Equilibrium constants for four different reaction are given as `K_(1)=10^(6), K_(2)=10^(-4), K_(3)=10`, and `K_(4)=1`. Which reaction will take maximum time to attain equilibrium?

Options

A. `K_(1)=10^(2)`
B. `K_(2)=10^(-4)`
C. `K_(3)=10`
D. `K_(4)=20`

Explanation

To determine which reaction will take the maximum time to attain equilibrium, we need to analyze the equilibrium constants (K) given for the four reactions. The relationship between the equilibrium constant and the time taken to reach equilibrium is inversely proportional. This means that a smaller equilibrium constant indicates a slower reaction and thus a longer time to reach equilibrium.

### Step-by-Step Solution:

1. **Identify the Given Equilibrium Constants:**
- \( K_1 = 10^6 \)
- \( K_2 = 10^{-4} \)
- \( K_3 = 10^1 \)
- \( K_4 = 1 \)

2. **Determine the Minimum Equilibrium Constant:**
- Among the given values, we need to find the smallest equilibrium constant since a smaller \( K \) indicates a reaction that favors reactants over products at equilibrium, thus taking longer to reach equilibrium.
- Comparing the values:
- \( K_1 = 10^6 \) (large)
- \( K_2 = 10^{-4} \) (smallest)
- \( K_3 = 10^1 \) (moderate)
- \( K_4 = 1 \) (intermediate)

3. **Identify the Reaction with the Minimum Equilibrium Constant:**
- The smallest equilibrium constant is \( K_2 = 10^{-4} \).

4. **Conclusion:**
- Therefore, the reaction corresponding to \( K_2 \) will take the maximum time to attain equilibrium.

### Final Answer:
The reaction with the equilibrium constant \( K_2 = 10^{-4} \) will take the maximum time to attain equilibrium.

---