In reverse osmosis, water flows out of a salt solution until the osmotic pressur

Question

In reverse osmosis, water flows out of a salt solution until the osmotic pressure of the solution equals the applied pressure. If a pressure of 47.0 bar is applied to seawater, what will be the final concentration of the seawater at 20 degree C when reverse osmosis stops? Assuming that seawater has a total ion concentration (a.k.a colligative molarity) of 1.10 M_c, calculate how many liters of seawater are needed to produce 77.4 L of fresh water at 20 degree C with an applied pressure of 47.0 bar.

Explanation / Answer

For question 1.

P = 47 bar

R = 0.083145 L bar / mol K

Mc = P/RT = 47 / (0.083145*293) = 1.9293 M

For question 2.

C1V1 = C2V2 or M1V1 = M2V2

(1.1 Mc) (x + (1.1 Mc x 77.4 L)) = 1.9293 Mc
(1.1 Mc) (x + 85.14) = 1.9293 Mc
85.14 = 1.9293 – 1.1 (x)
x = 85.14 / (1.9293 – 1.10)
x = 102.66 L
V1 = 102.66 + 85.14 = 187.8 L

Hope this helps

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