Equal masses of gaseous N2 and Ar are placed in separate flasks of equal volume at the same temperature. Tell whether each of the following statements is true or false.
Briefly explain your answer in each case.
(a) There are more molecules of N2 present than atoms of Ar.
(b) The pressure is greater in the Ar flask.
(c) The Ar atoms have a greater average speed than the N molecules.
(d) The N2 molecules collide more frequently with the walls of the flask than do the Ar atoms.
(a) False. To determine the number of molecules or atoms in a given amount of substance, we can use Avogadro's number, which tells us that one mole of any substance contains 6.022 × 10^23 particles. Since the masses of N2 and Ar are equal and their volumes are the same, we can assume that both flasks contain an equal number of moles of gas. Since both gases are monatomic and diatomic respectively, one mole of N2 consists of 2 moles of N2 molecules and one mole of Ar consists of 1 mole of Ar atoms. Therefore, in this case, the number of N2 molecules is equal to the number of Ar atoms.
(b) True. The pressure of a gas is determined by the number of collisions between gas molecules/atoms with the walls of the container. Since both flasks contain an equal number of moles of gas, but the masses of N2 and Ar are different (Ar has a larger atomic mass), there will be more Ar atoms than N2 molecules in the flask. Therefore, the rate of collisions with the walls of the flask will be higher for Ar atoms, resulting in a higher pressure in the Ar flask.
(c) False. The average speed of gas particles is determined by their mass and temperature. Since the temperature is the same for both gases, the ratio of their average speeds is given by the square root of the ratio of their molar masses. The molar mass of N2 is about 28 g/mol, while the molar mass of Ar is about 40 g/mol. Taking the square root of the ratio (28/40), we find that the average speed of N2 molecules is slightly higher than the average speed of Ar atoms. Therefore, N2 molecules have a greater average speed than Ar atoms.
(d) False. The frequency of gas molecule/atom collisions with the walls of the container is related to the speed and the cross-sectional area of the particles. Since the cross-sectional area of N2 molecules and Ar atoms is similar, the frequency of collisions will depend primarily on their respective speeds. As explained in the previous answer, the average speed of N2 molecules is slightly higher than the average speed of Ar atoms. Therefore, N2 molecules collide less frequently with the walls of the flask compared to Ar atoms.