Ideal gas law – problems and solutions

1. Ideal gases in a closed container initially have volume V and temperature T. The final temperature is 5/4T and the final pressure is 2P. What is the final volume of the gas?

Known :

Initial volume (V1) = V

Initial temperature (T1) = T

Final temperature (T2) = 5/4 T

Initial pressure (P1) = P

Final pressure (P2) = 2P

Wanted: Final volume (V2)

Solution :

Ideal gas law - problems and solutions 1

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2. Determine the volume of 2.00 moles of gases (ideal gas) at STP. STP = Standard Temperature and Pressure.

Known :

Moles of gas (n) = 2 moles

Standard temperature (T) = 0 oC = 0 + 273 = 273 Kelvin

Standard pressure (P) = 1 atm = 1.013 x 105 Pa

Universal gas constant (R) = 8.315 Joule/mole.Kelvin

Wanted : Volume of gases (V)

Solution :

Equation of Ideal gas law (in the number of moles, n)

Ideal gas law - problems and solutions 2

Volume 2 moles of gases is 44.8 liters.

Volume 1 mol of gases is 45.4 liters / 2 = 22.4 liters.

Volume 1 mol of any gases is 22.4 liters.

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3. 4 liters of oxygen gas has a temperature of 27°C and pressure of 2 atm (1 atm = 105 Pa) in a closed container. Universal gas constant (R) = 8.314 J.mole−1.K−1 and Avogadro’s number (NA) = 6.02 x 1023 molecules/mole. What are the molecules of oxygen gases in the container?

Known :

Volume of gases (V) = 4 liters = 4 dm3 = 4 x 10-3 m3

Temperature of gases (T) = 27oC = 27 + 273 = 300 Kelvin

Pressure of gases (P) = 2 atm = 2 x 105 Pa

Universal gas constant (R) = 8.314 J.mole−1.K−1

Avogadro’s number (NA) = 6.02 x 1023

Wanted : What is the molecules of oxygen gases in the container (N)

Solution :

Ideal gas law - problems and solutions 3

In 1 mole oxygen gases, there are 1.93 x 1023 oxygen molecules.

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4. A container containing a neon gas (Ne, atomic mass = 20 u) at standard temperature and pressure (STP) has a volume of 2 m3. Determine the mass of the neon gas!

Known :

Atomic mass of neon = 20 gram/mole = 0,02 kg/mole

Standard temperature (T) = 0oC = 273 Kelvin

Standard pressure (P) = 1 atm = 1.013 x 105 Pascal

Volume (V) = 2 m3

Wanted : mass (m) of neon gas

Solution :

At standard temperature and pressure (STP), 1 mole of any gases, include neon gas, have volume 22.4 liters = 22.4 dm3 = 0.0448 m3.

Ideal gas law - problems and solutions 4

In the volume of 2 m3there are 44.6 moles of neon gas.

Relative atomic mass of neon gas is 20 gram/mole.

This means that in 1 mole there are 20 grams or 0.02 kg of neon gas. Because in 1 mol there are 0.02 kg of neon gas then in 44.6 mole there are 44.6 moles x 0.02 kg/mole = 0.892 kg = 892 gram of neon gases.