In a sample of air at STP,the ratio of the root-mean-square velocity of O₂ to that of N₂,that is u_rms(O₂)/u_rms(N₂),is equal to ________. A)0.88 B)0.94 C)1.00 D)1.07 E)1.14

Question

Quizplus · Accepted Answer

The root-mean-square velocity of a gas is given by u_rms=√3kT/m, where k is the Boltzmann constant, T is the temperature, and m is the mass of the gas molecule. At STP, the temperature is 0°C or 273 K, and the molar mass of O2 is 2*16 = 32 g/mol, while that of N2 is 2*14 = 28 g/mol. Therefore, u_rms(O₂)/u_rms(N₂) = (√(3kT/mO2))/(√(3kT/mN2)) = √(mN2/mO2) = √(28/32) = 0.935 which is closest to 0.94. Therefore, the answer is B.

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