Question

Problem 5.76. Seawater has a salinity of 3.5%, meaning that if you boil away a kilogram of seawater, when you're finished you'll have 35 g of solids (mostly NaCl) left in the pot. When dissolved, sodium chloride dissociates into separate Na+ and clº ions. (a) Calculate the osmotic pressure difference between seawater and fresh water. Assume for simplicity that all the dissolved salts in seawater are NaCl. (b) If you apply a pressure difference greater than the osmotic pressure to a solution separated from pure solvent by a semipermeable membrane, you get reverse osmosis: a flow of solvent out of the solution. This process can be used to desalinate seawater. Calculate the minimum work required to desalinate one liter of seawater. Discuss some reasons why the actual work required would be greater than the minimum.

Answer 1

Answer: 5.76(a) let, The mass of seawater is of seawater is lleg. so, the volume Expressed as follows. Here, m is the mass p is the density. and for m Ikg and looo kg/m's for p substitute v= kg 1000 kg/m3 VE 10m state the molecular weight of Nach A = 239/mol +35159/mol A = 5815 g/mole Write the Expression for the number of moles of Nach number of grams formula weight of Nach HB = 11 substitute 35g form and 58.5g/mol for a

hoa 35g MB = 58.5 g/mole HB = 0.5983 moles ideal gas law in The particle form is, PVENKT Here, N is the number of particles K is the Boltzmann constant T is the absolute temperature U is the lolume. The ideal gas law in molar form is, Pl=nRT Here, nis the number of moles R is the universal gas Constant the Even above two Expressions Nk =nR The osmotic pressure difference between sea water and fresh water is as follows: Enpressed NISKT P2P = Substitute nR for Nk in the above Expression

o Substitute 0.5983 mules for his . 8.313/molole for d 3ook for T and 103 m3 for u 10.5983 mole) (8.215/moler le ) ( 30012) P2-B1 = 103 m3 P2-P1 - 1649x103 103 P2-P1 = (14a xo'pa) | atopa) I tolv ospa) There fore, (2-81 = 14.9 atm] seawater The osmatic pressure difference between 14.a atm and fresh water is done to desalinate one minimum work liter 1. The of water is as follows. - W = (P2-P;) cubstitute 1449 x 10 pa fol P2-Pp and looms for v lead = 114.9 xlos pa] (10-3m3) = 1490 I Therefore, The wolle needed to desalinate one liter of sea wates is 114905]

since, @ The sodium Cloride, nach is a solute. Calculate required desalinating Seawater by Considering only Mach. Stically, some other salts apart from Nach, which will are having less molecular weight than nach increase osmotic pressure than the calculated llalue. Hence, - The actual Wolle done will be more than the minimum