The Empirical Gas Law relationships are:
Boyles' Law: "Pressure" prop=(1/"Volume"); mass & Temperture remain constant.
=> "P"prop"(1/V)" => P=k(1/V) => k = (PV)
=> k_1=k_2 => P_1V1 = P_2V_2
Charles' Law: "Volume "prop" f(Temperature)"; Pressure & mass remain constant.
=> VpropT => V=kT => k = (V/T)
=> k_1=k_2 => (V_1/T_1)=(V_2/T_2)
Gay-Lussac Law: "Pressure "prop" f(Temperature)"; mass & Volume remain constant.
=> PpropT => P=kT => k = (P/T)
=> k_1=k_2 => (P_1/T_1)=(P_2/T_2)
Volume-Mass Law : "Volume "prop" f(mass)"; Pressure & Temperature remain constant.
=> Vpropn => V=kn => k = (V/n); n = moles
=> k_1=k_2 => (V_1/n_1)=(V_2/n_2)
Pressure-Mass Law: "Pressure "prop" f(mass)"; Pressure & Temperature remain constant.
=> Ppropn => P=kn => k = (P/n); n = moles
=> k_1=k_2 => (P_1/n_1)=(P_2/n_2)
Combined Gas Law
=>PVpropnT => PV=knT => k = ((PV)/(nT))
=> k_1=k_2 => ((P_1V_1)/(n_1T_1)) =((P_2V_2)/(n_2T_2))
Ideal Gas Law => Assumes one of the P,V,n,T condition sets of the Combined Gas Law is at Standard Temperature - Pressure conditions (STP). The other set of P,V,n,T conditions are Non-Standard Conditions.
STP => (P,V, n, T) (1.0Atm, 22.4L, 1"mole", 273K)
=> ((P_1V_1)/(n_1T_1)) = ((1Atm)(22.4L))/((1mol)(273K)) = 0.08206((L)(Atm))/((mol)(K))
= "Universal" "Gas" "Constant" (R)
Therefore, substituting 'R' into Combined Gas Law
=> R = ((PV)/(nT)) => PV = nRT
Note:
One can also use the same logic for deriving relationships for ...
Henry's Law of Gas Solubility => " Solubility of a gas" prop "Applied Pressure
Graham's Law of Gas Effusion Rates => "Effusion Rate" prop (1/sqrt(mol wt))
