Containers `A` and `B` have same, gases. Pressure, volume and temperature of `A` are all twice that of `B`, then the ratio of number of molecules of `A` and `B` are

Options

A. `1 : 2`
B. `2 : 1`
C. `1 : 4`
D. `4 : 1`

Answer

B

Explanation

Applying the ideal gas equation , we have for container `A`,
`p_(A)V_(A) = n_(A)RT_(A)`
For container `B , p_(B)V_(B) = n_(B)RT_(B)`
Dividing the two , we get
`(p_(A)V_(A))/(p_(B)V_(B)) = (n_(A)RT_(A))/(n_(B)RT_(B))`
Since `p_(A) = 2p_(B) , V_(A) = 2 V_(B)` , and `T_(A) = 2 T_(B)` , we have
`((2p_(B))(2V_(B)))/(p_(B)V_(B)) = (n_(A))/(n_(B)) = ((2T_(B)))/((T_(B)))`
` 4 = (n_(A))/(n_(B)) = 2`
or `(n_(A))/(n_(B)) = (4)/(2) = (2)/(1)`