Which of the following gases would have the highest root mean square speed at the same temperature?
Practice Questions
1 question
Q1
Which of the following gases would have the highest root mean square speed at the same temperature?
Oxygen (O2)
Nitrogen (N2)
Hydrogen (H2)
Carbon Dioxide (CO2)
Hydrogen (H2) has the lowest molar mass among the given gases, thus it will have the highest root mean square speed at the same temperature, as v_rms is inversely proportional to the square root of molar mass.
Questions & Step-by-step Solutions
1 item
Q
Q: Which of the following gases would have the highest root mean square speed at the same temperature?
Solution: Hydrogen (H2) has the lowest molar mass among the given gases, thus it will have the highest root mean square speed at the same temperature, as v_rms is inversely proportional to the square root of molar mass.
Steps: 6
Step 1: Understand that root mean square speed (v_rms) is a measure of the speed of gas molecules.
Step 2: Know that the formula for v_rms is v_rms = sqrt(3RT/M), where R is the gas constant, T is the temperature, and M is the molar mass of the gas.
Step 3: Recognize that as the molar mass (M) decreases, the root mean square speed (v_rms) increases.
Step 4: Identify the gases given in the question and find their molar masses.
Step 5: Compare the molar masses of the gases; the gas with the lowest molar mass will have the highest v_rms.
Step 6: 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.
