Question

Which of the following contain same number of molecules?
(1) $0.1 \,mol$ of $CO _{2}$
(2) $3.2 \,g$ of $O _{2}$
(3) $0.1 \,g$-atom of helium gas
(4) $11.2\, L$ of $SO _{2}$

• A. 1, 2 and 3 are correct
• B. 1 and 2 are correct
• C. 2 and 4 are correct
• D. 1 and 3 are correct

Answer 1

Answer: (A)

1. Number of molecules in $0.1$ mole of $CO _{2}$
$=0.1 \times N_{A}=0.1\, N_{A}$
2. Number of molecules in $3.2 \, g$ of $O _{2}$
$=\frac{3.2}{32} \times N_{A}=0.1 \, N_{A}$
3. Number of molecules in $0.1\, g$-atom of He gas
$=0.1 \times N_{A}=0.1 \, N_{A}$
4. Number of molecules in $11.2\, L$ of $SO _{2}$
$=\frac{11.2}{22.4} \times \dot{N}_{A}$
$=\frac{N_{A}}{2}$
$\therefore 0.1 \,mole$ of $CO _{2}, 3.2 \, g$ of $O _{2}$ and $0.1 \, g$-atom of He gas have the same number of molecules, ie, $0.1\, N _{ A }$