Two reactions and their equilibrium constants are given. A+2B 2C K = 2.81 2C D K2 5 = 0.248 Calculate the value of the equilibrium constant for the reaction D=A+2B. K =

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The image presents two chemical reactions with their respective equilibrium constants:

1. \( \text{A} + 2\text{B} \rightleftharpoons 2\text{C} \) with equilibrium constant \( K_1 = 2.81 \).
2. \( 2\text{C} \rightleftharpoons \text{D} \) with equilibrium constant \( K_2 = 0.248 \).

The task is to calculate the value of the equilibrium constant for the reverse reaction:

\[ \text{D} \rightleftharpoons \text{A} + 2\text{B} \]

The result of the calculation should be entered in the provided space labeled:
\[ K = \] 

**Explanation for Calculation:**

To find the equilibrium constant for the reverse reaction \( \text{D} \rightleftharpoons \text{A} + 2\text{B} \), the following relationship is used:

\[ K_{\text{reverse}} = \frac{1}{K_{\text{forward}}} \]

Thus, we first need to determine \( K_{\text{forward}} \) for the reaction \( \text{D} \rightleftharpoons \text{A} + 2\text{B} \), which can be found by combining the given reactions.

1. Reverse the second reaction to get \( \text{C} \rightleftharpoons \frac{1}{2}\text{D} \), where the equilibrium constant becomes \( \frac{1}{K_2} = \frac{1}{0.248} \).

2. The overall reaction is obtained by combining these adjusted reactions to yield \( \text{D} \rightleftharpoons \text{A} + 2\text{B} \).

3. The equilibrium constant for the overall reaction is calculated by multiplying the modified constants \( K_1 \) and \( \frac{1}{K_2} \).

Finally, take the reciprocal of this equilibrium constant to find \( K \) for the reverse reaction.
Transcribed Image Text:The image presents two chemical reactions with their respective equilibrium constants: 1. \( \text{A} + 2\text{B} \rightleftharpoons 2\text{C} \) with equilibrium constant \( K_1 = 2.81 \). 2. \( 2\text{C} \rightleftharpoons \text{D} \) with equilibrium constant \( K_2 = 0.248 \). The task is to calculate the value of the equilibrium constant for the reverse reaction: \[ \text{D} \rightleftharpoons \text{A} + 2\text{B} \] The result of the calculation should be entered in the provided space labeled: \[ K = \] **Explanation for Calculation:** To find the equilibrium constant for the reverse reaction \( \text{D} \rightleftharpoons \text{A} + 2\text{B} \), the following relationship is used: \[ K_{\text{reverse}} = \frac{1}{K_{\text{forward}}} \] Thus, we first need to determine \( K_{\text{forward}} \) for the reaction \( \text{D} \rightleftharpoons \text{A} + 2\text{B} \), which can be found by combining the given reactions. 1. Reverse the second reaction to get \( \text{C} \rightleftharpoons \frac{1}{2}\text{D} \), where the equilibrium constant becomes \( \frac{1}{K_2} = \frac{1}{0.248} \). 2. The overall reaction is obtained by combining these adjusted reactions to yield \( \text{D} \rightleftharpoons \text{A} + 2\text{B} \). 3. The equilibrium constant for the overall reaction is calculated by multiplying the modified constants \( K_1 \) and \( \frac{1}{K_2} \). Finally, take the reciprocal of this equilibrium constant to find \( K \) for the reverse reaction.
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