A vessel of volume V contains a mixture of ideal gases at temperature T. The gas mixture contains `n _(1), n _(2) and n _(3)` moles of three gases. Assuming ideal gas system, the pressure of the mixture is

Options

A. `((n _(1) + n _(2) + n _(3)) RT)/(V)`
B. `((n _(1) n_(2)n _(3))RT)/(V)`
C. `(RT)/((n_(1) + n_(2) + n_(3))V)`
D. `(RT)/(V( n _(1) n _(2) n_(3)))`

Answer

A

Explanation

By Dalton's law of partial pressure, pressure of mixture of three gses,
`p= p _(1) + p_(2) + p_(3)`
According ot the ideal gas equation,
`pV= nRT`
`P = ( nRT)/(V)`
Temperature T and volume V are same for all three gases, but number of moles are different, i.e.
`n _(1) , n _(2) and n _(3).`
So, `p = (n _(1) RT)/(V) + (n _(2) RT)/(V) + (n_(3) RT)/(V)`
`p = ((n _(1) + n _(2) + n _(3))RT)/(V)`