Question

A) Calculate the osmotic pressure difference between seawater and fresh water. For simplicity, assume thatall the dissolved salts in seawater are NaCl.
b) Reverse osmosis occurs when you apply a pressure difference greater than the osmotic pressure to asolution separated from a pure solvent by a membrane permeable only to the solvent. In this process, thesolvent flows out of the solution and this can be used to desalinate sea water. Use your result from Part (a)to find the minimum work required to desalinate one liter of water.

c) It is also possible to desalinate water by evaporation. The water vapor is recondensed and the salt is leftbehind. Compare your result from part (b) with the amount of heat that would be required to evaporate aliter of water. Assume that the water starts at a temperature of 300K and the latent heat of vaporization at apressure of one atmosphere is 40.7kJ/mol. Compare your result with that of Part (b)

Answer 1

Answer:

a)  Δπ = 1.264 atm

b) W = 128 joules

c)  ΔH >> W  ( a factor greater than 17,000 )

Explanation:

a) The osmotic pressure, π , is determined by :

π = nRT/V, where n= moles of solute

                          R= 0.0821 Latm/kmol

                          T = 300 K

calling π(sw) osmotic pressure for  for sea water and π (fw) for fresh water,

salinity of sea water = 3.5 g / 1L water   (assuming only NaCl for the salts)

salinity of fresh water = 0.5 parts per thousand (range: 0- 0.5 ppt)

πsw = (3.5 g/58.44 g/mol) (0.0821 Latm/Kmol) (300 K ) /1 L = 1.475 atm

πfw = (0.5 g/58.44 g/mol) (0.0821 Latm/Kmol) (300 K ) /1 L = 0.211 atm

d water = 1 g/cm³

Δ π = (1.475 - 0.211) = 1.264 atm

b) W = Δπ V = 1.426 atm x 1L = 1.43 L-atm

1 L-atm = 101.33 j

W =  101.33 j/ Latm x  1.43 Latm = 128 joules

c) ΔH = Q₁ + nΔH vap, where

            Q₁  = heat required to bring the solution from 300 K to boiling, 373 K

            ΔH vap = heat of vaporization

Q = mCΔT = 1000 g x 4.186 j x 73 K = 305.6 j = 0.3056 kj

ΔH vap = (1000 g/ 18 g/mol ) 40.7 kj/mol = 2,261 kj

ΔH =  0.3056 kj + 2,261 kj = 2,261.3 kj

Note = Q << ΔH vap and we could have neglected it.

This result shows why nobody talks about evaporation of sea water to produce fresh water ΔH >> W