At `3 0 ^(@)C, K _(P)` for the reaction `SO _(2) Cl _(2) (g) hArr SO _(2) (g) + Cl _(2) (g) is 2.9 xx 10 ^(-2)` atm. If the total pressure is 1 atm , calculate the degree of dissociation of `SO _(2) Cl _(2).`

Explanation

Given, `K _(P) = 2. 9 xx 10 ^(-1) atm , P = 1 atm`
For the given equilibrium, `K _(P) = ( alpha ^(2) P )/(1 - alpha ^(2) )or 2.9 xx10^(-2)atm =(alpha ^(2)xx 1 atm)/(1-alpha ^(2))`
Since `K _(P)` in this case is very small,` alpha ` would also be very small so that `alpha ^(2) lt lt 1` and can be neglected in the denominator given `K _(P) = alpha ^(2) P.`
Therefore , degree of dissociation at `P =1 atm, alpha = sqrt (K _(P)) = sqrt (2. 9 xx 10 ^(-2)) = 0. 17`