Determine the root-mean-square velocity of oxygen molecules at a temperature of 20 ° C.

Determine the root-mean-square velocity of oxygen molecules at a temperature of 20 ° C. At what temperature this speed will be equal to 500m / s.

From the molecular kinetic theory, the formula for the mean square velocity of molecules is known:

v = √3RT / M R – universal gas constant, T – temperature, M – molar mass.

T = 273 + 20 = 293 K.

An oxygen molecule consists of two atoms, its molar mass will be:

M = 2 * 8 * 10 ^ (- 3) = 16 * (10) ^ (- 3) kg.

Then:

v = √3 * 8.31 * 293/16 * 10 ^ (- 3) = 675.7 m / s.

Let’s express the temperature:

T = v ^ 2 * M / 3R = 500 * 16 * 10 ^ (- 3) / 3 * 8.31 = 160 K.

160K = 160 – 273 = -113 C.

Answer: the desired temperature is -113 C.