Question

At NTP, what is the mass of `"22.4 L"` of nitrogen gas?

Answer 1

Well, I can set things up for you to calculate the mass... but weight is in newtons, `"N"`, or `"kg"cdot"m/s"^2`... and you have to decide what the chemical formula of nitrogen is... you have a `50%` chance of guessing it right!

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Normal Temperature and Pressure, NTP, is apparently `20^@ "C"` and `"1 atm"`. This should not be confused with STP, which is at `0^@ "C"`, not `20^@ "C"`, and not `25^@ "C"`.

The "mass" version of the ideal gas law can be derived.

`PV = nRT`

`n = (PV)/(RT)`

To get the units from `"mols"` to `"g"`, simply multiply by the molar mass `M` in `"g/mol"`.

`nM -= m = (PVM)/(RT)`

In this case, we have:

• `P`, pressure, in `"atm"`, of the ideal gas within the container.
• `V`, volume, in `"L"`, of the ideal gas.
• `M`, molar mass, in `"g/mol"`, of the ideal gas.
• `R = "0.082057 L"cdot"atm/mol"cdot"K"`, the universal gas constant.
• `T`, temperature, in `"K"`, within the container filled with ideal gas.

In case you couldn't tell, we're assuming ideal gases... So, the mass is:

`color(red)(m) = (cancel"1 atm" cdot 22.4 cancel"L" cdot M" g/"cancel"mol")/(0.082057 cancel"L"cdotcancel"atm""/"cancel"mol"cdotcancel"K" cdot (20 + 273.15 cancel"K"))`

`= color(red)(???)`

Now, it's up to you to decide what the molar mass is.

What is the molar mass of "nitrogen"? Is it `"14.007 g/mol"`, or `"28.014 g/mol"`? Why would you have to choose? (It matters!)