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

Concept: Total number of atoms depends on number of moles of molecules and number of atoms per molecule. \[ \text{Total atoms} = (\text{moles of molecules}) \times (\text{atoms per molecule}) \]
Step 1: Case (I) Hydrogen gas \[ \text{Moles of } H_2 = \frac{90.8}{22.7} = 4 \] Each molecule has 2 atoms. \[ \text{Moles of atoms} = 4 \times 2 = 8 \]
Step 2: Case (II) Sucrose \(C_{12}H_{22}O_{11}\) Molar mass \(= 342\) \[ \text{Moles} = \frac{684}{342} = 2 \] Atoms in one molecule: \[ 12 + 22 + 11 = 45 \] \[ \text{Total atoms} = 45 \times 2 = 90 \]
Step 3: Case (III) Cyclohexane \(C_6H_{12}\) Atoms per molecule: \[ 6 + 12 = 18 \] \[ \text{Total atoms} = 2 \times 18 = 36 \]
Step 4: Compare \[ 90 > 36 > 8 \] Thus, \[ (II) > (III) > (I) \]