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Determine the mass concentration for N20 at a mixing ratio of 311 ppb at P = 1 atm, T= 298 K.

My work

#density of N20 = Concentration of N20 * #density air

PV = #moles of air R T

PV/RT = # moles of air

PV/RT = Numberofmolecules/Avagardo # = #moles of air

PV*Avagardo#/RT = Number of molecules of air = # density of air * V

# density of air = P*Avagardo's #/RT

So...

#Densityof N20 = Concentration of N20* P*Avagardo #/RT

DensityofN20 = # density of N20* Molar mass N20/Avagardo's #

DensityofN20 = P*Avagardo's #*Concentration of N20/(RT *molar mass of N20/Avagardo's #)

Avagardo's # cancels out leaving:

Density of N20 = P*Concentration of N20*Molar Mass of N20/(RT)

Now plugging in the numbers lead to

Density of N20 = (1 atm)*(1.101325*10^5 Pa/atm)*(311*10^-9 mol/mol)*(46.00 g/mol) /((8.314 J/mol K)*298 K) = 0.0006 g/m^3

Is this correct step and answer? If so where is the error? Just needs to be verified. Thanks.