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 calculate the equilibrium constant for the reaction, we will follow these steps:

### Step 1: Identify the rate constants
We are given the rate constants for the forward and backward reactions:
- Rate constant for the forward reaction, \( k_f = 2.38 \times 10^{-4} \)
- Rate constant for the backward reaction, \( k_b = 8.15 \times 10^{-5} \)

### Step 2: Write the formula for the equilibrium constant
The equilibrium constant \( K_{eq} \) is defined as the ratio of the rate constant of the forward reaction to the rate constant of the backward reaction:
\[ K_{eq} = \frac{k_f}{k_b} \]

### Step 3: Substitute the values into the formula
Now we will substitute the values of \( k_f \) and \( k_b \) into the formula:
\[ K_{eq} = \frac{2.38 \times 10^{-4}}{8.15 \times 10^{-5}} \]

### Step 4: Perform the calculation
Now we will perform the division:
\[ K_{eq} = \frac{2.38}{8.15} \times \frac{10^{-4}}{10^{-5}} = \frac{2.38}{8.15} \times 10^{1} \]
Calculating \( \frac{2.38}{8.15} \):
\[ \frac{2.38}{8.15} \approx 0.292 \]
So,
\[ K_{eq} \approx 0.292 \times 10^{1} = 2.92 \]

### Step 5: State the final answer
The equilibrium constant for the reaction is:
\[ K_{eq} \approx 2.92 \]

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