Page 365 - Water and wastewater engineering

9-4 WATER AND WASTEWATER ENGINEERING

(a) (b) (c)
Osmotic Reverse Osmotic
Osmosis equilibrium osmosis pressure
Osmotic
pressure

Water Water

Fresh Saline
water water
Low High Semipermeable Low High
TDS TDS membrane TDS TDS
FIGURE 9-3
Direct and reverse osmosis. ( Source: Davis and Cornwell, 2008.)

Chemical potential is defined as the change in Gibbs energy resulting from a change in the
amount of component i when the temperature and pressure are held constant
G

u (9-2)
i
n i

Thus, under constant temperature conditions, equilibrium ( G 0) will be achieved when

V P u n i (9-3)

i
The pressure ( P ) to balance the difference in chemical potential of a solute is called the osmotic
pressure (MWH, 2005). By convention it is given the symbol . The equation for osmotic pres-
sure can be derived thermodynamically using assumptions of incompressible and ideal solution
behavior:

iCRT (9-4)
where i number of ions produced during dissociation of solute

osmoticcoefficient unitless,
C concentration of all solutes, moles/L
3
R universal gas constant, 8.314 kPa · m /kg mole · K
T absolute temperature, K
The number of ions per mole, i, for example would be 2 for NaCl. The osmotic coefficient,
,
depends on the nature of the substance and its concentration. For NaCl it ranges from 0.93 to
1.03 over a concentration range of 10 to 120 g/L of salt. Seawater has an osmotic coefficient that
varies from 0.85 to 0.95 for the same concentration range. Robinson and Stokes (1959) provide
osmotic coefficients for a variety of electrolytes.