At constant temperature, in a closed vessel the following equilibrium establishes during decomposition of `NH_(4)Cl(s):NH_(4)Cl(s)to NH_(3)(g) +HCl (g)`. If pressure of the equilibrium mixture=P and value of equilibrium constant`=K_(p)`, then show that `P=2sqrt(K_(p))`.

Explanation

`{:(,NH_(4)Cl(s),hArr,NH_(3)(g),+,HCl(g)),("Initial no. of moles:",1,,0,,0),("Change in no. of moles:",-x,,+x,,+x),("No. of moles at equilibrium:",(1-x),,x,,x):}`
`therefore`Total number of moles at equilibrium=x+x=2x
`therefore p_(NH_(3))=((x)/(2x))p,p_(HC l)=((x)/(2x))P`
`therefore K_(p)=p_(NH_(3))xxp_(HC l)=((x)/(2x))Pxx((x)/(2x))P=(P^(2))/(4)`
`therefore K_(p)=(P^(2))/(4) or, P^(2)=4K_(p)" "therefore P=2sqrt(K_(p))`.