The equation of the gaseuos decomposition raction of PCl_5 with ICE table
PCl_5(g)" "rightleftharpoons" "PCl_3(g)" "+" "Cl_2(g)
I" "1" "mol" "0" "mol" "0" "mol
C" "alpha" "mol" "alpha" "mol" "alpha" "mol
E" "1-alpha" "mol" "alpha" "mol" "alpha" "mol
color(red)("where "alpha" degree of dissociation"=10%=0.1
Total no. of moles in the reaction mixture at equilibrium is given by
n=1-alpha+alpha+alpha=1+alpha
Mole fractions of the components at equilibrium
chi_(PCl_5)=(1-alpha)/(1+alpha)
chi_(PCl_3)=alpha/(1+alpha)
chi_(Cl_2)=alpha/(1+alpha)
If atequilibrium the total pressure of the reaction mixture is P then the partial pressures of the components in the mixture will be
p_(PCl_5)=((1-alpha)P)/(1+alpha)
p_(PCl_3)=(alphaP)/(1+alpha)
p_(Cl_2)=(alphaP)/(1+alpha)
"The equilibrium constant in respect of preesure"
K_p=(p_(PCl_3)xxp_(Cl_2))/p_(PCl_5)
Substituting respective values
K_p= ((alphaP)/(1+alpha))^2 / ((( 1- alpha)P)/(1+alpha))
=(alpha^2P)/(1-alpha^2)
Now it is given alpha=0.1 and P=5" atm"
So
K_p=((0.1)^2*5)/(1-(0.1)^2)~~0.05atm
