Question

Consider the reaction: P(s) + 5/2 Cl2(g)PCl5(g) Write the equilibrium constant for this reaction in terms of the equilibrium constants, Ka and Kb, for reactions a and b below: a.) P(s) + 3/2 Cl2(g) PCl3(g) Ka b.) PCl3(g) + Cl2(g) PCl5(g) Kb

Answer 1

Answer: The equilibrium constant for the overall reaction is $K_a\times K_b$

Explanation:

Equilibrium constant is defined as the ratio of concentration of products to the concentration of reactants each raised to the power their stoichiometric ratios.

a) $P(s)+\frac{3}{2}Cl_2(g)\rightarrow PCl_3(g)$

$K_a=\frac{[PCl_3]}{[Cl_2]^{\frac{3}{2}}}$

b) $PCl_3(g)+Cl_2(g)\rightarrow PCl_5(g)$

$K_b=\frac{[PCl_5]}{[Cl_2]\times [PCl_3]}$

For overall reaction on adding a and b we get c

c) $P(s)+\frac{5}{2}Cl_2(g)\rightarrow PCl_5(g)$

$K_c=\frac{[PCl_5]}{[Cl_2]^\frac{5}{2}}$

$K_c=K_a\times K_b=\frac{[PCl_3]}{[Cl_2]^{\frac{3}{2}}}\times \frac{[PCl_5]}{[Cl_2]\times [PCl_3]}$

The equilibrium constant for the overall reaction is $K_a\times K_b$