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Insulin forms crystals of orthorhombic type with unit cell dimensions of . If the density of the crySolid State Chemistry Question

Question

Insulin forms crystals of orthorhombic type with unit cell dimensions of $12.5 \times 8.0 \times 3.0 \text{ nm}^3$. If the density of the crystal is $1.5 \times 10^3 \text{ kg/m}^3$ and there are six insulin molecules per unit cell, the molar mass of insulin (in kg/mol) is

Answer: 0045

💡 Solution & Explanation

Volume of unit cell $V = 12.5 \times 8.0 \times 3.0 \times 10^{-27} \text{ m}^3 = 300 \times 10^{-27} \text{ m}^3 = 3 \times 10^{-25} \text{ m}^3$. Mass of unit cell $= d \times V = 1.5 \times 10^3 \times 3 \times 10^{-25} = 4.5 \times 10^{-22} \text{ kg}$. Molar mass $M = \frac{\text{Mass of unit cell} \times N_A}{Z} = \frac{4.5 \times 10^{-22} \times 6 \times 10^{23}}{6} = 45 \text{ kg/mol}$. Therefore, correct answer is 0045.

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