Question

If \(K_p\) for the reaction \(A(g) + 2B(g) \rightleftharpoons 3C(g) + D(g)\) is \(0.05\) atm at \(1000\,K\), its \(K_c\) in terms of \(\frac{x \times 10^{-5}}{R}\). Find \(x\).

Hint:

Always compute \(\Delta n = n_{\text{gaseous products}} - n_{\text{gaseous reactants}}\) carefully before using \(K_p = K_c(RT)^{\Delta n}\).

Answer 1

Correct Answer: 5

Concept: \[ K_p = K_c (RT)^{\Delta n} \]

Step 1:Calculate change in moles: \[ \Delta n = (3 + 1) - (1 + 2) = 4 - 3 = 1 \]

Step 2:Rearrange formula: \[ K_p = K_c (RT)^1 \Rightarrow K_c = \frac{K_p}{RT} \]

Step 3:Substitute values: \[ K_c = \frac{0.05}{R \times 1000} \] \[ K_c = \frac{5 \times 10^{-2}}{10^3 \, R} = \frac{5 \times 10^{-5}}{R} \]

Step 4:Compare with given form \(\frac{x \times 10^{-5}{R}\):} \[ x = 5 \]