At `30^(@)C, K_(p)` for the dissociation reaction :
`SO_(2)Cl_(2)(g) hArr SO_(2)(g)+Cl_(2)(g)`
is `2.9xx10^(-2)` atm. If the total pressure is 1 atm, the degree of dissociation of `SO_(2)Cl_(2)` is : (assume `1-alpha^(2)=1`).

Options

A. `87%`
B. `13%`
C. `17%`
D. `29%`

Answer

C

Explanation

`SO_(2)Cl_(2)hArr SO_(2)+Cl_(2)`
If degree of dissociation is `alpha`
`1-alpha " " alpha " " alpha`
Total no. of moles `=1-alpha+alpha+alpha=1+alpha`
`pSO_(2)=(alpha P)/(1+alpha)=(alpha)/(1+alpha)`
`pCl_(2)=(alpha P)/(1+alpha)=(alpha)/(1+alpha)`
`pSO_(2)Cl_(2)=(1-alpha)/(1+alpha)P=(1-alpha)/(1+alpha)`
`K_(p)=((pSO_(2))xx(pCl_(2)))/(p(SO_(2)Cl_(2)))`
`=(((alpha)/(1+alpha))((alpha)/(1+alpha)))/((1-alpha)/(1+alpha))`
`K_(p)=(alpha^(2))/(1-alpha^(2))=alpha^(2)`
`therefore alpha^(2)=K_(p)=2.9xx10^(-2)`
`= sqrt(2.9xx10^(-12))=0.17=17%`