Question

Determine the molar mass of each of the following gases:

1) 0.78 g of a gas that occupies 500 mL at 0 ∘C and 1.00 atm (STP).

2) 1.42 g of a gas that occupies 1.15 L at 0 ∘C and 760 mmHg (STP).

3) 1.57 g of a gas that occupies 1.25 L at 680 mmHg and 19.0 ∘C.

4) 2.7 g of a gas that occupies 2.4 L at 0.95 atm and 20 ∘C.

Answer 1

Solution:

1. Given data:

m = 0.78 g

V = 500 ml

T = 0 C , P = 1 atm

Lets calculate molar volume at STP

V/n = RT/P

= 0.08206 * 273/1

= 22.4 l/mol

But we have 500 ml that is 0.5 l of gas so the moles of gas is,

n = 0.5/22.4 = 0.02232 moles

Molar mass will be = mass / no of moles = 0.78/0.02232

molar mass = 34.946 g/mol

2. We have already calculated moar volume at STP i.e. 22.4 l/mol

So use the same method as previous,

moles of gas = 1.15/22.4 = 0.05134 moles

Molar mass = 1.42/0.05134 = 27.65 g/mole

3. Find out molar volume of the gas at given condition:

V/n = RT/P

R = 62.36 L mmHg/K mol

= 62.36 * (273 + 19)/680

= 26.77 l/mol

No of moles = 1.25/26.77 = 0.0467 moles

Molar mass = mass/moles = 33.61 g/mole

4. Molar volume = RT/P

= 0.08206 * 293/0.95

= 26.71 l/mol

Moles of gas = 2.4/26.71 = 0.08985 moles

Molar Mass = mass/moles = 2.7/0.08985

= 30.05 g/mol