The osmotic pressure of a solution at \( 0^{\circ}\text{C} \) is 2 atm. What will be its osmotic pressure at 819 K?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 6 atm
The osmotic pressure of a dilute solution is given by the van’t Hoff equation, \( \pi = CRT \), where C is the molar concentration and T the absolute temperature. For the same solution C and R do not change, so the osmotic pressure is directly proportional to the temperature in kelvin:
\( \displaystyle \frac{\pi_2}{\pi_1} = \frac{T_2}{T_1} \)
The temperature must be in kelvin: 0°C = 273 K.
\( \displaystyle \pi_2 = \pi_1 \times \frac{T_2}{T_1} = 2\ \mathrm{atm} \times \frac{819\ \mathrm{K}}{273\ \mathrm{K}} = 2\ \mathrm{atm} \times 3 = 6\ \mathrm{atm} \)
So the osmotic pressure at 819 K is 6 atm.