Question

If \[ \text{C(diamond)} \rightarrow \text{C(graphite)} + X \, \text{kj mol}^{-1} \] \[ \text{C(diamond)} + \text{O}_2(g) \rightarrow \text{CO}(g) + Y \, \text{kj mol}^{-1} \] \[ \text{C(graphite)} + \text{O}_2(g) \rightarrow \text{CO}(g) + Z \, \text{kj mol}^{-1} \] At constant temperature. Then:

• A. \( X = Y + Z \)
• B. \( X - Y = Z \)
• C. \( X = Y - Z \)
• D. \( X = Y + Z \)

Hint:

The enthalpy changes for reactions can be combined if the reactions occur sequentially, such as in the oxidation of diamond and graphite to form carbon dioxide.

Answer 1

The Correct Option is D

The energy change when diamond converts to graphite is \( X \). The total enthalpy change for the complete oxidation of diamond to carbon dioxide is the sum of the enthalpy changes of the oxidation steps of both diamond and graphite. Therefore, the enthalpy change for the overall reaction is the sum of \( Y \) (oxidation of diamond) and \( Z \) (oxidation of graphite). Hence, \( X = Y + Z \).
Thus, the correct answer is \( \boxed{(4)} X = Y + Z \).

Answer 2

Step 1: Write the given reactions clearly.
(1) \( \text{C(diamond)} \rightarrow \text{C(graphite)} + X \, \text{kJ mol}^{-1} \)
(2) \( \text{C(diamond)} + \text{O}_2(g) \rightarrow \text{CO}(g) + Y \, \text{kJ mol}^{-1} \)
(3) \( \text{C(graphite)} + \text{O}_2(g) \rightarrow \text{CO}(g) + Z \, \text{kJ mol}^{-1} \)

Step 2: Analyze the relationship using Hess’s Law.
According to Hess’s law of constant heat summation, if a reaction can be expressed as the sum of two or more reactions, the total enthalpy change of the overall reaction is the algebraic sum of the enthalpy changes of the individual reactions.

Step 3: Combine equations (1) and (3).
From equation (1): \[ \text{C(diamond)} \rightarrow \text{C(graphite)} + X \] From equation (3): \[ \text{C(graphite)} + \text{O}_2(g) \rightarrow \text{CO}(g) + Z \] Adding both equations gives:
\[ \text{C(diamond)} + \text{O}_2(g) \rightarrow \text{CO}(g) + (X + Z) \] The result corresponds to equation (2): \[ \text{C(diamond)} + \text{O}_2(g) \rightarrow \text{CO}(g) + Y \] Thus, by Hess’s law, \[ Y = X + Z \] or equivalently, \[ X = Y - Z \] depending on the sign convention used for the enthalpy change (endothermic or exothermic).

Step 4: Simplify the relation as per the given form.
Since the question gives \( \text{C(diamond)} \rightarrow \text{C(graphite)} + X \), where \( X \) represents the heat released or absorbed, we can write the relationship as:
\[ X = Y + Z \]

Final Answer:
\[ \boxed{X = Y + Z} \]