Helium atom is two times heavier than a hydrogen molecule. At 298 K, t...
Average kinetic energy depends only on temperature and does not depend upon the nature of the gas.
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Helium atom is two times heavier than a hydrogen molecule. At 298 K, t...
Average kinetic energy of gas molecules = 3/2 KT , it is independent of mass . Hence, the average kinetic energy of helium atom will be same to that of hydrogen molecule.
Helium atom is two times heavier than a hydrogen molecule. At 298 K, t...
Explanation:
Kinetic energy is directly proportional to the temperature and molecular weight of the gas. The formula for kinetic energy is KE = (3/2)RT, where R is the gas constant and T is the temperature.
Heading: Calculation of average kinetic energy of a helium atom
- The molecular weight of helium is 4 g/mol, and that of hydrogen is 2 g/mol.
- Therefore, the helium atom is two times heavier than the hydrogen molecule.
- However, the temperature of the gas is given as 298 K.
Heading: Comparison of kinetic energy between helium and hydrogen
- As stated earlier, the formula for kinetic energy is KE = (3/2)RT.
- Since the temperature is the same for both gases, we can compare their kinetic energies based on their molecular weight.
- The kinetic energy of a helium atom will be (3/2)RT, where R is the gas constant and T is the temperature.
- Similarly, the kinetic energy of a hydrogen molecule will be (3/4)RT, since it has two atoms.
- Therefore, the ratio of kinetic energies between helium and hydrogen will be:
KE(He)/KE(H2) = [(3/2)RT]/[(3/4)RT]
KE(He)/KE(H2) = 2
- From the above calculation, we can see that the kinetic energy of a helium atom is twice that of a hydrogen molecule.
Heading: Answer to the question
- The question asks for the average kinetic energy of a helium atom at 298 K, compared to that of a hydrogen molecule.
- Based on the above calculation, we can see that the kinetic energy of a helium atom is two times that of a hydrogen molecule.
- Therefore, the correct answer is option B - same as that of a hydrogen molecule.