How to derive equation for density of ideal gas?

1 Answer
Truong-Son N.
Nov 14, 2017

Well, you can start from the ideal gas law:

#PV = nRT#

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

Since density in #"g/L"# can be related back to molar density in #"mol/L"#, solve for #n/V#, the mols in #"mols"# divided by the volume in #"L"#:

#n/V = P/(RT)##" "##" ""units of mol/L"#

By unit conversion of both sides,

#cancel"mol"/"L" xx "g"/cancel"mol" = "g"/"L"#

Since the units of molar mass are #"g/mol"#, multiply both sides by #M#, the molar mass.

#(nM)/V -= D = (PM)/(RT)#

where #D# is the density in #"g/L"#. Therefore,

#color(blue)(barul(|stackrel(" ")(" "PM = DRT" ")|)#

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