One mole of an ideal gas occupies the volume V1, has a temperature T1 and a pressure P1.

One mole of an ideal gas occupies the volume V1, has a temperature T1 and a pressure P1. What is the volume of this gas, taken in an amount of 4 mol, at the same temperature and pressure 2P1.

1. We use the equation of state of an ideal gas (it is also called the Clapeyron-Mendeleev equation):

PV = nRT.

2. We have P1V1 = ν1RT1.
P2V2 = ν2RT2.

We get V2 / V1 = ν2 / 2ν1 = 4/2 * 1 = 2.
V2 = 2 V1.

We have: ν2 = 4 mol. ν1 – 1 mol.

P2 = 2P1.
T1 = T 2.

Answer: the volume of this gas taken in an amount of 4 mol is 2 times larger, at the same temperature and pressure 2P1.