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### Gas Laws and their Formulas

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Boyle’s Law for Pressure – Volume Changes

When the pressure goes up, the volume goes down. Similarly, when the pressure goes down, the volume goes up. In 1662, the British chemist Robert Boyle proposed a law to decribe this behavior of gases. Boyle’s law states that for a given mass of gas at a constant temperature, the volume of the gas varies inversely with the pressure. We can write Boyle’s law as:

Charles’ Law for Temperature – Volume Changes
In 1787 a French physicist, Jacques Charles, investigated the effect of temperature on the volume of a gass at a constant pressure. Charles summarized his observations into a law. Charles’ law states that the volume of a fixed mass of gass is directly proportional to its Kelvin temperature if the pressure is kept constant. Temperatures in gas law problems are always in Kelvin. We can write Charles’ law as:

Gay-Lussac’s Law for Temperature – Pressure Changes
On a hot summer day the pressure in a car tire increases. This illustrates a relation discovered in 1802 by Joseph Gay-Lussac, a French chemist. Gay-Lussac’s law states that the pressure of a gas is directly proportional to the Kelvin temperature if the volume is kept constant. We can write Gay-Lusaac’s law as:

The Combined Gas Law
The three gas laws found above can be combined into a single expression called the combined gas law. The other laws can be obtained from the combined gas law by holding one quantity (pressure, volume, or temperature) constant. We can write the combined gas law as:

The Ideal Gas Law
Sometimes we wish to calculate the number of moles of a gas in a fixed volume at a known temperature and pressure. Such a calculation is possible if the combined gas law is modified. The modification may be understood by recognizing that the volume occupied by a gas at a specified temperature and pressure is directly proportional to the number of particles in the gas. The number of moles, n, of gas is also directly proportional to the number of particles. Hence, moles must be directly proportional to the volume as well. Therefore, moles may be introduced into the combined gas law by placing n in the denominator on each side of the equation.

PV = nRT – where R is the ideal gas constant, and is equal to 8.314