Chapter U3, Problem 17STP

Interpretation Introduction

Interpretation:

The number of gas particles in samples of helium, He and argon, Ar gases kept at the same temperature and pressure needs to be determined.

Concept introduction:

The molar volume of a gas is defined as the volume of one mole of the gas under conditions of STP (standard temperature of 0ºC and 1 atm pressure) and is numerically equal to 22.4 L/mol at STP.

The mole is a unit of measurement of the amount of a substance and is numerically equal to $6.02\times {10}^{23}$ units (atoms, molecules or ions of the substance). The molecular weight or molar mass of a substance is taken to be equal to be the mass of one mole of the substance.

Answer to Problem 17STP

Option (C) is the correct answer.

Explanation of Solution

Reason for Correct Option:

The two balloons are filled with He and Ar gases at the same temperature and pressure and the volume of each gas, which is equal to the volumes of the gases contained in the balloons is 22.4 L at STP.

It is known that the volume 22.4 L occupied by a gas at STP is the molar volume, i.e, the volume of one mole of the gas. Since the volumes of the gases in both the balloons are the same at the same conditions of temperature and pressure, hence, the balloons contain the same amount, i.e, one mole of the gases and thus, the number of gas particles in the two balloons will be exactly the same.

Conclusion

Reasons for Incorrect Options:

One mole of all gases contain $6.02\times {10}^{23}$ gas molecules at STP and the numbers of gas molecules are independent of the molecular weight (molar mass) or the mass number of the elements concerned. Thus, the first two options, options (A) and (B) are incorrect.

Since the exact same number of particles is present in one mole of any substance under the same conditions of STP as per the definition of a mole, hence, the last option, option (D) is incorrect.