In a sample of air at STP, the ratio of the root-mean-square velocity of O₂ to that of N₂, that is urms(O₂)/urms(N₂), is equal to ________.

Question

Quizplus · Accepted Answer

The root-mean-square velocity of a gas is given by urms = sqrt(3kT/m), where k is the Boltzmann constant, T is the temperature in Kelvin, and m is the molar mass of the gas. According to this formula, urms is directly proportional to the square root of the temperature and inversely proportional to the square root of the molar mass. Since both gases are at the same temperature and pressure, the ratio of their urms values is only dependent on the ratio of their molar masses. The molar mass of O2 is 32 g/mol and the molar mass of N2 is 28 g/mol. Therefore, the ratio of their urms values is sqrt(28/32) = 0.94.

In a Sample of Air at STP, the Ratio of the Root-Mean-Square