Question

Calculate the molar mass of a gas at 501 torr and 95°C if 206 ng occupies 0.206μL.

Answer 1

Ans. Given, temperature, T = 95.0⁰C = (95.0 + 273.15) K = 368.15K

            Pressure, P = 501 torr = (501 / 760) atm = 0.659211 atm

            Volume of gas, V = 0.206 uL = 2.060 x 10^-7 L

# Ideal gas equation:           PV = nRT      - equation 1

            Where, P = pressure in atm

            V = volume in L                   

            n = number of moles

            R = universal gas constant= 0.0821 atm L mol^-1K^-1

            T = absolute temperature (in K) = (⁰C + 273.15) K

Putting the values in equation 1 -

0.659211 atm x (2.060 x 10^-7 L) = n x (0.0821 atm L mol^-1K^-1) x 368.15 K

            Or, 1.3580 x 10^-7 atm L = n x 30.225115 atm L mol^-1

            Or, n = (1.3580 x 10^-7 atm L) / (30.225115 atm L mol^-1)

            Hence, n = 4.4929 x 10^-9 mol

# So far we have,

            Moles of gas sample, n = 4.4929 x 10^-9 mol

            Mass of gas sample = 206 ng = 2.06 x 10^-7 g                              ; [1 ng = 10^-9 g]

Now,

            Molar mass of gas = Mass of gas sample / Moles of gas sample

                                                = 2.06 x 10^-7 g / (4.4929 x 10^-9 mol)

                                                = 45.850 g/mol

Therefore, molar mass of the gas = 45.850 g/ mol