Suppose you are given two 1-L flasks and told that one contains a gas of molar mass 30, the other gas of molar mass 60, both at the same temperature. The pressure in flask A is x atm, and the mass of gas in the flask is 1.2 g. The pressure in flask B is 0.5x atm, and the mass of gas in that flask is 1.2 g. Which flask contains the gas of molar mass 30, and which contains the gas of molar mass 60?

in flask A is the gas with molar mass 30 g/mol

In flask B is the gas with molar mass of 60 g/mol

Explanation:

Step 1: Data given

1 flask has a gas with molar mass of 30 g/mol, the other flask has a gas with molar mass of 60g/mol

Flask A:

⇒ volume = 1L

⇒ Pressure = x atm

⇒ mass of the gas = 1.2 grams

Flask B:

⇒ volume = 1L

⇒ Pressure = 0.5x atm

⇒ mass of the gas = 1.2 grams

Step 2: ideal gas law

p*V = n*R*T

⇒ the volume, gasconstant and the temperature are the same

Step 3: Calculate number of moles

n = p*V/R*T

We see the number of moles is lineair with the pressure. If number of moles increases, the pressure increases as well.

Calculate moles for the gas with molar mass 60 g/mol

number of moles = mass / molar mass

moles = 1.2 grams / 60 g/mol

moles = 0.02 moles

Calculate moles for the gas with molar mass 30 g/mol

moles = 1.2 grams / 30 g/mol

moles = 0.04 moles

The gas with molar mass 30 g/mol has a higher number of moles, so should have a higher pressure as well.

Step 4: Calculate pressure of gas with molar mass 30 g/mol

p = (n*R*T) / V

p = (0.04 * 0.08206 * T) / 1L

p = 0.00328 atm

Step 5: Calculate pressure of gas with molar mass 60 g/mol

p = (n*R*T) / V

p = (0.02 * 0.08206 * T) / 1L

p = 0.00164 atm

(Pressure of gas (30g/mol)) / (Pressure of gas (60g/mol))

0.00328/0.00164 = 2

This means the gas with molar mass 30 g/mol 2 * higher pressure than the gass with molar mass 60 g/mol

This means in flask A is the gas with molar mass 30 g/mol

In flask B is the gas with molar mass of 60 g/mol