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?

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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?

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Answer 1 · 2016-10-20T05:38:56

Yes, the point is that the quantity of gas is fixed. Since you can convert between mass and $mol$ $"mol"$ 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:

$P V = n R T$ $PV = nRT$
$P V M_{m} = m R T$ $PVM_m = mRT$
$P M_{m} = D R T$ $PM_m = DRT$

where:

$P$ $P$ is pressure in, say, $atm$ $"atm"$ or $bar$ $"bar"$ .

$V$ $V$ is volume in $L$ $"L"$ .

$n$ $n$ is the $mol$ $"mol"$ s of gas.

$M_{m}$ $M_m$ is the molar mass of the gas in $g/mol$ $"g/mol"$ .

$D$ $D$ is the density in $g/L$ $"g/L"$ .

$m$ $m$ is the mass in $g$ $"g"$ .

$R$ $R$ is the universal gas constant. If it is units of $L \cdot atm/mol \cdot K$ $"L"cdot"atm/mol"cdot"K"$ , then pressure is in $atm$ $"atm"$ . If it is in units of $L \cdot bar/mol \cdot K$ $"L"cdot"bar/mol"cdot"K"$ , then pressure is in units of $bar$ $"bar"$ . And so on.

$T$ $T$ is the temperature in $K$ $"K"$ .

You can interconvert between these.

$M_{m} \cdot P V = M_{m} \cdot n R T$ $M_m * PV = M_m * nRT$

$\Rightarrow P V M_{m} = m R T$ $=> color(blue)(PVM_m = mRT)$

$P V M_{m} \cdot \frac{1}{V} = \frac{m}{V} R T$ $PVM_m * 1/V = m/VRT$

$\Rightarrow P M_{m} = D R T$ $=> color(blue)(PM_m = DRT)$

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

$P_{1} V_{1} = n R T$ $P_1V_1 = nRT$
$P_{2} V_{2} = n R T$ $P_2V_2 = nRT$

$\Rightarrow P_{1} V_{1} = P_{2} V_{2}$ $=> color(blue)(P_1V_1 = P_2V_2)$ ,
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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?

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