Answer :
In a tank of mixed gases, consisting of H₂, N₂, Ar, and H₂O, is held at a constant temperature. The gas has the highest average velocity is H₂.
The velocity of all gas particles is inversely proportional to the molecular weight of the gas. Light gases have higher kinetic energy than heavy gases. From the list given, with an atomic mass of 2, N₂ with an atomic mass of 28, Ar with an atomic mass of 40, and H₂O with an atomic mass of 18. H₂ is the lightest of the four gases, and therefore the lightest. Velocity contributes to the kinetic energy of the particles.
Gas particles are always in motion, and all moving objects have kinetic energy (Ek). Molecules in a sample of gas share an average kinetic energy. However, individual molecules exhibit a kinetic energy distribution due to their velocity distribution. This velocity distribution arises from the collisions that occur between molecules in the gas phase. Although these collisions are elastic (no net loss of energy), the individual velocities of each molecule involved in the collision can change.
Kinetic molecule theory states that the average kinetic energy of gas particles is proportional to the absolute temperature of the gas. This can be expressed by the following equation, where k is the Boltzmann constant. The Boltzmann constant is simply the gas constant R divided by the Avogadro constant (NA). Bars above specific terms indicate that these are averages.
Ek = 3/2 (KT)
Since the average kinetic energy is related to both absolute temperature and molecular velocity, the above equation can be combined with the previous one to find the effective velocity.
Ek = 1/2(mu²) = 3/2 (KT)
=√u² =√(3KT/m)
This shows that the RMS velocity is related to temperature. This equation can be manipulated further by multiplying the numerator and denominator by the Avogadro constant (NA) to obtain a form using the gas constant (R) and molar mass (M).
√u² =√(3Rt/m)
The form of this equation shows that the effective velocity of gas molecules is also related to the molar mass of matter. Comparing two gases of different molar masses at the same temperature shows that the gas with the lower molar mass has a higher effective velocity, even though they have the same average kinetic energy.
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