The Gas Laws
The relationships between volume, pressure, temperature, and moles of a gas have defined laws that model the behavior. These scientific laws each have the name of a famous scientist associated with them.
Boyle's Law
Boyle's Law states that the pressure (\(P\)) of a gas is inversely proportional to the volume (\(V\)). This law is valid as long as the temperature and the amount of gas are constant. Any units will work here:
\[P\,V = k \hskip12pt{\rm (constant)}\]
The constant, \(k\), will depend on the number of moles and the temperature. As long as those two state functions are constant, \(k\) will be a constant and Boyle's Law will hold.
Most Boyle's Law problems have an initial set of conditions (condition 1: \(P_1V_1\)) and then a final set of conditions (condition 2: \(P_2V_2\)). BOTH conditions must satisfy Boyle's Law and therefore:
\[P_1V_1 = P_2V_2\]
Any units will work here for pressure and volume - just make sure the units are the same on each side of the equation.
Charles' Law
Charles' Law states that the volume of a gas is directly proportional to the absolute temperature of the gas. Here, the pressure and amount of gas are kept constant.
You can use any units for volume but remember, temperature must be in Kelvin:
\[{V\over T} = k \hskip12pt{\rm (constant)}\]
Here, the constant, \(k\) will be dependent on the number of moles of gas and the pressure.
Avogadro's Law
The volume of a gas is directly proportional to the amount of gas. The typical amount of gas is in moles. Avogadro's Law assumes that temperature and pressure are constant.
\[{V\over n} = k \hskip12pt{\rm (constant)}\]
Where \(n\) is in moles of gas.
As with the other gas laws (Boyle's and Charles'), Avogadro's Law is typically depicted when considering an initial set of conditions (condition 1) and a final set of conditions (condition 2).
\[{V_1\over n_1} = {V_2\over n_2}\]
This is exactly like Charles' Law except the temperature (\(T\)) has been replaced with number of moles (\(n\)).
Also keep in mind that mass is proportional to moles which means the mass of the gas can also be used here:
\[{V_1\over m_1} = {V_2\over m_2}\]
Where \(m\) is the mass of the gas. However, keep in mind that unlike for \(n\), the two conditions compared with the mass must compare the same gas (as different gases have different molar masses).