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: 49.7 - 49.9

To find the minimum pressure required to desalinate sea water containing 1 M NaCl using a membrane permeable only to water, we need to determine the osmotic pressure of the solution. 
The osmotic pressure (\( \pi \)) can be calculated using the formula: 

\(\pi = iCRT\)

Where:

• \(i\) is the van 't Hoff factor, which is 2 for NaCl because it dissociates into two ions: Na⁺ and Cl^-.
• \(C\) is the concentration of the solute, which is 1 M.
• \(R\) is the ideal gas constant, approximately 0.0831 L·bar/mol·K.
• \(T\) is the temperature in Kelvin, which is 300 K.

Plugging in the values, we get:
\(\pi = 2 \times 1 \times 0.0831 \times 300\) 
Simplifying, 
\(\pi = 49.86\) bars
Rounding off to one decimal place, the minimum pressure required is 49.9 bars.