Pressure of 1 g of an ideal gas A at `27^(@)C` is found to be 2 bar. When 2 g of another ideal gas B is introduced in the same flask at same temperature, the pressure becomes 3 bar. How much times molar mass of B is that of molar mass of A

Answer

4

Explanation

`pV = nRT`
For a gas, `p _(A) V = n _(A) RT " "...(i)`
Similarly for B gas, `p _(B) V = n _(B) RT ` ...(ii)
Number of moles of A gas, `n _(A) = (1)/( M _(A))`
`( M _(A)=` molar mass of gas A)
Number of moles of B gas, `n _(B) =(2)/( M_(B))`
(`M_(B) =` molar mass of gas B)
Pressure of gas `A, p _(A) = 2 ` bar
Total pressure , `p _("total") = p _(A) + p _(B) = 3 ` bar
Pressure of gas B, `p _(B) = p _("total") - p _(A) = 3-2=1` bar
V, R and T are same for both the gases.
Hence, from Equation (i) and (ii),
`( p _(A))/( p _(B)) = ( n _(A))/( n _(B)) = (1 xx M _(B))/( M _(A) xx 2)`
`( M_(B))/( M _(A)) = ( 2 p _(A))/( p _(B))`
`( M _(B))/( M _(A)) = (2 xx 2)/(1)`
`M _(B) = 4 M _(A)`