Consider the following reaction A2B(g)+1/2B2(g) If P is total pressure at equilibrium & KP is equilibrium constant.

Question

Consider the following reaction

\(A_2 B(g)\rightleftharpoons A_2(g)+\frac{1}{2}B_2(g)\)

If P is total pressure at equilibrium & K_P is equilibrium constant. Then \(\alpha\) in terms of K_P & P is (Assume \(\alpha\) << 1)

(1) \(\sqrt{\frac{K_p}{P}}\)  

(2) \(4\sqrt{\frac{K_p}{P}}\)  

(3) \(\sqrt{\frac{2K_p}{P}}\)  

(4) \(3\sqrt{\frac{2K^2_p}{P}}\)  

Answer 1

Correct option is (4) \(3\sqrt{\frac{2K^2_p}{P}}\)   

\(A_2 B(g)\rightleftharpoons A_2(g)+\frac{1}{2}B_2(g)\) 

t = 0   p₀ 

\(t=t_{eq}\ \ p_0(1-\alpha) \quad p_0\alpha \quad p_0\frac{\alpha}{2}\)  

\(P = p_0+p_0\frac{\alpha}{2}\)  

\(P=p_0(1+\frac{\alpha}{2})(P\approx p_0)\)