How does the pressure of a gas relate to the concentration of its particles?
The ideal gas law provides a relationship between the pressure, temperature, volume, and number of particles of gases in a system in accordance to the kinetic theory of gases. This is founded on four assumptions:
1) The particles of gases are negligibly small compared to the distance between them,
2) The particles of gases are not interacting and are not affected by each other other than during collision (which are always elastic) which happens instantaneously,
3) Gases are in continuous random motion,
4) The average kinetic energy for all gases in the system is the same at a given temperature regardless of the type of gas.
The ideal gas law states that:
`PV = nRT` where P is the pressure, V is the volume, n is the moles of gases, R is the ideal gas constant, and T is the temperature.
As can be seen here, keeping all things equal, as the number of moles increases, pressure increases. This is because an increase in the number of particles in the same volume will increase the number of collisions to the walls of the container, which causes pressure to increase. Since concentration is dependent on the number of particles, an increase in concentration will lead to an increase in pressure.
This can also be seen directly from the ideal gas law. By dividing both sides of the equation by the volume, V:
`P = MRT` ,
where M is now the molarity, or the number of moles (n) over the volume of the system. An increase in the molarity results to an increase in pressure due to their direct relationship. (Also, an increase in molarity results from an increase in the number of moles, which was stated in the previous paragraph).
In short, since PV = nRT, an increase in concentration will result in an increase in pressure, assuming all other things remain the same.