (C3H8): $\mathrm{C_3H_8\ (g) + 5\ O_2\ (g) \rightarrow 3\ CO_2\ (g) + 4\ H_2O\ (g)}$ $\mathrm{\Delta H_{rxn} = -2044\ kJ}$

• To calculate heat emitted for a given mass, convert mass to moles, then use ΔHrxn as a conversion factor.

Everyday Chemistry: Bunsen Burners

Bunsen burners allow adjustment of air (oxygen) mixed with methane. The flame changes color and temperature depending on air supply:

• No air: yellow, smoky, cooler flame.

• Optimum air: blue, smokeless, hottest flame.

• Too much air: cooler, may extinguish.

Key Terms and Concepts

• Stoichiometry: Quantitative relationships in chemical reactions.

• Limiting Reactant: Reactant that is completely consumed first.

• Theoretical Yield: Maximum possible product based on limiting reactant.

• Actual Yield: Product actually obtained experimentally.

• Percent Yield: $\mathrm{\frac{Actual\ Yield}{Theoretical\ Yield} \times 100\%}$

• Enthalpy of Reaction (ΔHrxn): Heat released or absorbed under constant pressure.

• Exothermic Reaction: Releases heat (ΔHrxn negative).

• Endothermic Reaction: Absorbs heat (ΔHrxn positive).

Summary Table: Limiting Reactant and Yield Calculations

Term	Definition
Limiting Reactant	Reactant that determines the maximum product
Theoretical Yield	Calculated maximum product from limiting reactant
Actual Yield	Measured product from experiment
Percent Yield	Actual Yield / Theoretical Yield × 100%

Learning Objectives

• Recognize numerical relationships in balanced equations.

• Perform mole-to-mole and mass-to-mass conversions.

• Calculate limiting reactant, theoretical yield, and percent yield.

• Calculate thermal energy emitted or absorbed in reactions.