Consider the reactions given below. On the basis of these reactions find out which of the algebric relations given in options (a) to (d) is correct ?
(i) `C_((g))+4H_((g))rarrCH_(4(g)),Delta_(r)H=x" kJ mol"^(-1)` (ii) `C_("(graphite, s)")+2H_(2(g))rarrCH_(4(g)),Delta_(r)H="y kJ mol"^(-1)` (A)x = y (B)x = 2y (C)x > y (D)x < y

Options

A. x = y
B. x = 2y
C. x gt y
D. x lt y

Explanation

To solve the problem, we need to analyze the two given reactions and their enthalpy changes.

### Given Reactions:
1. \( \text{C}_{(g)} + 4\text{H}_{(g)} \rightarrow \text{CH}_4_{(g)}, \Delta_rH = x \, \text{kJ mol}^{-1} \)
2. \( \text{C}_{(graphite, s)} + 2\text{H}_2_{(g)} \rightarrow \text{CH}_4_{(g)}, \Delta_rH = y \, \text{kJ mol}^{-1} \)

### Step-by-Step Solution:

**Step 1: Understand the First Reaction**
- In the first reaction, carbon is in the gaseous state and reacts with hydrogen gas to form methane gas. The enthalpy change for this reaction is \( x \).
- Since both reactants are in the gaseous state, the reaction proceeds without any additional energy requirement for phase changes.

**Step 2: Understand the Second Reaction**
- In the second reaction, graphite (solid carbon) reacts with hydrogen gas to form methane gas. The enthalpy change for this reaction is \( y \).
- Here, we must consider that converting solid graphite to gaseous carbon (if we were to consider it) requires energy (sublimation energy). Additionally, breaking the bonds in \( \text{H}_2 \) to form gaseous hydrogen atoms also requires energy (bond dissociation energy).

**Step 3: Compare the Enthalpy Changes**
- In the first reaction, no energy is consumed to convert the reactants to the gaseous state, so the enthalpy change \( x \) reflects the energy released when forming methane from gaseous reactants.
- In the second reaction, energy is consumed to convert solid graphite to gaseous carbon and to dissociate hydrogen molecules. Therefore, the enthalpy change \( y \) must account for this energy consumption, making it less than \( x \).

**Conclusion: Determine the Relationship Between \( x \) and \( y \)**
- Since energy is consumed in the second reaction, we can conclude that:
\[ y < x \]
- Therefore, the correct option is:
**(D) \( x > y \)**.