Question 2
Calculate the water activity of a 25%(w/w) solution of glucose in water, assuming
ideal behavior. What would be the effect of solute size on the result, assuming the
volume ratio glucose/water to be 6? Assuming that the observedaw¼0.960, then
what would you conclude?
Answer
The molar mass of glucose¼180 g/mol, that of water 18. We thus have in a kg of
solution 250/180¼1.39 mol glucose and 750/18¼41.67 mol water, and application
of Eq. (8.2) yieldsaw¼0.968. If no net interactions occur between solute and solvent
molecules, Eq. (8.4) withb¼1 can be applied to calculate the effect of solute size:
aw¼exp½ 0 : 032 ð 1 þ 1 = 26660 : 032 þÞ¼ 0 : 965 :The nonideality would thus be small.
If indeedawwere 0.960, that would imply net attraction between glucose and
water, i.e., hydration; Eq. (8.4) would then yield that the solute–solvent interaction
parameterb¼2.87, an unlikely high figure. Another way to calculate roughly the
hydration is as follows. We can write theawvalue of 0.965¼27.57/(27.57þ1),
where 1 stands for 1 mole of glucose. Assume now that one glucose molecule
‘‘removes’’xmolecules of water from the solution. For the ‘‘observed’’awwe would
then have
27 : 57 x
28 : 57 x¼ 0 : 960yieldingx¼3.6 molecules of water ‘‘removed’’ per molecule of glucose. This too is a
very unlikely high figure. In other words, the ‘‘observed’’awwould not be correct.
Indeed, exact determination has shownaw¼0.9666, implying thatbwould be<1.
8.2 SORPTION ISOTHERMS
Physical chemists distinguish between adsorption and absorption.Adsorp-
tion is a surface phenomenon. Consider a solid or liquid phase (the
adsorbent), in contact with another, fluid, phase. Molecules present in the
fluid phase may now adsorb onto the interface between the phases, i.e., form
a (usually monomolecular) layer ofadsorbate. This is discussed in more
detail in Section 10.2. The amount adsorbed is governed by the activity of
the adsorbate. For any combination of adsorbate, adsorbent, and
temperature, an adsorption isotherm can be determined, i.e., a curve that
gives the equilibrium relation between the amount adsorbed per unit surface
area, and the activity of the adsorbate. Powdered solid materials in contact