**Gas Laws **

In gases there are three different variables, which are pressure, temperature and volume, and all of these components are dependent on each other.

If one of these components is fixed and any of the other two are changed, the last component would also change with respect to the variable component. This can be seen in the following three relationships:

If the **temperature **is kept **constant **the relationship between Volume and Pressure would be an inversely proportional relationship, showing that when one component is increased, the other one would decrease. This can be seen in the following relationship:

which can be depicted as a graph as:

The equation can also be rearranged to give:

which can be depicted as a graph as:

showing that when PV is plotted against P or V it would, therefore, give a constant

If the **volume **is kept **constant **the relationship between Pressure and temperature would be a directly proportional relationship, indicating that one component increases, the other would decrease. This can be seen in the following relationship:

Which can also be written as:

If the **pressure **is kept **constant **the relationship between volume and temperature would be a directly proportional relationship, indicating that one component increases, the other would decrease. This can be seen in the following relationship:

Which can also be written as:

On combining these three equations two very important equations can be derived:

and

Where R 8.314kJ mol^{-1} is the gas constant and n is the number of moles.

The units for each of Pressure, Volume and Temperature are Pa, m^{3} and K respectively.

Now if this equation is analysed one can state that n is the number of moles, and therefore this can be said to be m/M (mass/Molecular mass) and thus the molecular mass can be found with the following equation:

It must be noted that this equation cannot be used for solids but it can be only used for volatile liquids and gases. For volatile liquids, the temperature would have to be increased so that the volatile liquid would turn into a gas. All volume measurements should be collected in a gas syringe.

__Gay Lussac’s Law__

Another important concept is the **Gay Lussac’s Law of combining of volumes **which states that when two different volumes are mixed the ratio of these two volumes would be proportional to the original ratio under the same pressure and temperature. If these two gases react the volume ratio between the original reactants and the final products would then depend on the stoichiometry of the reaction.

__Dalton’s Law of Partial Pressure__

In reality, most gases are found as mixtures and thus the pressure of one gas would not be equal to the total pressure. The relationship between volume and moles can be said to proportional and this can show that an increase in moles would increase the volume, but if the volume is constant this would affect the pressure.

Dalton’s Law state:

The total pressure exerted by a gaseous mixture is equal to the sum of the partial pressures of each individual component in a gas mixture.

__Ideal Gases/Real Gases__

Ideal gases have got a number of properties. They are:

- ideal gases occupy a negligible volume
- have negligible forces of attraction
- When particles collide their collision are negligible
- The average K. E. depends on the temperature of the sample
- The particles move randomly in straight lines, in all directions at different speeds.

while in reality it is known that collisions are not elastic while the molecules occupy a certain amount of volume. There are also interactions between different gaseous molecules.

These properties of real gases would then make the gas law into the Van der Waals Equation, which is the following:

Where a and b are constants and are different for each gas.

a takes in consideration the reduction in pressure that is present in real gases. The stronger the intermolecular forces are, the higher the value of a would be.

b is the volume of each individual atom/molecule.

The new equation gives a different graph of PV vs P.

For gases to approach ideality low pressure and high temperatures should be used.

__Maxwell Boltzmann Distribution__

The energy for each atom is different and is in a relationship with the temperature. As the temperature increases the average energy in the atoms increase.

It must be noted that the area under the graph is always the same while the average energy is shifted to the right on increasing temperature and shifted to the left on decreasing temperature.

__Experiment to determine the RMM of a volatile liquid__

The gas equation can be used to estimate the mass of a volatile liquid. A volatile liquid can be vaporized and the volume read from the syringe. The mass of the compound can be done by weighing the syringe before and after the experiment and the atmospheric pressure can either be read by the aid of a barometer or assumed to be approximately 1 atm.