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Question:

An HCl molecule has rotational, translational, and vibrational motions. If the rms velocity of HCl molecules in its gaseous phase is v, m is its mass, and k_B is the Boltzmann constant, then its temperature will be:

m v ^ 2 6 k _ B

m v ^ 2 3 k _ B

m v ^ 2 5 k _ B

m v ^ 2 7 k _ B

Solution:

Correct option is C. m v ^ 2 / 3 k _ B
V_rms = v = √(3 k_B T/m) ⇒ T = m v^2 / 3 k_B