Question

Which gas among the following contains maximum number of molecules at STP ?
(Molar masses in g mol$^{-1}$: CO$_2$ = 44, Ar = 39.9, CH$_4$ = 16, O$_2$ = 32)

• A. $24.0$ g of $\mathrm{O_2}$
• B. $16.0$ g of $\mathrm{CH_4}$
• C. $13.3$ g of $\mathrm{Ar}$
• D. $11$ g of $\mathrm{CO_2}$

Hint:

At the same conditions, number of molecules depends only on the number of moles, not on the nature of the gas.

Answer 1

The Correct Option is B

Step 1: Relation between moles and number of molecules.
The number of molecules present in a gas sample is directly proportional to the number of moles present.

Step 2: Calculation of moles for each option.
\[ \text{Moles of } \mathrm{O_2} = \frac{24.0}{32} = 0.75 \] \[ \text{Moles of } \mathrm{CH_4} = \frac{16.0}{16} = 1.0 \] \[ \text{Moles of } \mathrm{Ar} = \frac{13.3}{39.9} \approx 0.33 \] \[ \text{Moles of } \mathrm{CO_2} = \frac{11}{44} = 0.25 \]
Step 3: Comparison.
The sample containing the highest number of moles will have the maximum number of molecules. Here, $16.0$ g of $\mathrm{CH_4}$ has the highest number of moles.

Step 4: Conclusion.
Therefore, the gas sample with the maximum number of molecules is $16.0$ g of $\mathrm{CH_4$}.