Question

Molar mass of Ne atom is ten times of ${{\text{H}}_{\text{2}}}$molecule. Which of the following statement is/are true?
(This question has multiple correct options)
a.) Both these gases have the same kinetic energy at ${\text{27}^o}$.
b.) ${{\text{H}}_{\text{2}}}$ molecule will travel 10 times faster than a Ne atom at the same temperature.
c.) Pressure of 1 mole Ne atom and 1 mole ${{\text{H}}_{\text{2}}}$ molecules will be the same.
d.) Ten mole of ${{\text{H}}_{\text{2}}}$ and 1 mole of Ne will have the same volume at a temperature of ${\text{27}^o}$.

Answer 1

Hint: To solve this problem, you need to know some important relations of molecules. You need to know the formula for the average kinetic energy, that is, $\dfrac{{\text{3}}}{{\text{2}}}{\text{kT}}$. Also, you need to know the RMS speed of molecule, that is $\sqrt {\dfrac{{{\text{3kT}}}}{{\text{m}}}} $ and the ideal gas equation ${\text{pv = nRT}}$.

Complete step by step answer:
Let us check each options one by one:
In the option (a), we know that the formula for kinetic energy. From the formula$\dfrac{{\text{3}}}{{\text{2}}}{\text{kT}}$, it is clear that kinetic energy is independent of molar mass and depends only on temperature. So, the option (a) is correct.

In the option (b), we know the formula for the RMS speed of the molecule. According to the RMS speed formula, ${{\text{H}}_{\text{2}}}$ molecule will travel $\sqrt {{\text{10}}} $ times faster than Ne atom at same temperature. So, option (b) is not true.

In the option (c), since the pressure is independent of molar mass according to the ideal gas equation. So, option (c) is true.

In the option (d), we know that volume is independent of the molar mass of the gas but it depends on the number of moles according to the ideal gas equation. So, option (d) is not true.
So, the correct answer is “Option A and C”.

Note: Do not get confused between molar mass and number of moles as they are two different quantities. The unit of molar mass is "g" and the number of moles is just a number. However the mass of 1 mole of an atom is its molar mass.