The mass of an evacuated 245 mL flask is 143.577 g. The mass of the flask filled with 346 mbar of an unknown gas at 25 ∘C is 143.673 g. Calculate the molar mass of the unknown gas.

Question

Express the molar mass in grams per mole to three significant figures.

Answer 1

Hi Is S.!

To calculate molar mass, we need both the mass and the number of moles.

First, let's find the mass of the gas in the cylinder:

mass_gas = mass_{gas + cylinder} - mass_cylinder

<=> 143.673g - 143.577g

mass_gas = 0.096g = 96mg

Now that we know the mass, let's think of a way to find the moles. We know the pressure, volume and temperature already. Let's have a look at the ideal gas equation:

PV = nRT => n = PV/RT

To use the ideal gas law, we first need to convert the pressure from mbar into atm:

(346 mbar)(1 atm/1013 mbar) = 0.341 atm

We also need to convert the temperature into K:

25C + 273 = 298K

Now, let's see our ideal gas law equation again:

n = PV/RT

<=> (0.341atm*0.245L)/(0.0821 L*atm*mol^-1*K^-1*298K)

n = 3.42x10^-3 moles = 3.42 mmoles

We are finally ready to calculate the molar mass. The most obvious way to calculate it is as follows:

MW = mass*moles^-1

<=> 0.096g/3.42x10^-3 moles

MW = 28.1 g*mol^-1

However, we could also have found it with the following equivalent calculation:

MW = mass*moles^-1

<=> 96mg/3.42mmoles

MW = 28.1 mg*mmol^-1 = 28.1 g*mol^-1

Hope that helps!

Cheers