For an equilibrium reaction, the rate constants for the forward and the backward reaction are `2.38xx10^(-4)` and `8.15xx10^(-5)`, respectively. Calculate the equilibrium constant for the reaction.

Explanation

To solve the problem of calculating the equilibrium constant for the given reaction, we will follow these steps:

### Step-by-Step Solution:

1. **Identify the Rate Constants**:
- The rate constant for the forward reaction (KF) is given as:
\[ K_F = 2.38 \times 10^{-4} \]
- The rate constant for the backward reaction (KB) is given as:
\[ K_B = 8.15 \times 10^{-5} \]

2. **Understand the Relationship**:
- The equilibrium constant (K_eq) for a reaction at equilibrium is defined as the ratio of the rate constant of the forward reaction to the rate constant of the backward reaction:
\[ K_{eq} = \frac{K_F}{K_B} \]

3. **Substitute the Values**:
- Now substitute the values of KF and KB into the equation:
\[ K_{eq} = \frac{2.38 \times 10^{-4}}{8.15 \times 10^{-5}} \]

4. **Perform the Division**:
- First, divide the coefficients:
\[ \frac{2.38}{8.15} \approx 0.292 \]
- Next, handle the powers of ten:
\[ \frac{10^{-4}}{10^{-5}} = 10^{(-4) - (-5)} = 10^{1} = 10 \]

5. **Combine the Results**:
- Now, multiply the results from the coefficient division and the power of ten:
\[ K_{eq} \approx 0.292 \times 10 = 2.92 \]

6. **Final Result**:
- Therefore, the equilibrium constant for the reaction is:
\[ K_{eq} \approx 2.92 \]

### Summary:
The equilibrium constant for the reaction is approximately **2.92**.

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