For a fixed mass of gas at constant temperature, the volume is inversely proportional to the pressure. This is mathematically:
\[pV = constant\]
That means that, for example, if you double the pressure, you will halve the volume. If you increase the pressure 10 times, the volume will decrease 10 times.
Is this consistent with pV = nRT ?
- You have a fixed mass of gas, so n (the number of moles) is constant.
- R is always constant - it is called the gas constant.
- Boyle's Law demands that temperature is constant as well.
That means that everything on the right-hand side of pV = nRT is constant, and so pV is constant - which is what we have just said is a result of Boyle's Law.
This is easiest to see if you think about the effect of decreasing the volume of a fixed mass of gas at constant temperature. Pressure is caused by gas molecules hitting the walls of the container. With a smaller volume, the gas molecules will hit the walls more frequently, and so the pressure increases.
You might argue that this isn't actually what Boyle's Law says - it wants you to increase the pressure first and see what effect that has on the volume. But, in fact, it amounts to the same thing. If you want to increase the pressure of a fixed mass of gas without changing the temperature, the only way you can do it is to squeeze it into a smaller volume. That causes the molecules to hit the walls more often, and so the pressure increases.
But everything in the nR/p part of this is constant. That means that V = constant x T, which is Charles's Law.
Jim Clark (Chemguide.co.uk)