At 0°C and 1 atm pressure, the volume of nitrogen gas required to cover a sample of silica gel, assuming Langmuir monolayer adsorption, is found to be 168 cm³/g of the gel. The surface area (in m²) pe

Question

At 0°C and 1 atm pressure, the volume of nitrogen gas required to cover a sample of silica gel, assuming Langmuir monolayer adsorption, is found to be 168 cm³/g of the gel. The surface area (in m²) per gram of silica gel is (the area occupied by each nitrogen molecule is 0.16 nm²)

Prashant Kotian · Accepted Answer

Correct answer: 0720. Volume of N₂ adsorbed per gram at STP = 168 cm³ = 0.168 L. Moles of N₂ = 0.168 L / 22.4 L/mol = 0.0075 mol. Number of N₂ molecules = 0.0075 mol × 6.0 × 10²³ molecules/mol = 4.5 × 10²¹ molecules. Area occupied by one N₂ molecule = 0.16 nm² = 0.16 × 10⁻¹⁸ m². Total surface area per gram = 4.5 × 10²¹ × 0.16 × 10⁻¹⁸ m² = 0.72 × 10³ m² = 720 m². Therefore, correct answer is 0720.

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