Contents for this page | Related topics | |
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1. General properties of gases 2. Boyle's law 3. Experimental results 4. The kinetic theory explains Boyle's law 5. Additional questions |
The kinetic theory Charles' law The generalised gas law Dalton's law of partial pressures |
Data Glossary |

Learning Outcomes | ||

After studying this section, you will know (a) the general properties of gases,and (b) Boyle's law and its graphical representations. |

1. General properties of gases

The volume of a gas depends both on the pressure and temperature at which it is measured. Thus, whenever the volume of a gas is stated, the conditions of pressure and temperatures at which the measurement was made must also be stated.

The relationship between the volume of a gas and its pressure at a constant temperature was discovered by the Irish scientist Robert Boyle, and is known as *BOYLE'S LAW*.

The relationship between the volume of a gas and its temperature at constant pressure was discovered independently by the French physicists Jacques Charles and Joseph Gay-Lussac. It is known either as *CHARLE'S LAW* or *GAY-LUSSAC'S LAW*.

2. Boyle's law

The change in the volume of a gas with pressure at a constant temperature may be investigated using the apparatus shown on the left.

The gas is confined in a glass tube and its volume **a** read from the scale. The pressure in the reservoir **b** is transmitted by a column of oil **c**, to the gas. It may be changed, and its value read on the gauge **d**.

The results obtained in a typical experiment are shown below. Boyle's law may be stated as follows:

Boyle's Law |
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"At constant temperature, the volume occupied by a fixed amount of gas is inversely proportional to its pressure. |

3. Experimental results from a typical Boyle's law experiment

The volume (in cm^{3}) of a pure nitrogen sample at 25º C was measured at various pressures (kPa). The results are shown below. *NOTE THAT THE TEMPERATURE AT WHICH THE EXPERIMENT WAS CARRIED OUT IS CLEARLY STATED!*

It is clear from the table that *AS THE PRESSURE ON THE SAMPLE INCREASES, ITS VOLUME V, DECREASES*. The data in the table is plotted on a graph. Note that since volume is the dependent variable, it must be plotted on the y-axis, with **p**, the independent variable, on the x-axis.

The plot shown is that of a *RECTANGULAR HYPERBOLA*. The nature of this relationship between **p** and **v** is more obvious if one plots **v** against **1/p**:

The graph of **v** against **1/p** is a straight line through the origin. This means that the measured volume is *INVERSELY PROPORTIONAL* to its pressure (at constant temperature).

Expressed mathematically, **v ∝1/p**, or **v = k/p**, where **k** is a constant.

We can confirm that **v = k/p** by looking at a graph of **pv** against **p**.

If **v = k/p**, then **pv = k**. The graph of **pv** against **p** should be a straight line parallel to the p-axis, as shown above. In other words, the product **pv** is a constant at a fixed temperature.

Boyle's Law predicts that at very high pressures, a gas should have a negligible volume. This is not true for real gases, where the actual volume of the gas molecules becomes significant at elevated pressures, and the observed volume is greater than that predicted by Boyle's Law.

4. The kinetic theory explains Boyle's law

Why does the pressure of a gas increase when the volume of the container decreases? Remember that the pressure of a gas on the walls of the container is due to the collisions of the molecules on the walls of the container. The change in momentum of these molecules in unit time is a force exerted by the walls of the vessel on the molecules, which, by Newton's third law, exert an equal and opposite force on the walls of the vessel. This force, divided by the area of the walls in contact with the gas, is the pressure of the gas.

- If the volume of the container is reduced, the gas molecules have a shorter distance to travel before they collide with the walls of the container.
- This means that they collide with the walls more frequently.
- The change of momentum that takes place at the surface of the walls occurs in a shorter time, resulting in a greater force exerted by the molecules on the walls, and hence a greater pressure.

5. Additional questions

Pressure is a vector quantity defined as force applied per unit area. The SI unit for pressure is the *PASCAL (Pa)*, which is a force of 1 newton per square metre (N·m^{-2}).

Since the pascal is a very small pressure, one frequently measures pressure in kPa (kilopascal). Thus, normal atmospheric pressure at sea level is 101.3 kPa.