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^(6)`
B. `K_(2)=10^(-4)`
C. `K_(3)=10`
D. `K_(4)=1`

Explanation

To determine which reaction will take the maximum time to attain equilibrium based on the given equilibrium constants, we can follow these steps:

### Step 1: Understand the relationship between equilibrium constant (K) and time to reach equilibrium
The equilibrium constant (K) is a measure of the extent of a reaction at equilibrium. A larger K value indicates that the products are favored at equilibrium, while a smaller K value suggests that reactants are favored.

### Step 2: Analyze the given equilibrium constants
We have the following equilibrium constants for the reactions:
- \( K_1 = 10^6 \)
- \( K_2 = 10^{-4} \)
- \( K_3 = 10 \)
- \( K_4 = 1 \)

### Step 3: Determine the relationship between K and time
It is important to note that the time taken to reach equilibrium is inversely proportional to the value of the equilibrium constant (K). This means:
- A **larger K** value corresponds to a **shorter time** to reach equilibrium.
- A **smaller K** value corresponds to a **longer time** to reach equilibrium.

### Step 4: Identify the smallest K value
From the given values:
- \( K_1 = 10^6 \) (large)
- \( K_2 = 10^{-4} \) (smallest)
- \( K_3 = 10 \) (moderate)
- \( K_4 = 1 \) (moderate)

The smallest value is \( K_2 = 10^{-4} \).

### Step 5: Conclusion
Since \( K_2 \) is the smallest equilibrium constant, the reaction corresponding to \( K_2 \) will take the maximum time to reach equilibrium.

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

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