Question: 68. Among the following, choose the ones with equal number of atoms.A. 212 g of \mathrm{Na}_{2} \mathrm{CO}_{3}(\mathrm{~s}) [molar mass =106 \mathrm{~g} ]B. 248 g of \mathrm{Na}_{2} \mathrm{O}(\mathrm{s}) [molar mass =62 \mathrm{~g} ]
C. 240 g of \mathrm{NaOH}(\mathrm{s}) [molar mass =40 \mathrm{~g} ]
D. 12 g of \mathrm{H}_{2}(\mathrm{~g}) [molar mass =2 \mathrm{~g} ]
E. 220 g of \mathrm{CO}_{2}(\mathrm{~g}) [molar mass \left.=44 \mathrm{~g}\right]
Choose the correct answer from the options given below:
(1) A, B, and C only
(2) A, B, and D only
(3) B, C, and D only
(4) B, D, and E only
Answer: Option (2)
Explanation:
To compare the number of atoms, we first calculate the number of moles of each substance using:
\text{Number of moles} = \frac{\text{Given mass}}{\text{Molar mass}}A. \mathrm{Na}_{2} \mathrm{CO}_{3}
\text{Moles} = \frac{212}{106} = 2Each formula unit contains:
2 \mathrm{Na} + 1 \mathrm{C} + 3 \mathrm{O} = 6 \text{ atoms}Total atoms:
2 \times 6 = 12 \text{ moles of atoms}B. \mathrm{Na}_{2} \mathrm{O}
\text{Moles} = \frac{248}{62} = 4Each formula unit contains:
2 \mathrm{Na} + 1 \mathrm{O} = 3 \text{ atoms}Total atoms:
4 \times 3 = 12 \text{ moles of atoms}C. \mathrm{NaOH}
\text{Moles} = \frac{240}{40} = 6Each formula unit contains:
1 \mathrm{Na} + 1 \mathrm{O} + 1 \mathrm{H} = 3 \text{ atoms}Total atoms:
6 \times 3 = 18 \text{ moles of atoms}D. \mathrm{H}_{2}
\text{Moles} = \frac{12}{2} = 6Each molecule contains:
2 \text{ atoms}Total atoms:
6 \times 2 = 12 \text{ moles of atoms}E. \mathrm{CO}_{2}
\text{Moles} = \frac{220}{44} = 5Each molecule contains:
1 \mathrm{C} + 2 \mathrm{O} = 3 \text{ atoms}Total atoms:
5 \times 3 = 15 \text{ moles of atoms}Thus, A, B, and D each contain 12 \text{ moles of atoms}.
Therefore, the correct answer is Option (2).