At `500K, K_(p)` value for the reaction
`2SO_(2)(g)+O_(2)(g)hArr2SO_(3)(g)` is `2.5xx10^(10)`.
Find the value of `K_(p)` for each of followign reactions at the same temperature.
a. `SO_(2)(g)+1//2O_(2)(g)hArrSO_(3)(g)`
b. `SO_(3)(g)hArrSO_(2)(g)+1//2O_(2)(g)`
c. `3SO_(2)(g)+3//2O_(2)(g)hArr3SO_(3)(g)`

Explanation

1. `2SO_(2)(g)+O_(2)(g)hArr2SO_(3)(g)`
`K_(p)` for the above reaction is `2.5xx10^(10)`
a. `SO_(2)+1/2O_(2)hArrSO_(3)`
The `K_(p)` for this reaction is `sqrt(K_(p))` of the reaction 1
`K_(p)=sqrt(2.5xx10^(10))=1.58xx10^(5)`
b. `SO_(3)(g)hArrSO_(2)(g)+1/2O_(2)(g)`
For this reaction the `K_(p)` is either `1/(sqrt(K_(p)))`
of the reaction 1 or `1/(K_(p))` of the reaction (2).
`K_(p)=1/(sqrt(2.5xx10^(10))` or `1/(1.58xx10^(5))`
`=6.33xx10^(-6)`
c. `3SO_(2)(g)+3/2O_(2)(g)to3SO_(3)`
This reaction is obtained by multiplying the equatio a. with three or by multiplying the equation 1 with 1.5.
So `K_(p)` for this reaction `(K_(p))^(3)` of equaltion (a) `K_(p)=(1.58xx10^(5))^(3)=3.944xx10^(15)`