Question 49 of 50intermediate🔧 ApplyNumerical3 marks

Determine the amount of CaCl2 (i = 2.47) dissolved in 2.5 litre of water such that its osmotic pressure is 0.75 atm at 27° C.

Correct Answer

3.42 g of CaCl₂

Exercise: EXERCISES | Q: 1.40 | (Page 29)
For More Understanding

Explanation

This numerical problem requires applying the osmotic pressure formula π = iCRT with the given van't Hoff factor for CaCl₂. The student must convert temperature to Kelvin, rearrange the formula to find concentration, then calculate moles and finally mass using the molar mass of CaCl₂.

Solution Steps

  1. Step 1: Write the osmotic pressure formula: π = iCRT (where π = osmotic pressure, i = van't Hoff factor, C = molar concentration, R = gas constant, T = temperature in Kelvin)

  2. Step 2: Convert temperature to Kelvin: T = 27°C + 273 = 300 K

  3. Step 3: Rearrange formula to find concentration: C = π/(iRT) = 0.75/(2.47×0.08212.47 \times 0.0821 × 300) = 0.75/60.84 = 0.01233 mol L⁻¹

  4. Step 4: Calculate moles of CaCl₂: Moles = C × V = 0.01233×2.50.01233 \times 2.5 = 0.03083 mol

  5. Step 5: Calculate molar mass of CaCl₂: M = 40 + 2(35.5) = 111 g mol⁻¹

  6. Step 6: Calculate mass of CaCl₂: Mass = Moles × Molar mass = 0.03083×1110.03083 \times 111 = 3.42 g

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