Question

How do I choose which gas law to use???

Answer 1

Look at your question conditions. Start from the ideal gas law, and simply derive the relevant relation. No need to memorize specific forms of these equations...

`PV = nRT`

CASE I: Constant Pressure and Moles

`PV_1 = nRT_1`

`PV_2 = nRT_2`

Hence,

`color(green)((V_1)/(T_1) = (nR)/P = (V_2)/(T_2))`

which is Charles' Law, apparently, describing an isothermal process in a closed nonrigid container. But I didn't memorize this.

CASE II: Constant Volume and Moles

`P_1V = nRT_1`

`P_2V = nRT_2`

Hence,

`color(green)((P_1)/(T_1) = (nR)/V = (P_2)/(T_2))`

which is Gay-Lussac's Law, apparently, describing an isovolumetric process in a closed rigid container (which is quite easy to accomplish). Not something I memorized either.

CASE III: Constant Temperature and Moles

`P_1V_1 = nRT`

`P_2V_2 = nRT`

Hence,

`color(green)(P_1V_1 = nRT = P_2V_2)`

which is Boyle's Law, describing an isothermal process in a closed nonrigid container. This is the only one I do have memorized, because a vapor-pressure/atmospheric-pressure equilibrium occurs when boiling, and the liquid volume expands.

But again, we don't need to memorize it. Why do that when we can derive it?

CASE IV: Constant Pressure and Temperature

`PV_1 = n_1RT`

`PV_2 = n_2RT`

Hence,

`color(green)(V_1/n_1 = (RT)/P = V_2/n_2)`

which is Avogadro's principle. I hardly ever use this one... it says that the volume per mol of an ideal gas stays constant.