In the mixture of nonreacting ideal gases, the partial pressure of gas, mole fraction of gas, and total pressure of mixture are related as

Options

A. `p_(gas) = (p t o t a l)/(chi_(gas))`
B. `p_(gas) = chi_(gas) p_(t o t a l)`
C. `p_(gas) = p_(t o t a l)chi_(gas)^(2)`
D. `p_(gas) = (chi_(gas))/(p_(t o t al))`

Answer

B

Explanation

Consider a mixture of two nonreacting ideal gases `A` and `B` in a closed container of volume `V` at temperature `T`.
`p_(A)V = n_(A)RT`
`p_(B)V = n_(B)RT`
`p_(t o t a l)V = n_(t o t al)RT`
On dividing `p_(A)` by `p_(t o tal)`, we get
`(p_(A))/(p_(t o tal)) = chi_(A)`
where `chi_(A)` is called the mole fraction of gas `A`.
Thus, `p_(A) = chi_(A) p_(t o tal)`
In general,
`p_(i) = chi_(i)p_(t o tal)`
where `p_(i)` and `chi_(i)` , respectively are partial pressure and mole fraction of the `ith` gas.