Question

From given data (I) 90.8 lit of \(H_2(g)\) at STP (II) 684 gm of sucrose (III) 2 moles of cyclohexane Correct order of total number of atoms will be

• A. (I) \(>\) (II) \(>\) (III)
• B. (III) \(>\) (II) \(>\) (I)
• C. (II) \(>\) (III) \(>\) (I)
• D. (I) \(>\) (III) \(>\) (II)

Answer 1

The Correct Option is C

To determine the correct order of the total number of atoms for the given data, we first need to find the number of atoms in each case:

1. Hydrogen Gas \(H_2(g)\):
   • At STP (Standard Temperature and Pressure), 1 mole of any gas occupies 22.4 liters. Therefore, 90.8 liters of \(H_2(g)\) is equivalent to: \(\text{moles of } H_2 = \frac{90.8}{22.4} \approx 4.05 \text{ moles}\)
   • Since each molecule of \(H_2\) contains 2 atoms of hydrogen, the number of atoms is: \(\text{Total H atoms} = 4.05 \text{ moles} \times 2 \times 6.022 \times 10^{23}\)
   • Calculating gives: \(\approx 4.89 \times 10^{24} \text{ atoms}\)
2. Sucrose \(C_{12}H_{22}O_{11}\):
   • Molar mass of sucrose is \(12 \times 12 + 22 \times 1 + 11 \times 16 = 342 \text{ g/mol}\).
   • Given mass is 684 g, number of moles of sucrose: \(\text{moles of sucrose} = \frac{684}{342} = 2 \text{ moles}\)
   • Total atoms in one molecule of sucrose = \(12 + 22 + 11 = 45\).
   • Total number of atoms in 2 moles of sucrose: \(2 \text{ moles} \times 45 \times 6.022 \times 10^{23}\)
   • Calculating provides: \(\approx 5.42 \times 10^{25} \text{ atoms}\)
3. Cyclohexane \(C_6H_{12}\):
   • Each molecule of cyclohexane contains \(6+12=18\) atoms.
   • For 2 moles of cyclohexane, the total atoms are: \(\text{Total atoms} = 2 \times 18 \times 6.022 \times 10^{23}\)
   • After calculating: \(\approx 2.17 \times 10^{25} \text{ atoms}\)

This leads us to the order based on the number of atoms:

• (II) Sucrose with \( \approx 5.42 \times 10^{25} \) atoms.
• (III) Cyclohexane with \( \approx 2.17 \times 10^{25} \) atoms.
• (I) Hydrogen gas with \( \approx 4.89 \times 10^{24} \) atoms.

Thus, the correct order of the total number of atoms is Option (II) \(>\) (III) \(>\) (I).