`DeltaG^(ɵ)` for the reaction `X+YhArrC` is `-4.606 kcal` at `1000 K`. The equilibrium constant for the reverse mode of the reaction will be:

Options

A. `100`
B. `10`
C. `0.01`
D. `0.1`

Explanation

To find the equilibrium constant for the reverse reaction given the standard Gibbs free energy change (ΔG°) for the forward reaction, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Relationship Between ΔG° and K**:
The relationship between the standard Gibbs free energy change (ΔG°) and the equilibrium constant (K) is given by the equation:
\[ \Delta G° = -RT \ln K \]
where R is the universal gas constant and T is the temperature in Kelvin.

2. **Convert ΔG° to Appropriate Units**:
The given ΔG° is -4.606 kcal. Since we will use R in calories, we need to convert kcal to calories:
\[ -4.606 \text{ kcal} = -4606 \text{ cal} \]

3. **Use the Value of R**:
The value of R in calories is approximately 2 cal/(K·mol).

4. **Plug in the Values**:
At T = 1000 K, we can substitute the values into the equation:
\[ -4606 = -2 \times 1000 \ln K \]

5. **Simplify the Equation**:
Rearranging the equation gives:
\[ 4606 = 2000 \ln K \]

6. **Solve for ln K**:
Dividing both sides by 2000:
\[ \ln K = \frac{4606}{2000} = 2.303 \]

7. **Convert ln K to K**:
To find K, we exponentiate both sides:
\[ K = e^{2.303} \approx 10 \]

8. **Determine the Equilibrium Constant for the Reverse Reaction**:
For the reverse reaction, the equilibrium constant (K') is the reciprocal of K:
\[ K' = \frac{1}{K} = \frac{1}{10} = 0.1 \]

### Final Answer:
The equilibrium constant for the reverse reaction is **0.1**.