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

Apr 14, 2017

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...

$P V = n R T$

CASE I: Constant Pressure and Moles

$P {V}_{1} = n R {T}_{1}$

$P {V}_{2} = n R {T}_{2}$

Hence,

$\textcolor{g r e e n}{\frac{{V}_{1}}{{T}_{1}} = \frac{n R}{P} = \frac{{V}_{2}}{{T}_{2}}}$

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

${P}_{1} V = n R {T}_{1}$

${P}_{2} V = n R {T}_{2}$

Hence,

$\textcolor{g r e e n}{\frac{{P}_{1}}{{T}_{1}} = \frac{n R}{V} = \frac{{P}_{2}}{{T}_{2}}}$

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

${P}_{1} {V}_{1} = n R T$

${P}_{2} {V}_{2} = n R T$

Hence,

$\textcolor{g r e e n}{{P}_{1} {V}_{1} = n R T = {P}_{2} {V}_{2}}$

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

$P {V}_{1} = {n}_{1} R T$

$P {V}_{2} = {n}_{2} R T$

Hence,

$\textcolor{g r e e n}{{V}_{1} / {n}_{1} = \frac{R T}{P} = {V}_{2} / {n}_{2}}$

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