Documentation:CHBE Exam Wiki/6.3 - Hess's Law for Heats of Reaction

6.3 – Hess's Law for Heats of Reaction

6.3.0 – Learning Objectives

By the end of this section you should be able to:

1. Apply the concept of path dependence and independence.
2. Understand the concept of Hess's law.
3. Use Hess's law to solve standard heat of reaction problems.

6.3.1 – Introduction

Suppose you wish to determine the standard heat of reaction for the reaction

$C{\text{(s)}}+{\frac {1}{2}}{\text{ }}O_{2}{\text{(g)}}\longrightarrow CO{\text{(g)}}$

It is very difficult to measure the standard heat of reaction for this reaction because if these reactants are at $25^{\circ }C$ and $1$ atm, the rate of reaction will be very slow. Since calorimeters are used to measure heat of reaction and it impossible to make calorimeters perfectly insulated, it is impractical to measure the true amount of energy released. Imagine you are trying to measure how much energy is released in the oxidation of iron. It would be very impractical to measure how much energy is realized over the course of years. However, we can use Hess's law to find the standard heat of reaction for this reaction.

6.3.2 – Hess's Law

Since it is impractical to measure the standard heat of reaction for the reaction

$C{\text{(s)}}+{\frac {1}{2}}{\text{ }}O_{2}{\text{(g)}}\longrightarrow CO{\text{(g)}}$

we can use Hess's law by using other measurable standard heat of reactions to solve for the immeasurable quantity.

$C{\text{(s)}}+O_{2}{\text{(g)}}\longrightarrow CO_{2}{\text{(g)}}\quad \Delta {\hat {H}}_{r1}^{\circ }=-393.51{\text{ }}kJ/mol$

$CO{\text{(g)}}+{\frac {1}{2}}{\text{ }}O_{2}{\text{(g)}}\longrightarrow CO_{2}{\text{(g)}}\quad \Delta {\hat {H}}_{r2}^{\circ }=-282.99{\text{ }}kJ/mol$

If we subtract reaction two from reaction three, we will receive the first reaction stoichiometrically balanced and the heat of reaction from that reaction.

$C{\text{(s)}}+O_{2}{\text{(g)}}-CO{\text{(g)}}-{\frac {1}{2}}{\text{ }}O_{2}\longrightarrow CO_{2}{\text{(g)}}-CO_{2}{\text{(g)}}:\quad \Delta {\hat {H}}_{r1}^{\circ }=((-393.51)-(-282.99)){\text{ }}kJ/mol$

$C{\text{(s)}}+{\frac {1}{2}}{\text{ }}O_{2}{\text{(g)}}\longrightarrow CO{\text{(g)}}\quad \Delta {\hat {H}}_{r1}^{\circ }=-110.52{\text{ }}kJ/mol$

6.3.3 – Problem Statement

Problem 1

Question

The standard heats of the follow reactions are determined experimentally:

1. $2{\text{ }}C_{2}H_{6}{\text{(g)}}+7O_{2}{\text{(g)}}\rightarrow 4{\text{ }}CO_{2}{\text{(g)}}+6{\text{ }}H_{2}O{\text{(v)}}\quad \Delta {\hat {H}}_{r1}^{\circ }=-3119.6{\text{ }}kJ/mol$

2. $C{\text{(s)}}+O_{2}{\text{(g)}}\rightarrow CO_{2}{\text{(g)}}\quad \Delta {\hat {H}}_{r2}^{\circ }=-393.5{\text{ }}kJ/mol$

3. $2{\text{ }}H_{2}{\text{(g)}}+O_{2}{\text{(g)}}\rightarrow 2H_{2}O{\text{(v)}}\quad \Delta {\hat {H}}_{r3}^{\circ }=-285.8{\text{ }}kJ/mol$

Using Hess's law, determine the standard heat of reaction for the following reaction.

4. $C{\text{(s)}}+3{\text{ }}H_{2}{\text{(g)}}\rightarrow C_{2}H_{6}{\text{(g)}}\quad \Delta {\hat {H}}_{r4}^{\circ }=?$

Answer

To find the standard heat of reaction of the fourth formula, we must first balance the three previous one so that they equate to the last one. There is no simple trick to this, although, the more you practice, the easier it becomes.

${\big (}{\text{ }}formula_{{\text{ }}4}{\text{ }}{\big )}=2\times {\big (}{\text{ }}formula_{{\text{ }}2}{\text{ }}{\big )}+1.5\times {\big (}{\text{ }}formula_{{\text{ }}3}{\text{ }}{\big )}-0.5\times {\big (}{\text{ }}formula_{{\text{ }}1}{\text{ }}{\big )}$

Therefore,

$\Delta {\hat {H}}_{r4}=2\times {\Big (}\Delta {\hat {H}}_{r2}^{\circ }{\Big )}+1.5\times {\Big (}\Delta {\hat {H}}_{r3}^{\circ }{\Big )}-0.5\times {\Big (}\Delta {\hat {H}}_{r1}^{\circ }{\Big )}$

$\Delta {\hat {H}}_{r4}=2\times {\Big (}-393.5{\text{ }}{\frac {kJ}{mol}}{\Big )}+1.5\times {\Big (}-285.8{\text{ }}{\frac {kJ}{mol}}{\Big )}-0.5\times {\Big (}-3119.6{\text{ }}{\frac {kJ}{mol}}{\Big )}$

$\Delta {\hat {H}}_{r4}=-84.6{\text{ }}{\frac {kJ}{mol}}$

Question

Suppose heats of reaction at 25 °C are measured experimentally for the following set of reactions:

$A+B\longrightarrow C:{\text{ }}{\text{ }}\quad \Delta {\hat {H}}_{r1}^{\circ }=-1000{\text{ }}kJ/mol$

$A+D\longrightarrow 3C+E:{\text{ }}{\text{ }}\quad \Delta {\hat {H}}_{r2}^{\circ }=-2000{\text{ }}kJ/mol$

What is the heat of reaction of the equation involving 2D as part of the products?

Answer

$A+B\longrightarrow C$

$A+D\longrightarrow 3C+E$

$A+B\longrightarrow C$

$3C+E\longrightarrow A+D$

$2A+2B\longrightarrow 2C$

$6C+2E\longrightarrow 2A+2D$

$6C+2E+2B\longrightarrow 2C+2D:{\text{ }}{\text{ }}\quad \Delta {\hat {H}}_{r}^{\circ }=2000{\text{ }}kJ/mol$