A gas has a density of 0.791 g/L. What is the molar mass of this gas?

Question

I wonder why the formula is m (mass) = p x V (density multiply with volume)

But the answer key of the book is: Molar Mass (M) = g/L × 22.4 L/1 mole = p x V

SO , in this situation , do we find mass = molar mass= p x V ????

Answer 1

Assuming STP conditions and 22.4 L = 1 mole of gas, you can relate the following:

density = g/L x 22.4 L/mole = g/mole

0.791 g/L x 22.4 L/mole = 17.72 g/mole = 17.7 g/mole (3 sig. figs.)

Doing it the long way and using the ideal gas law: PV = nRT and assume standard temperature and pressure (since these variables aren't given in the question), then you have ...

P = 1 atm

V = 1 L

n = ? moles

R = 0.0821 Latm/Kmol

T = 273K

Solving for n (moles), we have...

n = PV/RT = (1 atm)(1 L)/(0.0821 Latm/Kmol)(273K)

n = 0.04462 moles

Since the 1 L contains 0.791 g, we now have...

0.791 g/0.04462 moles = 17.727 g/mole = 17.7 g/mole (to 3 significant figures)

The answer key of p x V is actually ρ x V where ρ is density or mass/volume, so you have

mass/volume x volume = mass (not molar mass). Not really sure what your question is regarding the ρ and V, but hopefully I've explained this sufficiently. If you have further questions, post them in the comments sections.