Question

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?

Answer 1

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

`PV = nRT`
`PVM_m = mRT`
`PM_m = DRT`

where:

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

You can interconvert between these.

`M_m * PV = M_m * nRT`

`=> color(blue)(PVM_m = mRT)`

`PVM_m * 1/V = m/VRT`

`=> 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"`s or density, Boyle's law holds true as long as if any of those are constant, in addition to the temperature.

`P_1V_1 = nRT`
`P_2V_2 = nRT`

`=> color(blue)(P_1V_1 = P_2V_2)`,
Boyle's Law