The degree of dissociation of `SO_(2)` is `alpha` at equilibrium pressure `P_(0)`.
`K_(P)"for"2SO_(3)(g)hArr2SO_(2)(g)+O_(2)(g)`is

Options

A. `[(P_(0)alpha^(3))//2(1-alpha)^(3)]`
B. `[(P_(0)alpha^(2))//(2+alpha)(1-alpha)^(2)]`
C. `[(P_(0)alpha^(2))//2(1-alpha)^(2)]`
D. None of these

Answer

B

Explanation

`2SO_(3)(g)hArr 2SO_(2)(g)+O_(2)(g)`
`{:(t=0,a,0,0),(t=t_(eq),a(1-alpha),aalpha,a((alpha)/(2))):}`
Total mole at eq.=`a(1+(alpha)/(2))`
`P_(SO_(3)=((1-alpha)/(2+alpha))P_(0)=[(2(1-alpha))/(2+alpha)]xxP_(0): P_(SO_(2))=((alpha)/(1+(alpha//2)))P_(0)=((2alpha)/(2+alpha))xxP_(0)`
`PO_(2)=((alpha//2)/(1+(alpha//2)))P_(0)`
`K_(P)=((4alpha^(2)(P^(@))^(2))/((2+alpha)^(2))xx((alpha)/(2+alpha))xxP^(@))/((4(1-alpha)^(2))/([2+alpha]^(2)).xx(P_(0))^(2))=[(alpha^(3)P^(@))/((2+alpha)(1-alpha)^(2))]`