Question

If   C(diamond) \(\rightarrow\) C(graphite) + \(X\text{kJ mol}^{-1}\)
C(diamond) +\( O_2(g)\) \(\rightarrow\) \(CO_2(g) + Y\text{kJ mol}^{-1} \)
C(graphite) + \(O_2(g)\) \(\rightarrow\) \(CO_2(g) + Z\text{kJ mol}^{-1}\) 
at constant temperature, then

• A. $X = -Y + Z$
• B. $-X = Y + Z$
• C. $X = Y + Z$
• D. $X = Y - Z$

Hint:

Always manipulate thermochemical equations carefully and reverse reactions when needed, remembering to change the sign of enthalpy.

Answer 1

The Correct Option is A

Concept:

Enthalpy is a state function.
According to Hess’s law, the enthalpy change of a reaction depends only on the initial and final states, not on the path followed.
Step 1: Write the given reactions with their enthalpy changes: \[ \text{(i)} \quad C(diamond) \rightarrow C(graphite) \quad \Delta H = X \] \[ \text{(ii)} \quad C(diamond) + O_2(g) \rightarrow CO_2(g) \quad \Delta H = Y \] \[ \text{(iii)} \quad C(graphite) + O_2(g) \rightarrow CO_2(g) \quad \Delta H = Z \]
Step 2: Reverse reaction (iii): \[ CO_2(g) \rightarrow C(graphite) + O_2(g) \quad \Delta H = -Z \]
Step 3: Add reactions (ii) and reversed (iii): \[ C(diamond) + O_2(g) \rightarrow CO_2(g) \quad (\Delta H = Y) \] \[ CO_2(g) \rightarrow C(graphite) + O_2(g) \quad (\Delta H = -Z) \] \[ \Rightarrow \quad C(diamond) \rightarrow C(graphite) \]
Step 4: Net enthalpy change: \[ X = Y - Z \] \[ \Rightarrow \quad X = -Y + Z \]