Twenty per cent of surface sites are occupied by N₂ molecules. The density of surface site is 6.023 × 10¹⁴ cm⁻² and total surface area is 1000 cm². The catalyst is heated to 300 K while N₂ is complete

Question

Twenty per cent of surface sites are occupied by N₂ molecules. The density of surface site is 6.023 × 10¹⁴ cm⁻² and total surface area is 1000 cm². The catalyst is heated to 300 K while N₂ is completely desorbed into a pressure of 0.001 atm and volume of 2.46 cm³. The number of active sites occupied by each N₂ molecule is

Prashant Kotian · Accepted Answer

Correct answer: 2. Total number of surface sites available = 6.023 × 10¹⁴ cm⁻² × 1000 cm² = 6.023 × 10¹⁷ sites. Sites occupied by N₂ = 20% of 6.023 × 10¹⁷ = 1.2046 × 10¹⁷ sites. Moles of N₂ desorbed = PV/RT = (0.001 atm × 2.46 × 10⁻³ L) / (0.0821 L·atm/(mol·K) × 300 K) = (2.46 × 10⁻⁶) / 24.63 = 10⁻⁷ mol. Number of N₂ molecules = 10⁻⁷ mol × 6.023 × 10²³ molecules/mol = 6.023 × 10¹⁶ molecules. Number of active sites occupied per N₂ molecule = (1.2046 × 10¹⁷ sites) / (6.023 × 10¹⁶ molecules) = 2. Therefore, correct answer is 2.

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