Question 50 of 50intermediate🔧 ApplyNumerical3 marks

Determine the osmotic pressure of a solution prepared by dissolving 25 mg of K2SO4 in 2 litre of water at 25° C, assuming that it is completely dissociated.

Correct Answer

The osmotic pressure of the solution is 5.27×105.27 \times 10⁻³ atm.

Exercise: EXERCISES | Q: 1.41 | (Page 29)
For More Understanding

Explanation

This numerical problem tests the application of osmotic pressure formula with van't Hoff factor for a completely dissociated electrolyte. From Table 1.4 in the context, K₂SO₄ has van't Hoff factor i = 3 for complete dissociation (as it dissociates into 2K⁺ and 1SO₄²⁻ ions). The student must calculate molar mass of K₂SO₄, find moles, then molarity, and finally apply π = iCRT formula.

Solution Steps

  1. Step 1: Calculate molar mass of K₂SO₄ Molar mass of K₂SO₄ = 2(39) + 32 + 4(16) = 78 + 32 + 64 = 174 g mol⁻¹

  2. Step 2: Calculate moles of K₂SO₄ Mass = 25 mg = 25×1025 \times 10⁻³ g = 0.025 g Moles (n) = 0.025 g / 174 g mol⁻¹ = 1.437×101.437 \times 10⁻⁴ mol

  3. Step 3: Calculate molarity of solution Volume (V) = 2 L Molarity (C) = n/V = (1.437×101.437 \times 10⁻⁴ mol) / 2 L = 7.18×107.18 \times 10⁻⁵ mol L⁻¹

  4. Step 4: Determine van't Hoff factor (i) From Table 1.4, for complete dissociation of K₂SO₄, i = 3 (dissociates into 2K⁺ + SO₄²⁻)

  5. Step 5: Apply osmotic pressure formula π = iCRT Temperature T = 25°C = 25 + 273 = 298 K R = 0.0821 L atm K⁻¹ mol⁻¹ π = 3 × (7.18×107.18 \times 10⁻⁵) × 0.0821×2980.0821 \times 298 π = 5.27×105.27 \times 10⁻³ atm

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