# Can I use Boyle's law for a situation where the mass of the particles is held constant within a closed container and no chemical change occurs to these particles?

Oct 20, 2016

Yes, the point is that the quantity of gas is fixed. Since you can convert between mass and $\text{mol}$s using the molar mass, it doesn't matter which one is held fixed; the other is held fixed by implication of the converted units.

The ideal gas law has three common formulations:

$P V = n R T$
$P V {M}_{m} = m R T$
$P {M}_{m} = D R T$

where:

• $P$ is pressure in, say, $\text{atm}$ or $\text{bar}$.
• $V$ is volume in $\text{L}$.
• $n$ is the $\text{mol}$s of gas.
• ${M}_{m}$ is the molar mass of the gas in $\text{g/mol}$.
• $D$ is the density in $\text{g/L}$.
• $m$ is the mass in $\text{g}$.
• $R$ is the universal gas constant. If it is units of $\text{L"cdot"atm/mol"cdot"K}$, then pressure is in $\text{atm}$. If it is in units of $\text{L"cdot"bar/mol"cdot"K}$, then pressure is in units of $\text{bar}$. And so on.
• $T$ is the temperature in $\text{K}$.

You can interconvert between these.

${M}_{m} \cdot P V = {M}_{m} \cdot n R T$

$\implies \textcolor{b l u e}{P V {M}_{m} = m R T}$

$P V {M}_{m} \cdot \frac{1}{V} = \frac{m}{V} R T$

$\implies \textcolor{b l u e}{P {M}_{m} = D R T}$

And furthermore, Boyle's law derives from the ideal gas law, so when the ideal gas law can use masses or $\text{mol}$s or density, Boyle's law holds true as long as if any of those are constant, in addition to the temperature.

${P}_{1} {V}_{1} = n R T$
${P}_{2} {V}_{2} = n R T$

$\implies \textcolor{b l u e}{{P}_{1} {V}_{1} = {P}_{2} {V}_{2}}$,
Boyle's Law