Which of the following has the greatest number of molecules?

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Accepted Answer

1. **Identify the Formula:** The number of molecules ($N$) in a given mass ($m$) of a substance is calculated using the number of moles ($n$) and Avogadro's constant ($N_A \approx 6.022 	imes 10^{23} 	ext{ mol}^{-1}$).
   $$ n = \frac{	ext{Mass (g)}}{	ext{Molar Mass (g/mol)}} $$
   $$ N = n 	imes N_A $$
   [Class 12 Chemistry, Ch 1, Example 1.1; Class 11 Physics, Appendix A 3]
2. **Calculate Moles for each option:**
   - **Option A ($64	ext{ g SO}_2$):** Molar Mass of $	ext{SO}_2 = 32 + 2(16) = 64	ext{ g/mol}$.
     $$ n = \frac{64}{64} = 1	ext{ mol} \implies 1 N_A 	ext{ molecules} $$
   - **Option B ($44	ext{ g CO}_2$):** Molar Mass of $	ext{CO}_2 = 12 + 2(16) = 44	ext{ g/mol}$.
     $$ n = \frac{44}{44} = 1	ext{ mol} \implies 1 N_A 	ext{ molecules} $$
   - **Option C ($48	ext{ g O}_3$):** Molar Mass of $	ext{O}_3 = 3(16) = 48	ext{ g/mol}$.
     $$ n = \frac{48}{48} = 1	ext{ mol} \implies 1 N_A 	ext{ molecules} $$
   - **Option D ($8	ext{ g H}_2$):** Molar Mass of $	ext{H}_2 = 2(1) = 2	ext{ g/mol}$.
     $$ n = \frac{8}{2} = 4	ext{ mol} \implies 4 N_A 	ext{ molecules} $$
3. **Conclusion:** $8	ext{ g of H}_2$ contains the greatest number of molecules ($4 N_A$).

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