The Foundations of Chemistry

Thus, the molarity of sucrose in the solution is

Msucrose

0

0

.1

.1

4

2

6

5

m

L

ol

1.17 mol/L

Now we can calculate the osmotic pressure.

MRT(1.17 mol/L)0.0821 

m

L

o

a

l

t



m

K

(298 K) 28.6 atm

You should now work Exercise 84.

Let’s compare the calculated values of the four colligative properties for the 1.25 m
sucrose solution.

vapor pressure lowering 0.524 torr (Example 14-4)

boiling point elevation 0.640°C (Example 14-7)

freezing point depression2.32°C (Example 14-9)

osmotic pressure 28.6 atm (Example 14-13)

The first of these is so small that it would be hard to measure precisely. Even this small
lowering of the vapor pressure is sufficient to raise the boiling point by an amount that
could be measured, although with difficulty. The freezing point depression is greater, but
still could not be measured very precisely without a special apparatus. The osmotic pres-
sure, on the other hand, is so large that it could be measured much more precisely. Thus,
osmotic pressure is often the most easily measured of the four colligative properties, espe-
cially when very dilute solutions are used.
The use of measurements of osmotic pressure for the determination of molecular
weights has several advantages. Even very dilute solutions give easily measurable osmotic
pressures. This method therefore is useful in determination of the molecular weights of
(1) very expensive substances, (2) substances that can be prepared only in very small
amounts, and (3) substances of very high molecular weight that are not very soluble.
Because high-molecular-weight materials are often difficult, and in some cases impossible,
to obtain in a high state of purity, determinations of their molecular weights are not as
accurate as we might like. Nonetheless, osmotic pressures provide a very useful method
of estimating molecular weights.

EXAMPLE 14-14 Molecular Weight from Osmotic Pressure

Pepsin is an enzyme present in the human digestive tract. A solution of a 0.500-gram sample
of purified pepsin in 30.0 mL of aqueous solution exhibits an osmotic pressure of 8.92 torr at
27.0°C. Estimate the molecular weight of pepsin.

Plan

As we did in earlier molecular weight determinations (Section 14-13), we must first find n,the
number of moles that 0.500 grams of pepsin represents. We start with the equation MRT.
The molarity of pepsin is equal to the number of moles of pepsin per liter of solution, n/V.We
substitute this for Mand solve for n.

Solution

MRT

V

n

RT or n

RT

V



An illustration of osmosis. When a

carrot is soaked in a concentrated

salt solution, water flows out of the

plant cells by osmosis. A carrot

soaked overnight in salt solution

(left) has lost much water and

become limp. A carrot soaked

overnight in pure water (right)

is little affected.

14-15 Osmotic Pressure 573

An enzyme is a protein that acts as a

biological catalyst. Pepsin catalyzes the

metabolic cleavage of amino acid

chains (called peptide chains) in other

proteins.