Textbook Question
At 25 °C (approximately room temperature) the rms velocity of an Ar atom in air is 1553 km/h. (c) What is the total kinetic energy of 1 mol of Ar atoms moving at this speed?
7. Gases
Kinetic Energy of Gases
Multiple Choice
Which of the following gases would have molecules with the greatest average kinetic energy at 25°C?
A
All have the same average kinetic energy
B
Helium (He)
C
Oxygen (O_2)
D
Nitrogen (N_2)
Verified step by step guidance1
Recall that the average kinetic energy of gas molecules depends only on the temperature and is independent of the type of gas. This is a key concept from the kinetic molecular theory.
Write down the formula for the average kinetic energy per molecule: \(\text{KE}_{avg} = \frac{3}{2} k_B T\), where \(k_B\) is the Boltzmann constant and \(T\) is the absolute temperature in kelvin.
Convert the given temperature from Celsius to kelvin using \(T(K) = T(^\circ C) + 273.15\). For 25°C, this becomes \$25 + 273.15 = 298.15$ K.
Note that since \(k_B\) is a constant and \(T\) is the same for all gases, the average kinetic energy \(\text{KE}_{avg}\) will be the same for helium, oxygen, and nitrogen at 25°C.
Conclude that all gases at the same temperature have the same average kinetic energy regardless of their molecular masses or identities.
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