Ideal gas law: changing gas state

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One of the most common uses of the ideal gas law is to compute how a property of a gas will change when another is altered.

For example, What will happen to the volume of a one mole sample of gas at 25.0⁰C and 1.00 atm pressure if we cool it to 0.00 ⁰C? The gas starts with a volume of 24.5 L: you can compute this from the ideal gas law:

PV = nRT

1.00 atm*V = 1.00 mol*0.0821(L*atm/mol*K)*298 K

V = 24.5 L

If we cool the gas to 0.00 ⁰C at constant pressure, we get a different volume

PV = nRT

1.00 atm*V = 1.00 mol*0.0821(L*atm/mol*K)*273 K

V = 22.4 L

Thus, the gas changes volume from 24.5 L to 22.4 L.

Example: If the volume occupied by a 10 gram sample of nitrogen gas at 25^oC and 1.0 atm pressure is 8.8L, what is the volume of the gas sample if the temperature is raised to 100⁰C and the pressure is kept at 1.0 atm?

Solution: We are given P,V,T and the weight of the gas in the initial setup of the problem. 10 grams of nitrogen gas (N₂) is 10 g/(28 g/mole) = 0.36 moles of gas. Now simply use the ideal gas law to compute the volume after raising the temperature

PV = nRT

1.0 atm * V = 0.36 moles * 0.0821 (L*atm)/(mol*K) * 373 K

V = 11 L

The gas expands from a volume of 8.8 L at 25⁰C to 11 L at 100⁰C.

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