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NEET 2022 - Target Batch - Aryan Raj Singh
To view explanation, please take trial in the course below.
NEET 2022 - Target Batch - Aryan Raj Singh
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The average kinetic energy of oxygen molecules and hydrogen molecules will be the same at any particular temperature. If we keep in mind that the formula for kinetic energy is 0.5mv2 it stands to reason that the lighter molecules(hydrogen) will have a greater speed than the oxygen molecules.
Since the average kinetic energy of oxygen and hydrogen are equal we can write the expression below.
However the molecular mass of oxygen is 32 and that of hydrogen is 2. So we can rewrite the above expression
Transforming the formula we obtain the expression below which gives the ratio of the average velocities of oxygen and hydrogen molecules
The average velocity of hydrogen molecules is 4 times greater than that of oxygen molecules.
It is important to note that although the average kinetic energy of all gases is the same at a particular temperature, the average velocity of the molecules is not. The heavier molecules tend to travel slower relative to the lighter ones.
Page 2
b) Draw a curve to show the distribution of energies for 2 mole of gas at 300 K
Student answer
Click the above link to see a possible student answer. Is the student's answer sufficient for 2 marks? If not what are the errors that you can point to.
Solution
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The correct answer is option 1) i.e. 1 : 1.
CONCEPT:
- The kinetic energy of gas: There are no attractive forces between the gas molecules of an ideal gas, and there is no rotation or vibration within these molecules.
- The kinetic energy due to the translational motion of an ideal gas is dependent on its temperature.
- The average kinetic energy per molecule of a gas is given by:
Where T is the temperature of the gas IN Kelvin and kB is the Boltzmann's constant (1.38 × 10-23 J/K)
CALCULATION:
Given that both hydrogen and oxygen molecules are at the same temperature:
⇒ KE ∝ T
The kinetic energy of H2,
The kinetic energy of O2,
Ratio =
Stay updated with the Physics questions & answers with Testbook. Know more about The Kinetic Theory of Gases and ace the concept of Translational Kinetic Energy.
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