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?

1 Answer
May 15, 2018

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?