One proposed method of producing fresh water from sea water is a process called reverse osmosis. In reverse osmosis enough pressure is applied to force water across a membrane from a solution of high solute concentration to one of low concentration. What is the minimum pressure (in atm) needed to have reverse osmosis if sea water may be approximated by a solution with a van't Hoff = 1.83 and a concentration of 0.616 M at 20 ° C?

Question

Quizplus · Accepted Answer

The minimum pressure required for reverse osmosis can be calculated using the formula:

ΔP = (nRT/V)ln(C1/C2)

Where: 
ΔP = minimum pressure required 
n = number of moles of solute per liter of solution 
R = the gas constant (0.08206 L·atm/mol·K) 
T = temperature in Kelvin (20°C = 293.15 K) 
V = volume of solution 
C1/C2 = the concentration ratio of the two solutions

Substituting the given values:

ΔP = (1.83 x 0.08206 x 293.15)/1 ln(0.616/0)

ΔP = 27.1 atm

Therefore, the minimum pressure required for reverse osmosis is 27.1 atm, which is closest to answer choice E.

One Proposed Method of Producing Fresh Water from Sea Water