Question

Sea water containing 1 M NaCl has to be desalinated at 300 K using a membrane permeable only to water. The minimum pressure (in bars) required on the sea-water side of the membrane is ......... (Round off to one decimal place)

Hint:

Osmotic pressure is a colligative property and can be calculated using the formula \( \Pi = \frac{nRT}{V} \) to determine the pressure required for processes like desalination.

Answer 1

Correct Answer: 24.8

Step 1: Understanding Osmotic Pressure Formula.
The osmotic pressure is given by the formula: \[ \Pi = \frac{nRT}{V} \] Where: \( n \) is the number of moles, \( R \) is the gas constant, \( T \) is the temperature, and \( V \) is the volume of solvent. We need to find the minimum pressure required to desalinate the seawater. For this, we use the formula for osmotic pressure, knowing the molarity of NaCl, the temperature, and the gas constant.

Step 2: Applying the Formula.
Using the given values for \( R = 8.3 \, \text{J mol}^{-1} \text{K}^{-1} \), \( T = 300 \, \text{K} \), and the molarity of NaCl (1 M), we calculate the osmotic pressure, which gives the minimum pressure required for desalination.

Step 3: Conclusion.
The minimum pressure required on the sea-water side of the membrane is 23.6 bars.