At 200 K, the molecules or atoms of an unknown gas, X, have an average velocity equal to that of Ar atoms at 400 K. What is X? (Assume ideal behavior.)

Question

Quizplus · Accepted Answer

The average velocity of gas molecules is inversely proportional to the square root of their molar mass and directly proportional to the square root of the temperature. Since the average velocity of gas X at 200 K is equal to that of Ar at 400 K, the molar mass of X must be four times that of Ar (since 400/200 = 2 and 2^2 = 4). Argon has a molar mass of approximately 40 g/mol, so X must have a molar mass of about 160 g/mol. HF has a molar mass of approximately 20 g/mol, which is incorrect. Upon reevaluation, the correct choice should be HBr, which has a molar mass close to 80 g/mol, fitting the conditions given.

At 200 K, the Molecules or Atoms of an Unknown