Question

The value of \( K_c \) for the reaction: \[ A + 3B \rightleftharpoons 2C \text{ at } 400^\circ C \text{ is } 0.5. \text{ Calculate the value of } K_p. \]

• A. \( 1.64 \times 10^{-4} \)
• B. \( 1.64 \times 10^{-6} \)
• C. \( 1.64 \times 10^{-5} \)
• D. \( 1.64 \times 10^{-3} \)

Hint:

The relationship between \( K_p \) and \( K_c \) helps convert between the equilibrium constants when dealing with gases.

Answer 1

The Correct Option is B

We can use the relationship between \( K_p \) and \( K_c \) for ideal gases: \[ K_p = K_c \left( RT \right)^{\Delta n} \] where \( \Delta n \) is the change in the number of moles of gas, \( R = 0.0821 \, \text{L·atm/mol·K} \), and \( T = 400 + 273 = 673 \, \text{K} \). After calculating \( \Delta n \), we find that the value of \( K_p \) is \( 1.64 \times 10^{-6} \).
Final Answer: \[ \boxed{1.64 \times 10^{-6}} \]