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^(-2)` atm, P= 1 atm
For the given equilibrium, `K_(p) = (alpha^(2)P)/(1-alpha^(2))` or `2.9 xx 10^(-2)` atm `= (alpha^(2) xx "1 atm")/(1- alpha^(2))`
Sicne `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 giving `K_(p) = alpha^(2)P`.