Question

The correct order of total number of atoms present in
(A) 2 moles of cyclohexane
(B) 684 g of sucrose
(C) 90.8 L of dihydrogen at STP
is:

• A. C > A > B
• B. C > B > A
• C. B > C > A
• D. B > A > C

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
To compare the total number of atoms across different substances, we first need to convert their given amounts (moles, mass, or volume) into the number of moles of molecules. Then, multiply by the atomicity (number of atoms per molecule) and Avogadro's number ($N_A$) to find the total atom count.
Step 2: Key Formula or Approach:
Moles from mass: $n = \frac{W}{M_{w}}$
Moles from volume at STP: $n = \frac{V(\text{in L})}{22.7}$ (or $22.4$)
Total Atoms = $n \times (\text{Atoms per molecule}) \times N_A$
Step 3: Detailed Explanation:
Let's evaluate each option:
(A) 2 moles of cyclohexane
Chemical formula of cyclohexane: $\text{C}_6\text{H}_{12}$
Atoms per molecule = $6 (\text{C}) + 12 (\text{H}) = 18$ atoms/molecule.
Number of moles = 2.
Total atoms = $2 \text{ mol} \times 18 \text{ atoms/molecule} \times N_A = 36 N_A$ atoms.
(B) 684 g of sucrose
Chemical formula of sucrose: $\text{C}_{12}\text{H}_{22}\text{O}_{11}$
Molar mass of sucrose = $12(12) + 22(1) + 11(16) = 144 + 22 + 176 = 342 \text{ g/mol}$.
Atoms per molecule = $12 + 22 + 11 = 45$ atoms/molecule.
Number of moles = $\frac{684 \text{ g}}{342 \text{ g/mol}} = 2$ moles.
Total atoms = $2 \text{ mol} \times 45 \text{ atoms/molecule} \times N_A = 90 N_A$ atoms.
(C) 90.8 L of dihydrogen at STP
Chemical formula of dihydrogen: $\text{H}_2$
Atoms per molecule = 2 atoms/molecule.
Using molar volume at STP as $22.7 \text{ L/mol}$ (standard IUPAC 1 bar condition):
Number of moles = $\frac{90.8 \text{ L}}{22.7 \text{ L/mol}} = 4$ moles.
(If using old standard $22.4 \text{ L/mol}$, $n = 4.05$ moles. It won't alter the relative order).
Total atoms = $4 \text{ mol} \times 2 \text{ atoms/molecule} \times N_A = 8 N_A$ atoms.
Comparing the quantities:
(B) $90 N_A$>(A) $36 N_A$>(C) $8 N_A$.
The correct descending order is B>A>C.
Step 4: Final Answer:
The correct order is B>A>C.