# Gas Laws

Gases behave ideally under reasonably high temperatures and low pressures. The gas laws are helpful in quantitatively relating pressure, volume, temperature, and molar units.

# Boyle's Law

According to Boyle's law, the volume of a fixed amount of gas is inversely proportional to the pressure, provided that the temperature is kept constant. A simple and good example with biological significance is the way we take air into our lungs. The way we breathe can be summarized as follows. As the respiratory centers signal, during inspiration the diaphragm contracts resulting in an increase in the thoracic volume, which in turn translates into an increase in the lung volume. This increase in lung volume results in a decrease in pressure. This decrease in pressure inside the lung results in the rushing of air into the lung from the outside â€“ inspiration. The exact opposite conditions result in expiration. The point is that at constant temperature, the volume of a gaseous sample is inversely proportional to its pressure.

This can be represented mathematically as shown below:

Example

200 ml of a gas is present in a cylinder at a pressure of 760 torr. If the gas is compressed by using a piston to a pressure of 950 torr, calculate the final volume occupied by the gas. (Assume the temperature to be constant)

Solution

This problem specifically tests your knowledge of Boyle's law. We know that *PV* is a constant, provided that the temperature is kept constant.

Since the temperature is constant, we can readily apply Boyle's law. We can equate the initial and final stages of the system. *P _{1}*and

*V*represent the initial pressure and volume respectively.

_{1}*P*and

_{2}*V*represent, the final pressure and volume respectively.

_{2}

*P _{1}V_{1} = P_{2}V_{2}*

Now it is just a matter of solving for

*V*._{2}(final volume)# Charles' Law

In 1787, Jacques Charles showed that gas expands to occupy a larger volume as the temperature increases. Volume can be plotted against the temperature as shown below:

When the temperature is increased, the volume increases. Charles found that the volume of a gas is directly proportional to its absolute temperature, provided that the pressure is kept constant. So the volume and temperature have a linear relationship as represented by the graph. Charles's law can be mathematically expressed as follows:

The volume-temperature graph shows that at zero volume, the corresponding temperature value is â€“273.15

^{o}C. This means that at â€“273.15^{o}C, the volume occupied by the gas is zero. This temperature is unique, and scientists so far have not been able to devise a way to lower the temperature to â€“273.15^{o}C.

# Combined Gas Law

The gas laws (Charles' and Boyle's law) can be combined to form the combined gas law. The resulting law can be represented mathematically as shown below:

This relationship can be used to do a variety of calculations involving gases, since it relates pressure, volume, and temperature.

# The Ideal Gas Law

This is an extension of the combined gas law. In the combined gas law, we saw the relationship between pressure, volume, and temperature. The ideal gas law can be expressed mathematically as follows:

Here,

*R*(molar gas constant)has values 0.082 L.atm/(K.mol), or 8.31 J/(K.mol), and of course the difference in values is due to the fact that the gas constant is expressed here in two different units.