20). The equilibrium constant, Ke, for the decomposition of COBR2 is 0.190. COBr2(g) =* CO(g) + Br2(g) K, = 0.19 What is K2 for the following reaction? 2C0(g) + 2B12(g) * 2COBr2(g) a. 0.0361 b. 2.63 c. 5.62 d. 27.7 е. 10.5

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**Equilibrium Constant Calculation**

**Problem 20:**
Given the equilibrium constant, \( K_c \), for the decomposition of COBr\(_2\) is 0.190.

\[ \text{COBr}_2(g) \rightleftharpoons \text{CO}(g) + \text{Br}_2(g) \quad \text{with} \quad K_1 = 0.19 \]

Determine \( K_2 \) for the reaction:
\[ 2\text{CO}(g) + 2\text{Br}_2(g) \rightleftharpoons 2\text{COBr}_2(g) \]

**Multiple Choices:**
a. 0.0361  
b. 2.63  
c. 5.62  
d. 27.7  
e. 10.5

To solve for \( K_2 \), it is essential to understand the relationship between the equilibrium constants of these reactions. The given reaction is the reverse of the balanced decomposition reaction, but multiplied by 2.

\[ K_1 = 0.19 \]
For the reversed reaction, \( K_{reverse} = \frac{1}{K_1} \)
Since the reaction is doubled, we raise \( K_{reverse} \) to the power of 2:
\[ K_2 = \left(\frac{1}{K_1}\right)^2 \]

\[ K_2 = \left(\frac{1}{0.19}\right)^2 = \left(5.263\right)^2 = 27.7 \]

Therefore, the correct answer is:  
d. 27.7
Transcribed Image Text:**Equilibrium Constant Calculation** **Problem 20:** Given the equilibrium constant, \( K_c \), for the decomposition of COBr\(_2\) is 0.190. \[ \text{COBr}_2(g) \rightleftharpoons \text{CO}(g) + \text{Br}_2(g) \quad \text{with} \quad K_1 = 0.19 \] Determine \( K_2 \) for the reaction: \[ 2\text{CO}(g) + 2\text{Br}_2(g) \rightleftharpoons 2\text{COBr}_2(g) \] **Multiple Choices:** a. 0.0361 b. 2.63 c. 5.62 d. 27.7 e. 10.5 To solve for \( K_2 \), it is essential to understand the relationship between the equilibrium constants of these reactions. The given reaction is the reverse of the balanced decomposition reaction, but multiplied by 2. \[ K_1 = 0.19 \] For the reversed reaction, \( K_{reverse} = \frac{1}{K_1} \) Since the reaction is doubled, we raise \( K_{reverse} \) to the power of 2: \[ K_2 = \left(\frac{1}{K_1}\right)^2 \] \[ K_2 = \left(\frac{1}{0.19}\right)^2 = \left(5.263\right)^2 = 27.7 \] Therefore, the correct answer is: d. 27.7
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