Stoichiometry and Energy in Chemical Reactions: Chapter 8 Study Notes

Quantities in Chemical Reactions

Introduction to Stoichiometry

Stoichiometry is the study of quantitative relationships between reactants and products in chemical reactions. It allows chemists to predict the amounts of substances consumed and produced in a given reaction.

• Stoichiometry: The numerical relationship between chemical quantities in a balanced chemical equation.

• Balanced chemical equation: Shows the proportions of reactants and products involved in a reaction.

• Application: Used to calculate how much product will form from a given amount of reactant, or how much reactant is needed to produce a desired amount of product.

Global Warming: Greenhouse Gases

Combustion of Fossil Fuels and CO2 Production

The combustion of fossil fuels, such as octane (a component of gasoline), produces water and carbon dioxide as products. Carbon dioxide is a major greenhouse gas responsible for global warming.

• Greenhouse gases: Gases that trap heat in the atmosphere, including carbon dioxide (CO2), methane (CH4), and water vapor (H2O).

• Greenhouse effect: Greenhouse gases allow sunlight to enter the atmosphere but prevent heat from escaping, leading to increased global temperatures.

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

Stoichiometry: Mole-to-Mole Relationships

Understanding Mole Ratios

A balanced chemical equation provides the "recipe" for how reactants combine to form products. Mole ratios are derived from the coefficients in the equation.

• Mole ratio: The ratio of moles of one substance to moles of another in a balanced equation.

• Example: For the reaction $3H_2(g) + N_2(g) \rightarrow 2NH_3(g)$, the mole ratio is 3 mol H2 : 1 mol N2 : 2 mol NH3.

• Application: If you have 3 mol N2 and excess H2, you can produce $3 \times 2 = 6$ mol NH3.

Stoichiometry: Mass-to-Mass Relationships

Converting Between Masses of Reactants and Products

Chemical equations allow conversion between masses of reactants and products using molar masses and mole ratios.

• General outline: Convert mass of reactant to moles, use mole ratio to find moles of product, then convert moles of product to mass.

• Example: For the combustion of octane:

  • $C_8H_{18}(l) + 25O_2(g) \rightarrow 16CO_2(g) + 18H_2O(g)$

  • To find mass of CO2 produced from 10.0 g octane:

    1. Convert 10.0 g octane to moles using molar mass ($114.3$ g/mol).

    2. Use mole ratio ($2$mol octane : $16$ mol CO2).

    3. Convert moles CO2 to grams using molar mass ($44.01$ g/mol).

Limiting Reactant, Theoretical Yield, and Percent Yield

Key Concepts and Calculations

In chemical reactions, the limiting reactant determines the maximum amount of product that can be formed. Theoretical yield is the calculated maximum, while actual yield is what is obtained experimentally. Percent yield measures efficiency.

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

• Theoretical yield: The maximum amount of product possible, based on the limiting reactant.

• Actual yield: The amount of product actually obtained from a reaction.

• Percent yield: $\text{Percent yield} = \frac{\text{Actual yield}}{\text{Theoretical yield}} \times 100\%$

• Example: If you have enough flour for 15 pancakes (theoretical yield), but only make 11 pancakes (actual yield), percent yield is $\frac{11}{15} \times 100\% = 73.3\%$.

Limiting Reactant Problems: Moles and Mass

Solving Limiting Reactant Problems

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

• Example (Moles): $Ti(s) + 2Cl_2(g) \rightarrow TiCl_4(s)$

  • Given: 1.8 mol Ti and 3.2 mol Cl2

  • Calculate moles of TiCl4 from each reactant; the smaller value is the theoretical yield.

• Example (Mass): $2Na(s) + Cl_2(g) \rightarrow 2NaCl(s)$

  • Given: 53.2 g Na and 65.8 g Cl2

  • Convert masses to moles, use mole ratio, then convert to mass of product.

Enthalpy: Heat in Chemical Reactions

Enthalpy of Reaction ($\Delta H_{rxn}$)

Enthalpy quantifies the heat emitted or absorbed during a chemical reaction at constant pressure.

• Exothermic reaction: Releases heat; $\Delta H_{rxn}$ is negative.

• Endothermic reaction: Absorbs heat; $\Delta H_{rxn}$ is positive.

• Example: Combustion of methane:

  • $CH_4(g) + 2O_2(g) \rightarrow CO_2(g) + 2H_2O(g)$

  • $\Delta H_{rxn} = -802.3$ kJ (exothermic)

• Example: Formation of nitrogen monoxide:

  • $N_2(g) + O_2(g) \rightarrow 2NO(g)$

  • $\Delta H_{rxn} = +182.6$ kJ (endothermic)

Stoichiometry of Enthalpy Changes

Calculating Heat Exchange in Reactions

The amount of heat exchanged depends on the amount of reactants used, as specified by the balanced equation and $\Delta H_{rxn}$.

• Example: Combustion of propane:

  • $C_3H_8(g) + 5O_2(g) \rightarrow 3CO_2(g) + 4H_2O(g)$

  • $\Delta H_{rxn} = -2044$ kJ per 1 mol $C_3H_8$

  • To find heat emitted from 1.18 x 104 g propane:

    1. Convert mass to moles using molar mass ($44.11$ g/mol).

    2. Multiply moles by $-2044$ kJ/mol to get total heat emitted.

Summary Table: Key Stoichiometric Concepts

Term	Definition	Formula/Example
Stoichiometry	Quantitative relationship between reactants and products	Use balanced equation coefficients
Limiting Reactant	Reactant consumed first, limits product	Compare product amounts from each reactant
Theoretical Yield	Maximum product possible	Based on limiting reactant
Actual Yield	Product actually obtained	Measured experimentally
Percent Yield	Efficiency of reaction	$\frac{\text{Actual yield}}{\text{Theoretical yield}} \times 100\%$
Enthalpy ($\Delta H_{rxn}$)	Heat exchanged at constant pressure	Negative for exothermic, positive for endothermic

Learning Objectives for Chapter 8

• Recognize numerical relationships in balanced chemical equations.

• Carry out mole-to-mole and mass-to-mass conversions.

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

• Calculate thermal energy emitted or absorbed in chemical reactions.