A sealed container holds equal masses of hydrogen and oxygen at the same temperature. Using the kinetic interpretation of temperature, what conclusion can be drawn about the average kinetic energy and speed of the two types of gas molecules?
Both gases have equal mean kinetic energies, but the lighter hydrogen molecules maintain a higher average speed.
To understand the problem of comparing the average kinetic energy and speed of gas molecules, let's delve into the kinetic theory of gases. According to this theory, the temperature of a gas is directly proportional to the average kinetic energy of the molecules.
The formula for the average kinetic energy of gas molecules in a container is given by:
E_{\text{avg}} = \frac{3}{2}kT
where E_{\text{avg}} is the average kinetic energy, k is the Boltzmann constant, and T is the absolute temperature.
Since both gases in the container are at the same temperature, according to the formula, their mean kinetic energies will be the same, irrespective of the type of gas.
Next, let's analyze the average speed of the gas molecules. The formula for the root mean square (rms) speed is given by:
v_{\text{rms}} = \sqrt{\frac{3kT}{m}}
where m is the mass of a single molecule. Given that the molar mass of hydrogen is much less than that of oxygen, the hydrogen molecules will have a higher rms speed compared to the heavier oxygen molecules because:
The lower the mass of a molecule, the higher the speed, provided temperature remains constant.
Therefore, the correct and logical conclusion is:
Both gases have equal mean kinetic energies, but the lighter hydrogen molecules maintain a higher average speed.
Thus, the correct answer to the given question is: Both gases have equal mean kinetic energies, but the lighter hydrogen molecules maintain a higher average speed.
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