Question

Compare the average kinetic energy at room temperature of a nitrogen molecule to that of an oxygen molecule. Which has the larger kinetic energy? a) oxygen molecule c) They have the same kinetic energy. b) nitrogen molecule d) It depends on the pressure.

Short answer

Answer: c) They have the same kinetic energy.

Step-by-step solution

Recall the equation for average kinetic energy

The equation for the average kinetic energy (K.E) of a gas molecule is given by: K.E = (3/2) * k * T Where k is the Boltzmann constant (1.38 * 10^{-23} J/K) and T is the temperature in Kelvin.

Convert room temperature to Kelvin

Room temperature is typically considered to be 20 degrees Celsius, which needs to be converted to Kelvin for the equation. To convert it to Kelvin, simply add 273.15 to the temperature in Celsius: T = 20 + 273.15 = 293.15 K

Calculate the average kinetic energy for both molecules

Now, we can use the average kinetic energy equation for both nitrogen and oxygen molecules at room temperature: K.E_N2 = (3/2) * k * T K.E_O2 = (3/2) * k * T Since both gas molecules are at the same temperature, their average kinetic energies are determined by the same value of T and k in the equation. Therefore, we can conclude that: K.E_N2 = K.E_O2

Compare the average kinetic energies and choose the correct answer

Since the average kinetic energies of the nitrogen and oxygen molecules are the same at room temperature, the correct answer is: c) They have the same kinetic energy.