The simple gas laws manipulate the four interdependent gas properties — pressure, temperature, volume, and the number of moles — to derive relationships between pairs of properties while holding the others constant.
According to Boyle’s law, when the temperature and number of moles of a gas are held constant, pressure and volume display an inverse relationship. As the volume decreases, the pressure exerted by the gas increases. The product of P and V, therefore, equals a constant. Under two different sets of conditions, the product of initial pressure and volume and the product of final pressure and volume are equal.
Now, if the volume and number of moles are held constant, pressure and temperature display a direct relationship. As the temperature rises, the particles move with greater speed and have more frequent high-energy collisions, and the pressure increases.
The ratio of P and T, therefore, equals a constant. This is the Gay-Lussac’s law, which is sometimes referred to as Amontons’s law. Under two different sets of conditions, the ratio of initial pressure and temperature and the ratio of final pressure and temperature are equal.
Next, consider a balloon that is inflated with a fixed number of moles of a gas. The external pressure of the atmosphere is constant. According to Charles’s law, if moles and pressure held constant, the volume of a gas and its temperature — in Kelvin — display a direct relationship.
With a rise in temperature, the gas particles move faster — resulting in a greater number of collisions and increasing the volume of the balloon. In contrast, lowering the temperature causes the balloon to shrink and decrease in volume.
The ratio of V and T equals a constant. Under two different sets of conditions, the ratio of initial volume and temperature and the ratio of final volume and temperature are equal.
Now, suppose the balloon is inflated with more air. According to Avogadro’s law, when the pressure and temperature are held constant, the volume of the gas and the number of moles display a direct relationship.
The increased number of moles crowds the particles, resulting in a greater number of collisions. This forces the balloon to expand its volume to accommodate the gas particles.
The ratio of volume and number of moles, therefore, equals a constant. Under two different sets of conditions, the ratio of initial volume and number of moles and the ratio of final volume and number of moles are equal.
Combining the expressions of three gas laws, and replacing the proportionality sign by incorporating the ideal gas constant R, gives the ideal gas law. R has the same value for all gases, and it is equal to 8.314 J/mol·K or 0.08206 L·atm/mol·K.
