Pressure Help Please

Question

A sample of gas is held at constant temperature. If the volume of this sample of gas is doubled and the number of moles of this sample of gas is halved, what happens to the pressure of the gas?

Answer 1

From the ideal gas law, PV = nRT we can also write the following relationship...

P1V1 / n1T1 = P2V2 / n2T2

In the present problem, temperature (T) is constant, so we can write

P1V1 / n1 = P2V2 / n2

If the original volume (V1) is 1 L and the original pressure (P1) is 1 atm, and the number of moles (n1) is 1, what happens to the pressure (P2) when the moles (n2) is halved and the volume (V2) is doubled?

(1 atm)(1 L) / 1 mol = (P2)(2 L) / 0.5

1 = 4P2

P2 = 1/4

So, the pressure will be 1/4 the original pressure

Or, you could use the Ideal Gas Law (twice) and see the effect that way:

PV = nRT

(P)(1 L) = 1 mol (298K)

P = 298 atm

PV = nRT

(P)(2 L) = 0.5 mol (298)

P = 74.5 atm

Again, the P in the second case is 1/4 that in the first case.