Question

X ⇌ Y;K₁ = 1
Y ⇌ Z; K₂ = 2
Z ⇌ W; K₃ = 4
Find K_eq for X ⇌ W

• A. 12
• B. 8
• C. 2
• D. 4

Answer 1

The Correct Option is B

To find the equilibrium constant \( K_{\text{eq}} \) for the reaction \( X \leftrightarrow W \), we need to use the relationship between the given reactions and their equilibrium constants. The given reactions and their equilibrium constants are:

1. \( X \leftrightarrow Y \) with \( K_1 = 1 \)
2. \( Y \leftrightarrow Z \) with \( K_2 = 2 \)
3. \( Z \leftrightarrow W \) with \( K_3 = 4 \)

The overall reaction for \( X \leftrightarrow W \) can be obtained by summing up the individual reactions:

1. X \leftrightarrow Y
2. Y \leftrightarrow Z
3. Z \leftrightarrow W

When combining these reactions, intermediate species (\( Y \) and \( Z \)) will cancel out, yielding:

1. X \leftrightarrow W

The equilibrium constant for the overall reaction is the product of the individual equilibrium constants:

K_{\text{eq}} = K_1 \times K_2 \times K_3

Substituting the given values:

K_{\text{eq}} = 1 \times 2 \times 4 = 8

Therefore, the equilibrium constant for the reaction \( X \leftrightarrow W \) is 8.

Thus, the correct answer is 8.