Chemistry, Third edition

OSMOSIS 189

wherecis the differencein the concentration of solute between the two solutions

used in the experiment, Ris the universal gas constant (present in the expression

even though we are talking about solutions!), and T the temperature of the

solutions. Solutions which obey this equation are said to be behaving ideally, and

this is usually true when the solute concentrations are low.

The key points about this equation are:

1.The osmotic pressure of a solution is unaffected by the membrane used. The only

assumption we make is that the membrane allows solvent to pass but not solute.

However, the equation says nothing about the speed (rate) at which the move-

ment of solvent occurs. The speed will be dependent upon the type and dimen-

sions of the membrane.

2.The osmotic pressure depends upon the difference in molarconcentration, i.e.

the difference in the numbers of solute molecules in equal volumes of both solu-

tions. The type of solute (sugar, salt, or a particular protein) is irrelevant. This

reminds us of the ideas behind the model of ideal gases, where gas pressure is

independent of the type of gas. However, the equation does assume that the

solute does not dissociate or otherwise react with the solvent, since this would

alter the number of particles per unit volume of solution.

3.Units – as with gases, we use pressure in units of Pa (N m^2 ), and cwill have units

of moles per cubic metre (mol m^3 ). Remember that 1000 mol m^3 

1 mol dm^3.

4.Although water is usually the solvent, the osmotic pressure does not depend on

the type of solvent used.

Example 11.3

A solution of sugar of concentration 0.30 mol dm^3 is separated

from pure water by a semipermeable membrane.

(i) Calculate the osmotic pressure at 20.0 C.

(ii)What would be the osmotic pressure if the water was replaced by a sugar

solution of concentration 0.10 mol dm^3?

Answer

(i) The difference in concentration is

c0.300.00 (water) 0.30 mol dm^3 0.30 103 mol m^3

cRT0.30 103 mol m^3 8.3145 J mol^1 K^1 293 K

 7.3 105 Pa ( 7.3 atm)

(ii)The difference in concentration is

c0.300.100.20 mol dm^3 0.20 103 mol m^3

cRT0.20 103 mol m^3 8.3145 J mol^1 K^1 293 K

 4.9 105 Pa ( 4.9 atm)