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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?

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Answer:

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

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