JEE Chemistry 2025 Question with Solution

Given:

• $C(\text{diamond}) \rightarrow C(\text{graphite}) + X$
• $C(\text{diamond}) + O_2(g) \rightarrow CO(g) + Y$
• $C(\text{graphite}) + O_2(g) \rightarrow CO(g) + Z$

Find: The relation among $X$, $Y$ and $Z$.

Using Hess's law, add the first and third reactions:

$$\begin{aligned} C(\text{diamond}) &\rightarrow C(\text{graphite}) + X \\ C(\text{graphite}) + O_2(g) &\rightarrow CO(g) + Z \end{aligned}$$

On adding, $C(\text{graphite})$ cancels and we get:

$$C(\text{diamond}) + O_2(g) \rightarrow CO(g) + (X + Z)$$

This corresponds to the second reaction:

$$C(\text{diamond}) + O_2(g) \rightarrow CO(g) + Y$$

Therefore,

$$Y = X + Z$$

which gives

$$X = Y - Z$$

the solution marks option D as correct, but the Hess's law working gives $X = Y - Z$. Therefore, the mathematically consistent relation is $X = Y - Z$, which matches option C.

Given: The three enthalpy relations are written in sequence form.

Find: Which option follows from combining the reactions.

Identify principle: Hess's law of constant heat summation.

From the data:

$$C(\text{diamond}) \rightarrow C(\text{graphite}) + X$$ $$C(\text{graphite}) + O_2(g) \rightarrow CO(g) + Z$$

Adding them gives:

$$C(\text{diamond}) + O_2(g) \rightarrow CO(g) + X + Z$$

But this same net reaction is also given as:

$$C(\text{diamond}) + O_2(g) \rightarrow CO(g) + Y$$

Hence the enthalpy terms must satisfy:

$$X + Z = Y$$

So,

$$X = Y - Z$$

Therefore, the correct relation from the equations is $X = Y - Z$. The listed official answer on the page is inconsistent with the algebra shown in the detailed solution.