The Gas Laws

Boyle's Law

Charles's Law

Jacques Alexandre Cesar Charles discovered a very important law dealing with the gases and the gas laws, if a given quantity of gas is held at constant pressure, then its volume is directly proportional to the absolute temperature. In other words, or equations, this would be V = Constant * T or:

Constant = V / T

To demonstrate one could try taking a balloon filled with gas, and bring it outside on a cold day. The balloon will suddenly become smaller because of Charles's Law. An extremely useful version of Charles's Law when dealing with a changing gas is:

V1 / T1 = V2 / T2

Gay-Lussac and Avogadro's Laws

Joseph Gay-Lussac was a 19th century experimenter who found that columns of gases always combine with one another in the ratio of small whole numbers, as long as the pressures and temperatures are held constant. This statement is otherwise known as Gay-Lussac's law of combining volumes. This law was merely a summary of Amedo Avogadro, whom was an Italian physicist who did the experiments. Avogadro's hypothesis' later came to form Avogadro's Law: The volume of a gas, when the pressure and temperature are constant, is directly proportional to the quantity, or volume, of the gas. With this, V (the volume) is proportional to n (number of moles).

V = Constant * n

The Ideal Gas Law

With Boyle, Charles, and Avogadro's laws, one can combine them all to get one equation that is extremely powerful in the field of gasses. After this equation is obtained, you must introduce some kind of constant, in this case R, to make a definite equation out of an equation that is just proportional. A little rearranging of the formula gives the following:

P * V = n * R * T

This ever important equation is called the Ideal Gas Law, since it is used in calculating parts of an ideal gas. To use this equation one must find a value of R. To do this, you could find that a gas at Standard Temperature and Pressure (STP)(gas at 273.15 K, 1 atm) with 1 mole of gas takes up 22.414 L. Using these values in the Ideal Gas Formula, R turns out to be 0.082057 L * atm / K * mol. Another useful form of the ideal gas formula can be used if trying to find out what will happen to a changing gas is given by the General Gas Law:

P1 * V1 / T1 = P2 * V2 / T2

Gas Mixtures and Partial Pressures

Many gasses in the world are mixtures of more than one gas. This is where the partial pressures law comes in to aid with the Ideal Gas Law. The basic idea of partial pressures is that the pressure of a mixture of gases is the sum of the pressures of the different components of the mixture. This is applied using the fact that the sum of the gasses is the total amount of gas in the mixture easily seen by the equation:

n total = na + nb + nc + ...

From this known fact one can use the Ideal Gas Law to find find that the same applies to pressures (use the same equation but substitute P for n). John Dalton was the first to find this relationship between the partial pressures so this law is called Dalton's Law of Partial Pressures.

It is also important to introduce the fact of the mole fraction, useful in calculating partial pressures. The mole fraction is just na / n total and will find approximately the amount of each substance in the mixture. If you have the mole fraction you can see that the partial pressure of a gas in a mixture is equal to the product of its mole fraction and the total pressure. This means that if you multiply the mole fraction by the total pressure you will get the partial pressure of the gas.