Freon-12, CF₂Cl₂, which has been widely used in air conditioning systems, is considered a threat to the ozone layer in the stratosphere. Calculate the root-mean-square velocity of Freon-12 molecules in the lower stratosphere where the temperature is -65°C.

Question

Quizplus · Accepted Answer

The root-mean-square velocity of a gas molecule is given by the formula,

vrms = ((3kT)/m)^1/2

where k is the Boltzmann constant, T is the temperature in Kelvin, and m is the molar mass of the gas.

First, we need to convert the temperature from Celsius to Kelvin.

T = -65°C + 273.15 = 208.15 K

The molar mass of Freon-12 is 120.91 g/mol or 0.12091 kg/mol. Using this, and the given formula, we get:

vrms = ((3kT)/m)^1/2
     = ((3 * 1.38 x 10^-23 J/K * 208.15 K) / 0.12091 kg)^1/2
     = 207 m/s

Therefore, the correct answer is choice C.

Freon-12, CF2Cl2, Which Has Been Widely Used in Air Conditioning

Freon-12, CF₂Cl₂, Which Has Been Widely Used in Air Conditioning