Question

The equilibrium constants for the reactions a, b, and c are as given:
a) N$_2$ + 3H$_2$ = 2NH$_3$ : K$_1$
b) N$_2$ + O$_2$ = 2NO : K$_2$
c) 2H$_2$ + O$_2$ = 2H$_2$O : K$_3$
What would be the equilibrium constant for the reaction:
4NH$_3$ + 5O$_2$ = 4NO + 6H$_2$O; K$_x$

• A. K$_x$ = K$_2^2$ K$_3^3$/K$_1^2$
• B. K$_x$ = K$_1$/K$_2$ K$_3$
• C. K$_x$ = 1/K$_1^2$ + K$_2^2$ + K$_3^3$
• D. K$_x$ = K$_1^2$/K$_2$ K$_3$

Hint:

To derive the equilibrium constant for a combined reaction, manipulate the given reactions by multiplying or reversing them, and then combine the equilibrium constants by raising them to the appropriate powers.

Answer 1

The Correct Option is A

The equilibrium constant for a reaction can be calculated by manipulating the equilibrium constants of the given reactions. To determine the equilibrium constant \( K_x \) for the reaction: \[ 4NH_3 + 5O_2 \rightarrow 4NO + 6H_2O, \] we must first combine the given reactions in such a way that we arrive at the desired reaction. Let's proceed step by step: - Reaction (a) gives us the equilibrium constant \( K_1 \) for: \[ N_2 + 3H_2 \rightarrow 2NH_3 \] - Reaction (b) gives us the equilibrium constant \( K_2 \) for: \[ N_2 + O_2 \rightarrow 2NO \] - Reaction (c) gives us the equilibrium constant \( K_3 \) for: \[ 2H_2 + O_2 \rightarrow 2H_2O \] To derive the desired reaction, we can: 1. Multiply Reaction (a) by 2 to get \( 4NH_3 \) on the left side. 2. Multiply Reaction (b) by 2 to get \( 4NO \) on the right side. 3. Multiply Reaction (c) by 3 to get \( 6H_2O \) on the right side. Thus, the equilibrium constant for the new reaction is the product of the equilibrium constants of the individual reactions raised to the appropriate powers: \[ K_x = \frac{K_2^2 \cdot K_3^3}{K_1^2} \]