Which gas would have the highest root mean square speed at the same temperature?

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Question: Which gas would have the highest root mean square speed at the same temperature? (2019)

Options:

Correct Answer: Hydrogen (H2)

Exam Year: 2019

Solution:

Hydrogen (H2) has the lowest molar mass among the given gases, thus it has the highest root mean square speed at the same temperature.

Which gas would have the highest root mean square speed at the same temperature? (2019)

Which gas would have the highest root mean square speed at the same temperature? (2019)

Step 1: Understand that root mean square speed (rms speed) is a measure of the speed of gas molecules at a given temperature.
Step 2: Know that the formula for root mean square speed is: rms speed = sqrt(3RT/M), where R is the gas constant, T is the temperature, and M is the molar mass of the gas.
Step 3: Realize that at the same temperature (T), the rms speed depends on the molar mass (M) of the gas.
Step 4: Remember that a lower molar mass means a higher rms speed.
Step 5: Identify the gases in the question and find their molar masses.
Step 6: Compare the molar masses of the gases. The gas with the lowest molar mass will have the highest rms speed.
Step 7: Conclude that Hydrogen (H2) has the lowest molar mass among the gases, so it has the highest root mean square speed at the same temperature.

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