Question 31 of 50advanced🔧 ApplyNumerical5 marks

Two elements A and B form compounds having formula AB2 and AB4. When dissolved in 20 g of benzene (C6H6), 1 g of AB2 lowers the freezing point by 2.3 K whereas 1.0 g of AB4 lowers it by 1.3 K. The molar depression constant for benzene is 5.1 K kg mol-1. Calculate atomic masses of A and B.

Correct Answer

Atomic mass of A = 25.6 g mol⁻¹ Atomic mass of B = 42.6 g mol⁻¹

Exercise: EXERCISES | Q: 1.21 | (Page 28)
For More Understanding

Explanation

This question requires calculating molar masses of both compounds using freezing point depression formula, then solving simultaneous equations to find atomic masses of individual elements.

Solution Steps

  1. Step 1: Calculate molar mass of AB₂ using the formula: M₂ = (Kf × w₂ × 1000) / (ΔTf × w₁)

  2. Step 2: M(AB₂) = (5.1 K kg mol⁻¹ × 1 g × 1000 g kg⁻¹) / (2.3 K × 20 g) = 5100 / 46 = 110.87 g mol⁻¹

  3. Step 3: Calculate molar mass of AB₄ using the same formula: M(AB₄) = (5.1 K kg mol⁻¹ × 1 g × 1000 g kg⁻¹) / (1.3 K × 20 g) = 5100 / 26 = 196.15 g mol⁻¹

  4. Step 4: Let atomic mass of A = 'a' and atomic mass of B = 'b'. Set up equations: a + 2b = 110.87 and a + 4b = 196.15

  5. Step 5: Subtract first equation from second: (a + 4b) - (a + 2b) = 196.15 - 110.87, giving 2b = 85.28, so b = 42.64 g mol⁻¹

  6. Step 6: Substitute b in first equation: a + 2(42.64) = 110.87, giving a = 25.59 g mol⁻¹

  7. Step 7: Final answer: Atomic mass of A = 25.6 g mol⁻¹ and Atomic mass of B = 42.6 g mol⁻¹

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