Hess's Law and Enthalpy Calculations

What is Hess's Law?

Hess's Law states that the total enthalpy change for a reaction is the same, no matter how many steps the reaction is carried out in. This is because enthalpy is a state function, meaning it depends only on the initial and final states, not the path taken.

In simpler terms, if you can find a different route to the same chemical change, the total energy change will be the same.

Using Hess's Law

• Identify the target reaction for which you need to find the enthalpy change.
• Use known enthalpy changes of other reactions to form a cycle that includes the target reaction.
• Apply Hess's Law to calculate the unknown enthalpy change.

Enthalpy Calculations Using Hess's Law

To calculate the enthalpy change of a reaction using Hess's Law, follow these steps:

1. Write the target equation: Identify the chemical equation for which you need the enthalpy change.
2. Find known reactions: Look for other reactions with known enthalpy changes that can be combined to give the target equation.
3. Adjust equations: Reverse or multiply the known reactions as needed, remembering to adjust their enthalpy changes accordingly.
4. Add equations: Combine the adjusted equations to form the target equation.
5. Calculate: Sum the enthalpy changes of the adjusted reactions to find the enthalpy change for the target reaction.

Example

Calculate the enthalpy change for the reaction:

$$\text{C} + \text{O}_2 \rightarrow \text{CO}_2$$

Given:

• $\text{C} + \frac{1}{2} \text{O}_2 \rightarrow \text{CO}$, $\Delta H = -110 \text{ kJ/mol}$
• $\text{CO} + \frac{1}{2} \text{O}_2 \rightarrow \text{CO}_2$, $\Delta H = -283 \text{ kJ/mol}$