Lesson 5.4: Hess’s Law and Enthalpy Calculations in Thermochemistry

Hess’s Law in Thermochemistry

Introduction to Hess’s Law

Hess’s law is a fundamental principle in thermochemistry that allows chemists to determine the enthalpy change of a reaction by using the enthalpy changes of multiple related reactions. This law is based on the observation that the total enthalpy change for a chemical process is independent of the pathway taken, provided the initial and final conditions are the same.

• Definition: Hess’s law states that the enthalpy change for the conversion of reactants to products is the same whether the process occurs in one step or several steps.

• Path Independence: The enthalpy change (ΔH) depends only on the initial and final states, not on the route taken between them.

• Analogy: Like climbing a mountain by different paths, the total elevation gained is the same regardless of the route.

Enthalpy Change and Hess’s Law

Experimental evidence shows that the enthalpy change in a chemical process is independent of the path taken. This means that whether a reaction occurs in a single step or through multiple intermediate steps, the overall enthalpy change remains constant.

• Example: The formation of nitrogen dioxide (NO2) from nitrogen (N2) and oxygen (O2) can occur in one or two steps, but the total ΔH is the same:

Single-step reaction:

$\mathrm{N_2(g) + 2\ O_2(g) \rightarrow 2\ NO_2(g)} \qquad \Delta H = 68\ \mathrm{kJ}$

Two-step process:

$\mathrm{N_2(g) + O_2(g) \rightarrow 2\ NO(g)} \qquad \Delta H = 180\ \mathrm{kJ}$

$\mathrm{2\ NO(g) + O_2(g) \rightarrow 2\ NO_2(g)} \qquad \Delta H = -112\ \mathrm{kJ}$

Sum: $180\ \mathrm{kJ} + (-112\ \mathrm{kJ}) = 68\ \mathrm{kJ}$

Rules for Enthalpy Changes (Applying Hess’s Law)

To use Hess’s law for calculating enthalpy changes, follow these two main rules:

1. Reversing a Reaction: If you reverse a chemical equation, you must also reverse the sign of ΔH.

2. Scaling a Reaction: If you multiply the coefficients in a balanced equation by a factor, multiply ΔH by the same factor.

• Example: For the reaction $\mathrm{Xe(g) + 2\ F_2(g) \rightarrow XeF_4(s)}$, $\Delta H = -251\ \mathrm{kJ}$, reversing the reaction gives $\Delta H = +251\ \mathrm{kJ}$.

• Proportionality: Doubling the amount of reactants doubles the enthalpy change.

Applications and Importance of Hess’s Law

Hess’s law is especially useful for reactions that are too fast, too slow, or too dangerous to measure directly using calorimetry. By combining known thermochemical equations, chemists can determine the enthalpy change for complex reactions.

• Example: The reaction of glycerine with potassium permanganate is too vigorous for direct calorimetry, but Hess’s law allows calculation of ΔH using related reactions.

Sample Problems Using Hess’s Law

Sample Problem 1: Conversion of Graphite to Diamond

• Given:

  • $\mathrm{C_{graphite}(s) + O_2(g) \rightarrow CO_2(g)} \qquad \Delta H = -394\ \mathrm{kJ}$

  • $\mathrm{C_{diamond}(s) + O_2(g) \rightarrow CO_2(g)} \qquad \Delta H = -396\ \mathrm{kJ}$

• Required: $\mathrm{C_{graphite}(s) \rightarrow C_{diamond}(s)}$

• Solution: Reverse the second equation and add to the first:

$\mathrm{C_{graphite}(s) + O_2(g) \rightarrow CO_2(g)} \qquad \Delta H = -394\ \mathrm{kJ}$ $\mathrm{CO_2(g) \rightarrow C_{diamond}(s) + O_2(g)} \qquad \Delta H = +396\ \mathrm{kJ}$

Sum: $\mathrm{C_{graphite}(s) \rightarrow C_{diamond}(s)} \qquad \Delta H = 2\ \mathrm{kJ}$

Sample Problem 2: Production of Ethene from Ethane

• Given:

  • $\mathrm{C_2H_6(g) + 3.5\ O_2(g) \rightarrow 2\ CO_2(g) + 3\ H_2O(l)} \qquad \Delta H = -1559\ \mathrm{kJ}$

  • $\mathrm{C_2H_4(g) + 3\ O_2(g) \rightarrow 2\ CO_2(g) + 2\ H_2O(l)} \qquad \Delta H = -1411\ \mathrm{kJ}$

  • $\mathrm{2\ H_2(g) + O_2(g) \rightarrow 2\ H_2O(l)} \qquad \Delta H = -572\ \mathrm{kJ}$

• Required: $\mathrm{C_2H_6(g) \rightarrow C_2H_4(g) + H_2(g)}$

• Solution: Manipulate and sum the equations to obtain:

$\Delta H = 138\ \mathrm{kJ}$ per mole of ethane.

Practice Problems

• Practice applying Hess’s law to calculate enthalpy changes for various reactions using provided thermochemical equations. Problems include reactions involving ammonia, water, chlorine fluorides, iron(III) oxide, phosphorus, nitric oxide, hydrazine, calcium carbide, and neutralization reactions.

Summary Table: Rules for Manipulating Thermochemical Equations

Operation	Effect on ΔH
Reverse the reaction	Change the sign of ΔH
Multiply equation by n	Multiply ΔH by n
Add equations	Add ΔH values

Conceptual Questions

• State Hess’s law in your own words.

• What happens to ΔH when a reaction is reversed?

• How does scaling a reaction affect ΔH?

• How is Hess’s law consistent with the law of conservation of energy?

• What property of enthalpy change is the basis of Hess’s law?

Summary

• Hess’s law states that the enthalpy change of a process is the same whether the process takes place in one step or in a series of steps.

• By applying Hess’s law, we can manipulate and combine different chemical equations to determine the enthalpy change of a reaction of interest.