In the reaction `AB(g) hArr A(g) + B(g)` at `30^(@)C, k_(p)` for the dissociation equilibrium is `2.56xx10^(-2) atm`. If the total pressure at equilibrium is 1 atm, then the percentage dissociation of AB is

Options

A. 0.87
B. 0.13
C. `43*5 %`
D. 0.06

Explanation

`{:(AB (g),hArr,A(g),+,B (g) ), (1 "mole",,,,), (1-alpha,,alpha,,alpha" Total moles"1+alpha),("If P is total pressure,",,,,):}`
`p_(AB)=(1-alpha)/(1+alpha) P,p_(A)= alpha/(1+alpha)P,p_(B)=alpha/(1+alpha)P`
`K_(p)=(alpha^(2)P)/(1-alpha^(2))=alpha^(2)/(1-alpha)" " ( :'P=1 "atm")cong alpha^(2)`
`alpha = sqrt(K_(p)) = sqrt (2*56 xx 10^(-2))=0.16, i.e., 16 % `