Question

Which sample of oxygen gas contains molecules with the fastest average speed?

A. 1.73 x 10^5 J

B. 2.73 x 10^3 J

C. 5.06 x 10^4 J

D. 1.50 x 10^4 J

Answer 1

A. 1.73 x 10^5 J

Step-by-step explanation:

The internal energy of a gas is related to the average speed of the molecules of the gas. In fact:

- The internal energy, U, is directly proportional to the temperature of the gas, T, according to

`U=(3)/(2)nRT`

- The temperature of the gas, T, is proportional to the square of the average speed of the molecules, v, according to

`(3)/(2)kT=(1)/(2)mv^2`

where both terms represent the average kinetic energy of the molecules.

- Therefore, we can conclude that the higher the internal energy, the faster the average speed of the molecules: among the choices given, the sample with highest internal energy is sample A.