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#
