A gas has a density of #3.18*g*L^-1# at a temperature of #347*K#, and a pressure of #1.2*atm#. What is its molecular mass?

1 Answer
Apr 3, 2017

Answer:

We use the Ideal Gas equation to get #"molecular mass"=75.5*g*mol^-1#

Explanation:

We assume ideality, and so #PV=nRT#, and thus,

#PV=("mass"/"molar mass")RT# because #n="mass"/"molar mass"#

On rearrangement, #"molar mass"="mass"/Vxx(RT)/P#

But #"mass"/V=rho, "density"#, and thus...........

#"molar mass"=(rhoRT)/P=#

#(3.18*g*L^-1xx0.0821*(L*atm)/(K*mol)xx347*K)/(1.2*atm)#

Let's just cancel out the units to see if we have got this right. I am not immune to mistakes.............

#"Molar mass"=(3.18*g*cancel(L^-1)xx0.0821*cancel(L*atm)/(cancelK*mol)xx347*cancelK)/(1.2*cancel"atm")#

And this gives, I think, an answer of........

#75.5*g*mol^-1#. Because we have got consistent units, I think our order of operations is correct.