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:
Total atoms can be calculated by finding the number of moles of each substance, multiplying by the number of molecules per mole (Avogadro's number, \( N_A \)), and then multiplying by the "atomicity" (number of atoms in one molecule).

Step 2: Key Formula or Approach:
1. Moles \( n = \frac{\text{Mass}}{\text{Molar Mass}} \) or \( \frac{\text{Volume at STP}}{22.7 \text{ L/mol}} \).
2. Total atoms = \( n \times N_A \times \text{atomicity} \).

Step 3: Detailed Explanation:
(A) 2 moles of cyclohexane (\( C_6H_{12} \)):
Atomicity = \( 6 + 12 = 18 \).
Total atoms = \( 2 \times 18 \times N_A = 36 N_A \).
(B) 684 g of sucrose (\( C_{12}H_{22}O_{11} \)):
Molar mass = \( 12 \times 12 + 22 \times 1 + 11 \times 16 = 342 \text{ g/mol} \).
Moles = \( 684 / 342 = 2 \text{ moles} \).
Atomicity = \( 12 + 22 + 11 = 45 \).
Total atoms = \( 2 \times 45 \times N_A = 90 N_A \).
(C) 90.8 L of dihydrogen (\( H_2 \)) at STP:
Using 22.7 L/mol as standard volume at STP:
Moles = \( 90.8 / 22.7 = 4 \text{ moles} \).
Atomicity = 2.
Total atoms = \( 4 \times 2 \times N_A = 8 N_A \).
Comparing the counts: \( 90 N_A (B)>36 N_A (A)>8 N_A (C) \).

Step 4: Final Answer:
The order is B > A > C.