For the chemical reaction X Y , the standard reaction Gibbs energy depends on temperature T (in K) as `Delta_rG^0` ( in kJ `mol^(-1)` ) = `120-3/8`T . The major component of the reaction mixture at T is

Options

A. X if T=315 K
B. Y if T =300 K
C. Y if T =280 K
D. X if T =350 K

Explanation

To solve the problem, we need to analyze the given equation for the standard reaction Gibbs energy and determine the major component of the reaction mixture at a specified temperature.

### Step-by-Step Solution:

1. **Understand the Gibbs Energy Equation**:
The standard reaction Gibbs energy is given by:
\[ \Delta_r G^0 = 120 - \frac{3}{8}T \]
where \( T \) is the temperature in Kelvin.

2. **Determine the Equilibrium Condition**:
At equilibrium, the Gibbs free energy change (\( \Delta G \)) is zero. Therefore, we set the equation to zero to find the equilibrium temperature:
\[ 0 = 120 - \frac{3}{8}T \]

3. **Solve for Temperature**:
Rearranging the equation to solve for \( T \):
\[ \frac{3}{8}T = 120 \]
\[ T = 120 \times \frac{8}{3} = 320 \text{ K} \]

4. **Analyze the Reaction Direction**:
- If \( T < 320 \) K, then \( \Delta_r G^0 > 0 \) (the reaction is non-spontaneous in the forward direction), and the major component will be \( X \).
- If \( T > 320 \) K, then \( \Delta_r G^0 < 0 \) (the reaction is spontaneous in the forward direction), and the major component will be \( Y \).

5. **Evaluate the Given Temperature**:
- If we consider \( T = 315 \) K (which is less than 320 K), according to our analysis, \( X \) will be the major component.
- If we consider \( T = 300 \) K (also less than 320 K), \( X \) remains the major component.
- If we consider \( T = 325 \) K (which is greater than 320 K), \( Y \) will be the major component.

6. **Conclusion**:
Based on the analysis, if the temperature is less than 320 K, \( X \) is the major component. If the temperature is greater than 320 K, \( Y \) is the major component.

### Final Answer:
The major component of the reaction mixture at \( T = 315 \) K is \( X \).