Nitrogen molecules are 14 times more massive than hydrogen molecules. If sample – [Free] B49
Nitrogen molecules are 14 times more massive than hydrogen molecules. If samples of these two gases are at the same temperature, what must be true about the motion of the molecules? (There may be more than one correct choice.) Check all that apply. The rms molecular speed is the same for both gases.The average kinetic energy is the same for both gases.The rms speed of the hydrogen molecules is 1–√4 times greater than that of the nitrogen molecules.The rms speed of the hydrogen molecules is 14 times greater than that of the nitrogen molecules.
Gas Molecule Motion Comparison
Question:
Nitrogen molecules are 14 times more massive than hydrogen molecules. If samples of these two gases are at the same temperature, what must be true about the motion of the molecules? (There may be more than one correct choice.)
- The rms molecular speed is the same for both gases.
- The average kinetic energy is the same for both gases.
- The rms speed of the hydrogen molecules is √14 times greater than that of the nitrogen molecules.
- The rms speed of the hydrogen molecules is 14 times greater than that of the nitrogen molecules.
Answer and Explanation:
✔️ The average kinetic energy is the same for both gases.
✔️ The rms speed of the hydrogen molecules is √14 times greater than that of the nitrogen molecules.
✖️ The rms molecular speed is the same for both gases.
✖️ The rms speed of the hydrogen molecules is 14 times greater than that of the nitrogen molecules.
Explanation:
At the same temperature, the average kinetic energy for all ideal gas molecules is given by:
KE_avg = (3/2)·k·T
Since temperature is equal, both gases have the same kinetic energy per molecule.
However, the rms speed of a gas is inversely proportional to the square root of its molecular mass:
v_rms = √(3kT/m)
Therefore:
v_rms(H₂) / v_rms(N₂) = √(m_N₂ / m_H₂) = √14
Hydrogen molecules move √14 times faster than nitrogen molecules.