# How to Determine Enthalpy Change of Reaction Using Hess' Law

Here's the question that we want to discuss this week.

Given the energy cycle showing the energy changes of a set of reactions, we want to deduce which of the following statements are correct.

We can make use of Hess' Law to work out the relationship between different reactions.

Hess' Law states that the enthalpy change of a reaction is independent of the path taken from the initial to final state.

For example, the overall enthalpy change from reactant A to product B is the same for the following pathways:

A → B directly

A → X → B

A → X → Y → Z → B

**1. Enthalpy change for R to U is endothermic**

We can draw an arrow from R to U directly.

According to Hess' Law, enthalpy change for the following pathways are the same:

R → U directly

R → T → U

In practice we can use vector sum to determine enthalpy change for R to U.

Notice the terms R, U and T form an energy cycle (highlighted in yellow).

Based on this cycle, all the clockwise pathways is equal to all the counter-clockwise pathways.

Hence we can put this into an equation and solve for ΔH_{1}.

Enthalpy change for R to U is +17 kJ mol^{-1} which is endothermic.

Hence statement 1 is correct.

**2. Enthalpy change for S to T is +226 kJ mol ^{-1}**

We can draw an arrow from S to T directly.

Using Hess' Law, enthalpy change for following pathways are the same:

S → T directly

S → R → T

Using vector sum, we make use of the energy cycle involving R, S and T and determine the clockwise and counter-clockwise pathways.

All the clockwise pathways is equal to all the counter-clockwise pathways, hence we can solve for ΔH_{2}.

Enthalpy change for S to T is +226 kJ mol^{-1} hence statement 2 is correct.

**3. Enthalpy change for S to U is +151 kJ mol ^{-1}**

Using Hess' Law, enthalpy change for following pathways are the same:

S → U directly

S → R → T → U

Again we can use vector sum (total clockwise pathway equal total counter-clockwise pathway) to solve for ΔH_{3}.

Enthalpy change for S to U is +151 kJ mol^{-1} hence statement 3 is correct.

Topic: Energetics, Physical Chemistry, A Level Chemistry, Singapore

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