1.11 g of calcium chloride (CaCl2) is dissolved in water to make 250 mL of solution. What is the osmotic pressure of this solution at 300 K, assuming that CaCl2 dissociates completely? (Molar mass of CaCl2 = 111 g mol−1; R = 0.083 L bar mol−1 K−1)
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 2.99 bar
The osmotic pressure of a dilute solution is proportional to its molarity, Π = CRT.
CaCl2 dissociates completely into one Ca2+ ion and two Cl− ions, so the number of particles is three times the number of formula units. The van’t Hoff factor is therefore i = 3, and Π = iCRT.
\( \displaystyle \ce{CaCl2 -> Ca^2+ + 2Cl^-} \qquad i = 3 \)
\( \displaystyle n_2 = \frac{1.11\ \mathrm{g}}{111\ \mathrm{g\ mol^{-1}}} = 0.010\ \mathrm{mol} \)
\( \displaystyle C = \frac{0.010\ \mathrm{mol}}{0.250\ \mathrm{L}} = 0.040\ \mathrm{mol\ L^{-1}} \)
\( \displaystyle \Pi = i\,C\,R\,T = 3 \times 0.040 \times 0.083 \times 300\ \mathrm{bar} = 2.99\ \mathrm{bar} \)
NCERT (2026-27 edition):
1.6.4 Osmosis and Osmotic Pressure – “…For dilute solutions, it has been found experimentally that osmotic pressure is proportional to the molarity, C of the solution at a given temperature T. Thus:”
\( \displaystyle \Pi = C\,R\,T \qquad (1.39) \)
1.7 Abnormal Molar Masses – “…In case of association, value of i is less than unity while for dissociation it is greater than unity. … Inclusion of van’t Hoff factor modifies the equations for colligative properties as follows: … Osmotic pressure of solution, Π = i n2 R T / V”