Question

An empty glass container has a mass of 658.572 g. After it has been filled with nitrogen gas, it has a mass of 659.452 g and a pressure of 790. torr at 15.0C. The container is avacuated and filled with an unknown gas A and has a mass of 6660.59 g and a pressure og 745 torr at 26C

Identify gas A (Type the symbol)

Answer 1

Ans. Part 1: Determine the volume of Container:

Mass of N₂ gas = Mass of filled container – Mass of empty container

                                    = 659.452 g – 658.572 g

                                    = 0.880 g

Moles of N₂ = Mass / Molar mass = 0.88 g / (28.01348 g/ mol) = 0.031413 mol

# Given,

            Pressure, P = 790 torr = (790 / 760) atm = 1.0395 atm

            Temperature, T = 15.0⁰C = 288.15 K

# Using 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 -

            1.0395 atm x V = 0.031413 mol x (0.0821 atm L mol^-1K^-1) x 288.15 K

            Or, V = 0.743140953495 atm L / 1.0395 atm = 0.71490 L

            Hence, V = 0.7149 L

Therefore, volume of container = 0.7149 L

# Part 2: Determine the moles of unknown gas taken and its identification

Mass of gas A = 660.590 g – 658.572 g = 2.018 g

# Given,

            Pressure, P = 745 torr = (745 / 760) atm = 0.9803 atm

            Temperature, T = 26.0⁰C = 299.15 K

            Volume, V = 0.7149 L          - as calculated in #Part 1

# Putting the values in equation 1 -

            0.9803 atm x 0.7149 L = n x (0.0821 atm L mol^-1K^-1) x 299.15 K

            Or, n = 0.70081647 atm L / 24.560215 atm L mol^-1 = 0.02853 mol

Therefore, moles of unknown gas take = 0.02853 mol

# Now,

            Molar mass of gas = Mass of unknown gas taken = Moles of gas

                                                = 2.018 g / 0.02853 mol

                                                = 70.73 g/ mol

Hence, molar mass of the gas = 70.73 g/ mol

# Identification: The gas is most likely to be Cl₂ (Theoretical molar mass = 70.9045 g/mol).