Contents for this page | Related topics | |
---|---|---|

1. The generalised gas law 2. Deviations from the gas laws 3. Numerical problems involving the gas laws 3. Using the generalised gas law 4. Additional questions |
The kinetic theory Boyle's law Charles' law Dalton's law of partial pressures |
Data Glossary |

Learning Outcomes | ||

After studying this section, You will understand and be able to apply the generalized gas law pv = nRT, and (b) solve problems involving the gas laws. |

1. The general gas law

For an *IDEAL GAS*, the relationship between pressure, volume and temperature is given by :

where:

**p** is the pressure in pascals

**v** is the volume in m^{3}

**n** is the amount of gas in moles

**T** is the temperature in K

**R** is the *UNIVERSAL GAS CONSTANT*, 8.314 J·K^{-1}·mol^{-1}

Note that the above means that the volume of a given mass of gas will be inversely proportional to its molar mass, since **n = mass/molar mass**.

Derivation of above equation

How do we know the value of the gas constant?

How do we know the dimensions of the gas constant?

Note that the product **pv** has the dimensions of energy. Check that it is so!

2. Deviations from the gas laws

The gas laws apply strictly speaking only to ideal gases, where the gas molecules have a volume which is always negligible in comparison with the gas volume, and where there are no interactions between the molecules.

*THERE IS NO SUCH THING AS AN IDEAL GAS!* Most real gases obey the gas laws reasonably well at moderate pressures and at temperatures which are significantly higher than their liquefaction point, and thus one can use the gas equations in order to give results which are accurate enough for most practical purposes.

Graphs of **pv** against **p** for real gases deviate at high pressures from the behaviour expected from an ideal gas (**line IG** on the graph shown above).

3. Numerical problems involving the gas laws

In order to solve numerical problems which involve gases, one needs to use the gas equation which is applicable to the situation described by the problem.

When the *TEMPERATURE IS KEPT CONSTANT*, Boyle's law can be applied:

If any three of the quantities are known, the fourth one can be calculated.

If the *TEMPERATURE IS NOT CONSTANT*, the situation will be one of the following:

where **T** is temperature in kelvin (K). Remember that **K = ºC + 273.2**

Strictly speaking, these equations only apply to ideal gases . For the purpose of the examples given in this section, the real gases which are involved are assumed to behave ideally.

4. Using the generalised gas law

For an ideal gas, **pv = nRT**, where **v** is the volume occupied by **n** mol of the gas at a pressure **p** and Kelvin temperature **T**. **R** is the *GAS CONSTANT* which has the value of 8.314 J·K^{-1}·mol^{-1}.

(Remember that if you are using this value of R, all the other quantities in the equation must be in S.I. units. Specifically, **p** must be in pascal, Pa, and **v** in m^{3}. *BE ON THE LOOKOUT FOR "TRAPS" SET BY THE EXAMINERS*, notably, pressure given in kPa or atmospheres and/or volumes in cm^{3} or dm^{3}) (That would be rather nasty!)

The general gas equation **pv = nRT** is not only used to calculate the volume occupied by a given amount of gas at some stated temperature and pressure, but it may also enable one to calculate the molar mass **M _{r}** of the gas:

where **m** is the mass (in g) of gas of molar mass **M _{r}** which takes up a volume

Additional questions

Derivation of the General Gas Equation

From Boyle's Law, **pv = k**, where **k** is a constant at constant temperature.

However, both **p** and **v** are directly proportional to the Kelvin temperature **T**. Thus, **pv = k'T**, where **k'** is some other constant.

Since, from Avogadro's law, the volume of a gas under specified conditions of pressure and temperature is directly proportional to the number of moles, **n**, we have **pv = nRT** where **R**, the gas constant, is **k'/n**, referring to the equation above.

The value of the gas constant

We know that one mole of an ideal gas at S.T.P. occupies 22.4 dm^{3} (0.0224 m^{3}).

Standard pressure is 101.3 kPa (1.103 x 105 Pa) and standard temperature is 273.2K. Substituting these values in the gas equation **pv = nRT** gives

The dimensions of the gas constant

**pv = nRT, R = pV/nT**. The pressure, **p**, has units Pa, which are N·m^{-2}, and the volume, **v**, has units m^{3}. The dimensions of **R** are:

**N.m ^{-2} x m^{3} x mol^{-1} x K^{-1} = N.m x mol^{-1} x K^{-1} = J.mol^{-1}.K^{-1}**.

pv is an energy term

The product **pv** has units pascals·volume, or, Pa·m^{3}.

But 1 Pa = 1 N·m^{-2}, therefore, **pv** has units N·m^{-2}·m^{3} = N·m = J, which is the unit of energy.