PV=nRT

According to Boyle’s law, the pressure exerted by a given quantity of gas increases as the volume of the gas decreases at a constant temperature. According to Charles’s law, at a constant pressure, the volume occupied by a given quantity of gas decreases as the temperature of the gas decreases. According to Avogadro’s principle, the volume occupied by a gas depends directly on the number of gas particles at a constant temperature and pressure. If all three of these laws are combined, the result is V= R*((nT)/P). R is the universal gas constant which is equal to 0.0821 L*atm/mol K (Kelvin). By multiplying both sides of this equation by P, the equation would become PV=nRT, the ideal gas law. Note: P=Pressure (atm), V=Volume (L), n=number of moles, and T= Temperature (Kelvin)).

Other equations can be derived from the ideal gas law:

Example 1: PV=nRT

P₁V₁=nRT

P₂V₂=nRT

P₁V₁=P₂V₂

This equation shows that pressure and volume are inversely related. This means that as pressure increases, volume decreases and vise versa.

Example 2: PV=nRT

V₁/T₁=nR/P (Divide T and P on both sides of the equation)

V₂/T₂=nR/P

V₁/T₁=V₂T₂ (Substitute)

This equation shows that volume and temperature are directly related. This means that as volume increases, the temperature also increases and vise versa.

Example 3: PV=nRT

P₁V₁/T₁=nR (Divide T on both sides of the equation)

P₂V₂/T₂=nR

P₁V₁/T₁=P₂V₂/T₂

This equation is a combination of the first two, in which pressure and volume are inversely related and both pressure and volume are directly related to temperature.

Sample Questions:

1. A volume of 22.40 L of H₂S gas measured at 283'C and 4.000 atm will contain how many moles of hydrogen sulfide?

2. A 25.0 liter cylinder contains 14.2 mol of He gas at 40'C, what is the pressure in atmospheres of the He gas?