17] Mass density, p, is related to the molar volume by: Vm M/p (with M being the

Question

17] Mass density, p, is related to the molar volume by: Vm M/p (with M being the molar mass). Starting from the ideal gas equation in terms of V rewrite it in terms of M and p. (a) At 100 °C and 16.0 kPa, the mass density of phosphorus vapour is 0.6388 kg m3. What is the molecular formula of phosphorus under these conditions? It's pretty clever to get at this property that way. (b) In an experiment to measure the molar mass of a gas, 250 cm of the gas was confined in a glass vessel. The pressure was 152 Torr at 298 K, and after correcting for buoyancy effects, the mass of the gas was 33.5 mg. What is the molar mass of the gas?

Explanation / Answer

We start with the ideal gas equation:

PV = nRT

and we clear an expression equal to Vm = M / :

V / n = Vm = RT / P = M /

a) From the expression obtained previously, we perform the calculation of the molar mass:

= 0.6388 Kg / m3 = 0.6388 gr / L

T = 100 ºC + 273 = 373 K

P = 16 kPa * (1 atm / 101.325 kPa) = 0.1579 atm

M = * R * T / P = 0.6388 gr / L * 0.082 atm * L / gmol * K * 373 K / 0.1579 atm = 123.7387 gr / gmol

b) We determine density:

= m / V = 33.5 mg / 250 cm3 * (1 g / 1000 mg) * (1000 cm3 / 1 L) = 0.134 g / L

P = 152 Torr * (1 atm / 760 Torr) = 0.2 atm

and we calculate the molar mass:

M = * R * T / P = 0.134 g / L * 0.082 atm * L / gmol * K * 298 K / 0.2 atm = 16.37 gr / gmol.

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