how much faster does a helium atom travel faster than a nitrogen molecule at the same temperature?
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.
Bot---Doesn't a He atom move faster than a N2 atom?
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.
Given that the He atoms move faster than N2 atoms then how much faster does a He atom move than a N2 atom.
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.
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.
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.