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At the same temperature and pressure, which one of the following gases will have the highest kinetic energy per mole?
(A) Hydrogen
(B) Oxygen
(C) Methane
(D) All of the above

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Last updated date: 30th May 2024
Total views: 47.7k
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Answer
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Hint: Think about the concept of moles and how it will influence the kinetic energy. Also, consider the formula for kinetic energy and what other factors influence it.

Complete step by step solution:
The kinetic energy here is defined as the sum of the kinetic energies of all the individual molecules that are present in a certain volume. We know that this total kinetic energy is defined to be proportional to the average ambient temperature of the substance. The formula to calculate the total kinetic energy is:
\[KE=\dfrac{3}{2}nRT\]
Where, $KE$ is the total kinetic energy,
$n$ is the number of moles of the substance present,
$R$ is the universal gas constant, and
$T$ is the temperature of the substance.
Now, looking at the problem, one mole of each gas is present at the same temperature and pressure.
We know that one mole of any substance contains the same number of molecules; which is equal to the Avogadro’s number $6.023\times {{10}^{23}}$. Thus, the formula will be modified to:
\[KE=\dfrac{3}{2}RT\]
Since the number of molecules is the same, any difference in the properties of one mole of the given substance will only be due to the difference in the molecular and molar masses of the substances. But from the formula, we can see that the total kinetic energy does not depend on the molecular or molar mass at all and only depends on the temperature. It has been given the problem that the temperature is the same for all the substances; so, the total kinetic energy of one mole of all the substances given will be the same.

Hence, the answer to this question is ‘D. All of the above’

Note: Remember that this kinetic energy is not the average energy of each molecule present. To obtain that, you will have to divide the total kinetic energy by the number of molecules that are present.