A substance has a density of 2 kg dm-3 and it crystallizes in a fcc lattice with an edge length equal to 700 pm, then the molar mass of the substance is:
Correct answer: B. 103.30 g mol-1
- A. 74.50 g mol-1
- B. 103.30 g mol-1
- C. 56.02 g mol-1
- D. 65.36 g mol-1
Explanation
To find the molar mass of the substance in an fcc lattice, use the formula:M = (density × NA × a3) / Z, where:Density = 2 kg dm-3 = 2000 g dm-3a = edge length = 700 pm = 700 × 10-12 mNA = Avogadro's number = 6.022 × 1023 mol-1Z = number of atoms per unit cell for an fcc lattice = 4Convert the edge length to dm: a = 700 × 10-10 dm.Plug these values into the formula to calculate M:M = (2000 × 6.022 × 1023 × (700 × 10-10)3) / 4 = 103.30 g mol-1.Therefore, the correct answer is 103.30 g mol-1.Other options result from incorrect calculations due to errors in unit conversion, misapplication of the formula, or incorrect assumptions about the lattice structure.
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