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

##### 1 Answer

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 **boil**ing, 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.