From the combination of boyel's Charle's and Avogadro's law show that PM=dRTwhere P=pressure of gas M equals to molecular mass of gas equals to density of gas equals to temperature are equals to molar gas constant?

Boyle's law was `PV = "const"`, Charles' law was `V/T = "const"`, and Avogadro's principle was `V/n = "const"`. In each of these scenarios some natural variables were held constant, such as temperature and/or pressure.

From this we find:

• `V prop T`
• `V prop n`

Thus, `PV prop nT`, and the constant of proportionality is `R`, the universal gas constant, so

`PV = nRT`

is the ideal gas law, where:

• `P` is the pressure in `"atm"` if `R = "0.082057 L"cdot"atm/mol"cdot"K"`.
• `V` is the volume in `"L"`.
• `n` is the mols of ideal gas.
• `T` is the temperature in `"K"`.

Now, the units of molar mass are `"g/mol"`, so if density is in `"g/L"`, then

`overbrace("g"/cancel"mol")^(M) xx (overbrace(cancel("mol"))^(n))/underbrace("L")_(V) = overbrace("g"/"L")^(d)`

and it follows that `M cdot n/V = d`, where `M` is the molar mass in `"g/mol"` and `d` is the density.

As a result, by multiplying by molar mass on both sides,

`PVM = nMRT`

`=> color(blue)(PM) = (nMRT)/V = color(blue)(dRT)`

So if a gas has a density of `"0.08988 g/L"` at STP (`0^@ "C"` and, let's say `"1 atm"`), let's solve for its molar mass.

`M = (dRT)/P`

`= ("0.08988 g/"cancel"L" cdot 0.082057 cancel"L"cdotcancel"atm""/mol"cdotcancel"K" cdot 273.15 cancel"K")/cancel"1 atm"`

`=` `"2.0145 g/mol"`

Given that this gas is a homonuclear diatomic molecule, what is it?