BLBS102-c05 BLBS102-Simpson March 21, 2012 12:2 Trim: 276mm X 219mm Printer Name: Yet to Come
94 Part 1: Principles/Food AnalysisIn a solution, the number of moles of a component divided
by the total number of moles of all components is themole
fractionof that component. This is a useful parameter, and the
mole fraction of any pure substance is unity. When 1 mol of
sugar dissolves in 1.0 kg (55.56 mol) of water, the mole fraction
of water is reduced to 0.9823, and the mole fraction of sugar
is 0.0177. Raoult’s law applies to aqueous solutions. According
to it, the vapor pressure of a solution at temperatureTis the
product of mole fraction of the solvent and its vapor pressure at
T. Thus, the vapor pressure of this solution at 373 K is 99.53 kPa
(0.9823 atm). In general, the vapor pressure of a solution at
the normal bp is lower than that of pure water, and a higher
temperature is required for the vapor pressure to reach 101.3 kPa
(1 atm). The net increase in the boiling temperature of a solution
is known as theboiling point elevation.
Ice formed from a dilute solution does not contain the solute.
Thus, the vapor pressure of ice at various temperatures does not
change, but the vapor pressure of a solution is lower than that
of ice at the freezing point. Further cooling is required for ice
to form, and the net lowering of vapor pressure is thefreezing
point depression.
The freezing points and bps are temperatures at ice–water
and water–vapor (at 101.3 kPa) equilibria, not necessarily the
temperatures at which ice begins to form or boiling begins. Of-
ten, the temperature at which ice crystals start to form is lower
than the mp, and this is known assupercooling. The degree
of supercooling depends on many other parameters revealed by
a systematic study of heterogeneous nucleation (Wilson et al.
2003). Similarly, the inability to form bubbles results insuper-
heating. Overheated water boils explosively due to the sudden
formation of many large bubbles. Supercooling and superheat-
ing are nonequilibrium phenomena, and they are different from
freezing point depression and bp elevation.
The temperature differences between the freezing points and
bps of solutions and those of pure water are proportional to
the concentration of the solutions. The proportionality constants
aremolar freezing point depression(Kf=−1.86 K mol−^1 kg)
and themolar boiling point elevation(Kb=0.52 K mol−^1 kg),
respectively. In other words, a solution containing one mole of
nonvolatile molecules per kilogram of water freezes at 1.86◦
below 273.15 K, and boils 0.52◦above 373.15 K. For a solution
with concentrationC, measured in moles of particles (molecules
and positive and negative ions counted separately) per kilogram
of water, the bp elevation or freezing point depressionTcan
be evaluated:T=KC,whereKrepresentsKforKbfor freezing point depression or
bp elevation, respectively. This formula applies to both cases.
Depending on the solute, some aqueous solutions may deviate
from Raoult’s law, and the above formulas give only estimates.
In freezing or boiling a solution of a nonvolatile solute, the
solid and vapor contain only H 2 O, leaving the solute in the
solution. A solution containing volatile solutes will have a total
vapor pressure due to all volatile components in the solution. Its
bp is no longer that of water alone. Freezing point depression and
bp elevation are both related to the vapor pressure. In general,a solution of nonvolatile substance has a lower vapor pressure
than that of pure water. The variations of these properties have
many applications, some in food chemistry and biochemistry.
It is interesting to note that some fish and insects have an-
tifreeze proteins that depress the freezing point of water to pro-
tect them from freezing in the arctic sea (Marshall et al. 2004).
Osmotic pressureis usually defined as the pressure that must
be applied to the side of the solution to prevent the flow of
the pure solvent passing a semipermeable membrane into the
solution. Experimental results show that osmotic pressure is
equal to the product of total concentration of molecules and ions
(C), the gas constant (R=8.3145 J/mol/K), and the temperature
(Tin K):Osmotic pressure=CRT.The expression for osmotic pressure is the same as that for
ideal gas. Chemists calculate the pressure using a concentration
based on mass of the solvent. Since solutions are never ideal, the
formula gives only estimates. The unit of pressure works out if
the units forCare in mol/m^3 ,since1J=1Pam^3. Concentration
based on mass of solvent differs only slightly from that based
on volume of the solution.
Anisotonic solution(isosmotic) is one that has the same
osmotic pressure as another. Solutions with higher and lower
osmotic pressures are calledhypertonic(hyperosmotic), and
hypotonic(hypoosmotic), respectively. Raw food animal and
plant cells submerged in isotonic solutions with their cell flu-
ids will not take up or lose water even if the cell membranes
are semipermeable. However, in plant, soil, and food sciences,
water potential gradientis the driving force or energy directing
water movement. Water moves from high-potential sites to low-
potential sites. Water moves from low osmotic pressure solutions
to high osmotic pressure solutions. For consistency and to avoid
confusion, negative osmotic pressure is defined asosmotic po-
tential. This way, osmotic potential is a direct component of
water potential for gradient consideration. For example, when
red blood cells are placed in dilute solutions, their osmotic po-
tential is negative. Water diffuses into the cells, resulting in the
swelling or even bursting of the cells. On the other hand, when
cells are placed in concentrated (hypertonic) saline solutions,
the cells will shrink due to water loss.
Biological membranes are much more permeable than most
man-made phospholipid membranes because they have specific
membrane-bound proteins acting as water channels. Absorption
of water and its transport throughout the body is more compli-
cated than osmosis.Solution of ElectrolytesSolutions of acids, bases, and salts contain ions. Charged ions
move when driven by an electric potential, and electrolyte so-
lutions conduct electricity. These ion-containing substances are
calledelectrolytes. As mentioned earlier, the high dielectric con-
stant of water reduces the attraction of ions within ionic solids
and dissolves them. Furthermore, the polar water molecules sur-
round ions, forminghydrated ions. The concentration of all ions