Question

how much faster does a helium atom travel faster than a nitrogen molecule at the same temperature?
Answered by hqwq
Bot---Doesn't a He atom move faster than a N2 atom?
Answered by hqwq
Given that the He atoms move faster than N2 atoms then how much faster does a He atom move than a N2 atom.
Answered by hqwq
That's right.
(rate He/rate N2) = sqrt (molar mass N2/molar mass He)
(rate He/rate N2 = sqrt (28/4)
rate He/rate N2 = sqrt 7 = 2.64. Therefore,
rate He = 2.64*rate N2.
Answered by GPT 3.5
At the same temperature, the average velocity of gas particles is directly proportional to the square root of their mass.

The mass of a helium atom (He) is approximately 4 atomic mass units (amu), while the mass of a nitrogen molecule (N2) is approximately 28 amu.

Therefore, the square root of the ratio of their masses is:

√(4/28) ≈ 0.377

This means that, at the same temperature, a helium atom would travel approximately 0.377 times faster than a nitrogen molecule.
Answered by GPT 3.5
Apologies for the confusion. Yes, a helium atom does move faster than a nitrogen molecule at the same temperature. The average velocity of gas particles at a given temperature is directly proportional to the square root of their mass. Since helium has a lower mass compared to nitrogen, helium atoms would, on average, have a higher velocity or speed than nitrogen molecules at the same temperature.
Answered by GPT 3.5
To compare the speeds of helium (He) and nitrogen (N2) molecules, we can use the root-mean-square (RMS) speed formula:

v_rms = √(3kT/m)

where v_rms is the RMS speed, k is the Boltzmann constant, T is the temperature in Kelvin, and m is the mass of the molecule.

The mass of a helium atom (He) is approximately 4 atomic mass units (amu), while the mass of a nitrogen molecule (N2) is approximately 28 amu.

Assuming the temperature (T) is the same, we can calculate the ratio of the RMS speeds:

(v_rms He) / (v_rms N2) = √((3kT/m He) / (3kT/m N2))
= √(m N2 / m He)

Substituting the masses gives:

(v_rms He) / (v_rms N2) = √(28 amu / 4 amu)
= √7

Therefore, a helium atom would move approximately √7 times faster than a nitrogen molecule at the same temperature.
Answered by GPT 3.5
Apologies for the earlier confusion. Yes, you are correct. The ratio of the speeds can be calculated as the square root of the ratio of the molar masses:

(rate He / rate N2) = √(molar mass N2 / molar mass He)
(rate He / rate N2) = √(28 / 4)
(rate He / rate N2) = √7 ≈ 2.64

Thus, the helium atom would move approximately 2.64 times faster than the nitrogen molecule. Thank you for providing the correct calculation.