Question

A plastic bag is weighed and then filled successively with twogases, X and Y. the following data are gathered:

Temperature: 0.0^oC (273K)

Pressure: 1.00 atmosphere

Mass of empty bag: 20.77g

Mass of bag filled with gas X: 24.97g

Mass of 1.12 liters of air at conditions given: 1.30g

Volume of bag: 1.12 liters

Molar volume at STP: 22.4 liters

The mass of 1.12 litersof gas Y is found to be 6.23g.

The bag is emptied and refilled, successively, with gases X and Y, this time with 1 atm pressure and a temperature 30 C higher. Assume that the volume of the bag is the same as before. Which one of the following statements is wrong?

a. the full bag contains fewer molecules of each gas than it did at 0.0 C

b. the ratio of the density of gas Y to the density of gas X is the same as at 0.0 C

c. the molar masses of the two gases are the same as they were at 0.0 C

d. the mass of each gas filling the bag is now 303/273 times the mass held at 0.0 C

e. the average velocity of the molecules of gas X at 30 C is higher than it was at 0 C

Answer 1

Ans. #a. Given, Pressure remains constant at 1.0 atm. Volume remains constant.

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

Since PV remains constant, equation 1 can be written as-

            n₁RT₁ (at T = 0.0⁰C) = n₂RT₂ (at T = 20.0⁰C)

            Or, n₁T₁ = n₂T₂

Or, n₂ = n₁T₁ / T₂

Since T₂ is greater than T₁, n₂ would become lower than n₁.

So, option a is true.

#b. The volume and pressure remains constant. Equal volume of gas constitute equal volume at specified temperature.

Increasing temperature (say, from 0.0⁰C to 20.0⁰C) removes proportionate amount of the two gases in order to keep pressure and volume at constant. So, the ratio of number of moles of the two gases remains constant at all temperature long as P and V is kept constant.

Since volume is kept constant, the relative ratios of number of moles of the two gases per unit volume also remains constant irrespective of temperature.

So, the ratio of the density (mass or moles of the gas per unit volume) of the two gases also remain constant because the ratio of number of moles of the two gases remains constant at all temperatures as long as P and V is constant.

Note that the ratio of densities remains constant however the actual density of the two gases decrease by the same factor due to removal of gas molecules. Also note that filling the bag at elevated temperature is equivalent to removing some gases from a bag kept at lower temperature.

So, option b is also true.

#c. option c is true. Molar mass of a gas is independent of temperature, pressure and other variables. So, change in temperature does not affect the molar mass of gases.

#d. Option d is false. Filling the bag at elevated temperature (20.0⁰C) is equivalent to removing some gases from the bag at 0.0⁰C in order to keep P and V constant. So, the bag at 20.0⁰C consists of fewer number of moles than the bag at 0.0⁰C at constant P and V.

Also, at constant P and V, number of moles in a vessel is inversely proportional to temperature. So, increase in temperature removes the gas molecules from bag- which further results in decrease in mass of both the gases.

A 303/273 = 1.11 means that increasing temperature increases mass 1.11 times that of the bag at 0.0⁰C – it is practically not possible – removing gas must cause loss in mass.

So, increasing temperature decrease the mass of the bag 273/303 = 0.900 times than that of the bag at 0.0⁰C.

#e. Option e is true. Average velocity of a gas molecule (or other particles) increases with increase in temperature.

Conclusion/ Correct option: The wrong/incorrect statement is – option d.