Question

For the given hypothetical reactions, the equilibrium constants are as follows:
\[ X \rightleftharpoons Y; \, K_1 = 1.0 \]
\[ Y \rightleftharpoons Z; \, K_2 = 2.0 \]
\[ Z \rightleftharpoons W; \, K_3 = 4.0 \]
The equilibrium constant for the reaction
\[ X \rightleftharpoons W\]
is:

• A. 6.0
• B. 12.0
• C. 8.0
• D. 7.0

Answer 1

The Correct Option is C

The equilibrium constant for the overall reaction \( X \rightleftharpoons W \) is determined by combining the three provided reactions and their equilibrium constants (\( K_1, K_2, \) and \( K_3 \)).

1. The individual reactions and their constants are:
   • \( X \rightleftharpoons Y \) with \( K_1 = 1.0 \)
   • \( Y \rightleftharpoons Z \) with \( K_2 = 2.0 \)
   • \( Z \rightleftharpoons W \) with \( K_3 = 4.0 \)
2. The overall reaction \( X \rightleftharpoons W \) is the sum of these three reactions: \( X \rightleftharpoons Y \), \( Y \rightleftharpoons Z \), and \( Z \rightleftharpoons W \).
3. The equilibrium constant \( K \) for the overall reaction is the product of the individual equilibrium constants: \( K = K_1 \times K_2 \times K_3 \).
4. Substituting the given values yields: \( K = 1.0 \times 2.0 \times 4.0 \).
5. Performing the multiplication gives: \( K = 8.0 \).

Therefore, the equilibrium constant for the reaction \( X \rightleftharpoons W \) is \(8.0\).

Evaluating the provided options:

• 6.0: Incorrect calculation.
• 12.0: Irrelevant to the calculated result.
• 8.0: Correct, derived from \( 1.0 \times 2.0 \times 4.0 \).
• 7.0: Incorrect and irrelevant.

The correct answer is 8.0.