For the dissociation reaction `N_(2)O_($) (g)hArr 2NO_(2)(g)`, the degree of dissociation `(alpha)`interms of `K_(p)` and total equilibrium pressure P is:

Explanation

`{:(N_2O_4(g)hArr,2NO_2(g)),(1,0),((1-alpha),2alpha):}`
`K_p=((n_(NO_2))^2/(n_(N_2O_4)))[P/(sumn)]^(Deltan_(g))`
`=((2alpha)^2/((1-alpha)))[P/((1-alpha+2alpha))]^((2-1))`
`=(4alpha^2)/((1-alpha))xx(P/((1+alpha)))^1=(4alpha^2)/((1-alpha^2))xxP`
`rArr(4P)/(K_p)=((1-alpha^2))/(alpha^2)=1/(alpha^2)-1`
`rArr 1/(alpha^2)=(1+(4P)/(K_p))=(4P+K_p)/(K_p)`
`rArr alpha^2=(K_p)/(4P+K_p)`
`alpha=sqrt((K_p)/(4P+K_p))`