Answer: The equilibrium constant for the overall reaction is [tex]K_a\times K_b[/tex]
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) [tex]P(s)+\frac{3}{2}Cl_2(g)\rightarrow PCl_3(g)[/tex]
[tex]K_a=\frac{[PCl_3]}{[Cl_2]^{\frac{3}{2}}}[/tex]
b) [tex]PCl_3(g)+Cl_2(g)\rightarrow PCl_5(g)[/tex]
[tex]K_b=\frac{[PCl_5]}{[Cl_2]\times [PCl_3]}[/tex]
For overall reaction on adding a and b we get c
c) [tex]P(s)+\frac{5}{2}Cl_2(g)\rightarrow PCl_5(g)[/tex]
[tex]K_c=\frac{[PCl_5]}{[Cl_2]^\frac{5}{2}}[/tex]
[tex]K_c=K_a\times K_b=\frac{[PCl_3]}{[Cl_2]^{\frac{3}{2}}}\times \frac{[PCl_5]}{[Cl_2]\times [PCl_3]}[/tex]
The equilibrium constant for the overall reaction is [tex]K_a\times K_b[/tex]
