Question

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?

Answer 1

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.