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

To solve the given problem, we need to understand the thermochemical equations related to the conversion and combustion of diamond and graphite. Let's break down each equation:

1. First, we have the phase transition of diamond to graphite, which is represented as: \(C(\text{diamond}) \rightarrow C(\text{graphite}) + X \text{kJ mol}^{-1}\).
2. The combustion of diamond in oxygen is: \(C(\text{diamond}) + O_2(g) \rightarrow CO_2(g) + Y \text{kJ mol}^{-1}\).
3. Similarly, the combustion of graphite in oxygen is: \(C(\text{graphite}) + O_2(g) \rightarrow CO_2(g) + Z \text{kJ mol}^{-1}\).

Given these equations, we can apply Hess's Law, which states that the total enthalpy change for a reaction is the same regardless of the path by which the reaction takes place. We can express the conversion of diamond into graphite as a combination of these combustion reactions.

Using Hess's Law:

• Consider the complete combustion of diamond: \(C(\text{diamond}) + O_2(g) \rightarrow CO_2(g) + Y \text{kJ mol}^{-1}\).
• And the complete combustion of graphite: \(C(\text{graphite}) + O_2(g) \rightarrow CO_2(g) + Z \text{kJ mol}^{-1}\).

To connect equation 1 to equation 3, we realize:

1. By flipping the graphite combustion equation to go from \(CO_2(g)\) back to graphite, we must invert the sign of Z:
   • \(CO_2(g) \rightarrow C(\text{graphite}) + O_2(g) - Z \text{kJ mol}^{-1}\).
2. Combine this with the diamond combustion equation. The diamond to graphite conversion can be represented as:
   • \(C(\text{diamond}) + O_2(g) \rightarrow CO_2(g) + Y \text{kJ mol}^{-1}\)
   • \(CO_2(g) \rightarrow C(\text{graphite}) + O_2(g) - Z \text{kJ mol}^{-1}\)
   • Overall, \(C(\text{diamond}) \rightarrow C(\text{graphite}) + X \text{kJ mol}^{-1}\), where \(X = -Y + Z\).

Thus, the correct relationship between the enthalpy changes for these reactions is \(X = -Y + Z\).