A mixture of `SO_(3), SO_(2)` and `O_(2)` gases is maintained in a `10 L` flask at a temperature at which the equilibrium constant for the reaction is `100`:
`2SO_(2)(g)+O_(2)(g)hArr2SO_(3)(g)`
a. If the number of moles of `SO_(2)` and `SO_(3)` in the flask are equal. How many moles of `O_(2)` are present?
b. If the number of moles of `SO_(3)` in flask is twice the number of moles of `SO_(2)`, how many moles of oxygen are present?

Explanation

`2SO_(2(g))+O_(2(g))hArr2SO_(3(g))`
`K_(c)=100=([SO_(3)]^(2))/(([SO_(2)]^(2)[O_(2)])` ….(`1`)
(`a`) `:' [SO_(3)]=[SO_(2)]`
By eq. (`1`), `100=(1)/([O_(2)])`
or `[O_(2)]=(1)/(100)`
or `("Mole of" O_(2))/(Volume)=(1)/(100)` (`:' V=10litre`)
`:. "Mole of" O_(2)=(1)/(100)xx10=0.1 "mole"`
(`b`) `[SO_(3)]=2[SO_(2)]`
By eq. (`1`), `100=(4)/([O_(2)])`
or `[O_(2)]=(4)/(100)`
`:. "Mole of "O_(2)=(4)/(100)xx10=0.4 "mole"`