Question

Molar mass of a Ne atom is ten times of ${{H}_{2}}$molecule. Which of the following statements is/are true?
This question has multiple correct options
A. Both these gases have same kinetic energy at ${{27}^{\circ }}C$
B. ${{H}_{2}}$ molecules will travel 10 times faster than Ne atoms at the same temperature.
C. Pressure of 1 mole Ne and 1 mole ${{H}_{2}}$molecules will be the same.
D. Ten mole of${{H}_{2}}$ and 1 mole of Ne will have same volume at a temperature of ${{27}^{\circ }}C$

Answer 1

Hint: Molar mass is the mass of the sample of that compound divided by the amount of substance in that sample, it is measured in moles. We see that the molar mass of neon is 20.17 u and that of hydrogen is 1.0078 u. So, we can say that the molar mass of Ne atom is ten times of ${{H}_{2}}$molecule

Complete answer:
A. Let’s discuss about option (a), we know that kinetic energy is related to temperature by the equation:
\[K.E=\frac{3}{2}\times {{K}_{b}}\times T\]
Where, ${{K}_{b}}$ is a constant and T is the temperature. Here, we can see that the value 3/2 and${{K}_{b}}$ are constant and hence kinetic energy is dependent on temperature and here both neon and hydrogen have the same temperature. Hence, this is the correct option.
Let's discuss option(b) , here we can apply the formula of rate of diffusion, that is rate of diffusion is inversely proportional to square root of molecular weight. Now, we can see that the ratio of rate of diffusion of hydrogen to that of neon is:
\[r\propto \frac{1}{\sqrt{{{M}_{w}}}}\]
Where, r is the rate of diffusion and is the molecular weight
\[\frac{{{r}_{{{H}_{2}}}}}{{{r}_{Ne}}}=\sqrt{\frac{10}{1}}\]
So, the rate of hydrogen is $\sqrt{\frac{10}{1}}$ times more than that of Neon. And therefore we can say that the option is incorrect.
C. Here in option(c), standard temperature and pressure of both are given the same and moles of both are the same, standard temperature is 273k and pressure is 1 atm. Both are given the same mole hence this statement is correct.

D. Let’s discuss statement (d), according to mole concept, the value of 1 mole of anything will be 22.4 L litre only. Here 1 mole of Ne is given that is equal to 22.4 L, and we know that 1mole of ${{H}_{2}}$ will be also 22.4 L, but in statement it is said that 10 mole of ${{H}_{2}}$ will have same volume, which is incorrect because 10 litres will have volume equal to 22.4 $\times $10 litre that is equal to 224 L.

Hence, we can conclude that the statements (a) and (c) are correct statements.

Note: Here, we can see that both hydrogen and neon are gases and hence many of the properties of both are the same.
- We should not get confused in terms of molar mass and molecular mass. Molecular mass is the sum of all atoms in a molecule. Whereas, molar mass is the mass of a sample of a compound divided by the amount of substance present in that sample.