Question

At what temperature will the molar kinetic energy of \[0.3\]mol of helium be the same as that of \[0.4\]mol of argon at \[400\]K?
A. \[700K\]
B. \[533K\]
C. \[800K\]
D. \[400K\]

Answer 1

Hint: We need to know that the energy is mainly divided into two types and that is kinetic energy and potential energy. The kinetic energy is formed by moving an object. For example, when the earth moves around the sun, there is a kinetic energy. And the molecules present in space are always moving. Hence, all the moving particles have a kinetic energy. The helium is a chemical compound having the formula, $'He'$ with atomic number two. And the argon is a chemical element with atomic number\[18\] having the symbol $'Ar'$.

Complete answer:
According to the question, the number of moles of helium is equal to \[0.3\] and the number of moles of argon is equal to \[0.4\].
Hence, the temperature will the molar kinetic energy of \[0.3\]mol of helium be the same as that of \[0.4\]mol of argon at\[400\]K can be find out by using the formula,
\[K.E = \dfrac{3}{2}nRT\]
Where, n is equal to the number of moles of helium and argon. R Is the universal gas constant and the T is equal to temperature. Given the temperature of argon is equal to \[400\]K. Substitute the value of temperature in the above equation will get,
\[{\left[ {\dfrac{3}{2} \times 0.3 \times R \times T} \right]_{Helium}} = {\left[ {\dfrac{3}{2} \times 0.4 \times R \times 400} \right]_{Argon}}\]
By simplifying the above equation, will get;
\[T = 533K\]

So, the correct answer is “Option B”.

Note:
We have to know that the average kinetic energy of the particles present in the substance is directly proportional to the kelvin temperature of that substance. The average kinetic energy of the molecules of any gas with the same temperature are always the same. And the average kinetic energy of all the molecules present in a substance is defined as a temperature.