Reverse osmosis

Question

In reverse osmosis, water flows out of a salt solution until the osmotic pressure of the solution equals the applied pressure. Assume seawater has a colligative molarity of 1.10 M, and you want to use reverse osmosis to produce freshwater from the seawater. Calculate the volume of seawater (in liters) required to produce 21.0 liters of freshwater when a pressure of 65 atm is applied to the seawater at 25 °C. The ideal gas constant is 0.08206 L･atm/mol･K.

Answer 1

First, calculate the osmotic pressure of the seawater:

π = iMRT

π = osmotic pressure in atm = ?

i = van't Hoff factor = 2 for NaCl

M = molarity (mol/L) = 1.10 M

R = gas constant = 0.08206 Latm/Kmol

T = temperature in K = 25 + 273 = 298K

Solving for π we have...

π = (2)(1.10 mol/L)(0.08206 Latm/Kmol)(298K)

π = 53.80 atm

Need pressure > 53.80 atm to make water move from salt water to fresh water, and since we have an applied pressure of 65 atm, this will take place.

V_s = π_s V_f / P_a - π_s

V_s = volume of seawater = ?

π_s = osmotic pressure of seawater = 53.8 atm

V_f = volume of fresh water = 21.0 L

P_a = pressure applied = 65 atm

Solving for V_s we have ...

V_s = (53.8)(21.0) / 65 - 53.8

V_s = 1129.8 / 11.2

V_s ≈ 101 L