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?

Options

A. 0.1 and 0.4
B. 0.5 and 0.7
C. 0.8 and 0.4
D. 0.1 and 4

Answer

A

Explanation

`2SO_(2) (g)+O_(2) (g) Leftrightarrow 2SO_(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) (therefore V=10"litre")`
Mole of `O_(2)=(1)/(100) xx 10=0.1`
(b) `[SO_(3)]=2[SO_(2)]`
By Eq. (1) `100=(4)/([O_(2)]) or [O_(2)]=(4)/(100)`
Mole of `O_(2)=(4)/(100) xx 10=0.4`