Write down the given reactions and their enthalpy changes.

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Here's how to determine the enthalpy change for the conversion of graphite to diamond using Hess's Law:

Write down the given reactions and their enthalpy changes.
1. Combustion of graphite: $\text{C(graphite)} + \text{O}_2\text{(g)} \longrightarrow \text{CO}_2\text{(g)}; \quad \Delta H_1 = -393 \text{ kJ/mol}$
2. Combustion of diamond: $\text{C(diamond)} + \text{O}_2\text{(g)} \longrightarrow \text{CO}_2\text{(g)}; \quad \Delta H_2 = -395 \text{ kJ/mol}$
Identify the target reaction.
The reaction we want to find the enthalpy change for is:
$\text{C(graphite)} \longrightarrow \text{C(diamond)}$
Manipulate the given reactions to match the target reaction.
We need $\text{C(graphite)}$ on the reactant side, so we keep Reaction 1 as it is:
$\text{C(graphite)} + \text{O}_2\text{(g)} \longrightarrow \text{CO}_2\text{(g)}; \quad \Delta H_1 = -393 \text{ kJ/mol}$
We need $\text{C(diamond)}$ on the product side. In Reaction 2, $\text{C(diamond)}$ is a reactant, so we reverse Reaction 2. Reversing a reaction changes the sign of its enthalpy change:
$\text{CO}_2\text{(g)} \longrightarrow \text{C(diamond)} + \text{O}_2\text{(g)}; \quad \Delta H_{\text{reversed 2}} = -(-395 \text{ kJ/mol}) = +395 \text{ kJ/mol}$
Add the manipulated reactions and their enthalpy changes.
Adding the two manipulated reactions:
$(\text{C(graphite)} + \text{O}_2\text{(g)} \longrightarrow \text{CO}_2\text{(g)}) + (\text{CO}_2\text{(g)} \longrightarrow \text{C(diamond)} + \text{O}_2\text{(g)})$
The $\text{O}_2\text{(g)}$ and $\text{CO}_2\text{(g)}$ cancel out on both sides, leaving the target reaction:
$\text{C(graphite)} \longrightarrow \text{C(diamond)}$
The total enthalpy change is the sum of the enthalpy changes of the manipulated reactions:
$\Delta H_{\text{target}} = \Delta H_1 + \Delta H_{\text{reversed 2}}$ $\Delta H_{\text{target}} = -393 \text{ kJ/mol} + 395 \text{ kJ/mol}$ $\Delta H_{\text{target}} = +2 \text{ kJ/mol}$
The enthalpy change for the conversion of graphite to diamond is $\boxed{\text{+2 kJ/mol}}$ .

Write down the given reactions and their enthalpy changes.

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Step-by-step solution

Write down the given reactions and their enthalpy changes.

Identify the target reaction.

Manipulate the given reactions to match the target reaction.

Add the manipulated reactions and their enthalpy changes.

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