Q. What is the RMS speed of an ideal gas in terms of its temperature and molar mass?
A.sqrt((3RT)/M)
B.sqrt((2RT)/M)
C.sqrt((RT)/M)
D.sqrt((3M)/RT)
Solution
The RMS speed (v_rms) of an ideal gas is given by the formula v_rms = sqrt((3RT)/M), where R is the universal gas constant, T is the absolute temperature, and M is the molar mass.
Q. What is the RMS speed of an ideal gas in terms of temperature and molar mass?
A.sqrt((3RT)/M)
B.sqrt((RT)/M)
C.sqrt((3kT)/m)
D.sqrt((2RT)/M)
Solution
The RMS speed (v_rms) of an ideal gas is given by the formula v_rms = sqrt((3RT)/M), where R is the universal gas constant, T is the temperature in Kelvin, and M is the molar mass.
Q. What is the root mean square speed of gas molecules at temperature T?
A.(3RT/M)^0.5
B.(RT/M)^0.5
C.(2RT/M)^0.5
D.(RT/3M)^0.5
Solution
The root mean square speed (v_rms) is given by the formula v_rms = (3RT/M)^0.5, where R is the gas constant, T is the temperature, and M is the molar mass.
Q. What is the root mean square speed of gas molecules directly proportional to?
A.The square root of the temperature.
B.The square of the temperature.
C.The mass of the gas molecules.
D.The volume of the gas.
Solution
The root mean square speed of gas molecules is directly proportional to the square root of the absolute temperature, as given by the equation v_rms = sqrt(3kT/m).
Correct Answer: A — The square root of the temperature.
Q. What is the root mean square speed of gas molecules in a container at temperature T?
A.sqrt(3kT/m)
B.sqrt(2kT/m)
C.sqrt(kT/m)
D.sqrt(3RT/M)
Solution
The root mean square speed (v_rms) is given by the formula v_rms = sqrt(3kT/m) where k is the Boltzmann constant, T is the temperature, and m is the mass of a gas molecule.
Q. What is the root mean square speed of gas molecules in an ideal gas at temperature T?
A.sqrt(3RT/M)
B.sqrt(2RT/M)
C.sqrt(RT/M)
D.sqrt(3kT/m)
Solution
The root mean square speed (v_rms) is given by the formula v_rms = sqrt(3RT/M), where R is the gas constant, T is the temperature, and M is the molar mass.
Q. Which of the following gases has the highest RMS speed at the same temperature?
A.Oxygen (O2)
B.Nitrogen (N2)
C.Hydrogen (H2)
D.Carbon Dioxide (CO2)
Solution
RMS speed is inversely proportional to the square root of molar mass. Hydrogen (H2) has the lowest molar mass among the options, thus it has the highest RMS speed.
Q. Which of the following gases will have the highest root mean square speed at the same temperature?
A.O2
B.N2
C.H2
D.CO2
Solution
The root mean square speed is inversely proportional to the square root of the molar mass. H2 has the lowest molar mass, hence it has the highest root mean square speed.
Q. Which of the following gases would have the highest average speed at a given temperature?
A.Oxygen (O2)
B.Nitrogen (N2)
C.Hydrogen (H2)
D.Carbon Dioxide (CO2)
Solution
At a given temperature, lighter gases like hydrogen (H2) have higher average speeds compared to heavier gases like oxygen (O2) or carbon dioxide (CO2).
Q. Which of the following gases would have the highest root mean square speed at the same temperature?
A.Oxygen (O2)
B.Nitrogen (N2)
C.Hydrogen (H2)
D.Carbon Dioxide (CO2)
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.