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move through the cell membrane until the chemical potentials of H O, of B, of C, . . . Section 12.5
2
are equalized on each side of the membrane. If the fluid surrounding a cell is more Two-Component Phase Diagrams
concentrated in solutes L, M, . . . than the cell fluid is, the cell will lose water by os-
mosis; the surrounding fluid is said to be hypertonic with respect to the cell. If the sur-
rounding fluid is less concentrated in L, M, . . . than the cell, the cell gains water from
the surrounding hypotonic fluid. When there is no net transfer of water between cell
and surroundings, the two are isotonic.
Blood and lymph are approximately isotonic to the cells of an organism.
Intravenous feeding and injections use a salt solution that is isotonic with blood. If
water were injected, the red blood cells would gain water by osmosis and might burst.
Plant roots absorb water from the surrounding hypotonic soil fluids by osmosis.
Living cells are able to transport a chemical species through a cell membrane from
a region of low chemical potential of that solute to a region of high chemical poten-
tial, a direction opposite that of spontaneous flow. Such transport (called active trans-
port) is accomplished by coupling the transport with a process for which G is neg-
ative (Sec. 11.10). For example, a certain protein in cell membranes simultaneously

(a) actively transports K ions into cells from surrounding fluids having lower K

concentrations, (b) actively transports Na ions out of cells, and (c) hydrolyzes ATP
to ADP (a reaction for which G decreases—Fig. 11.8). About one-third of the ATP

consumed by a resting animal is used for active transport (“pumping”) of Na and K
across membranes. A resting human consumes about 40 kg of ATP in 24 hr, and this

ATP must be continually resynthesized from ADP. The active transport of Na out of

cells makes possible the spontaneous, passive flow of Na into cells, and this sponta-

neous inward flow of Na is coupled to and drives the active transport of glucose and
amino acids into cells.
There is a logical gap in our derivation of the osmotic pressure. In Sec. 4.7, we derived
a
b
m m (the equality of chemical potentials in different phases in equilibrium) under the
A
A
a
b
a
suppositions that T a T b and P P . However, in osmotic equilibrium, P P b
(where a and b are the phases separated by the semipermeable membrane). Hence we
b
must show that m a A m at equilibrium even when the phases are at different pressures.
A
The proof is outlined in Prob. 12.27. [In a steady-state system with a temperature gradient
(for example, Fig. 15.1), the chemical potential of a species differs in regions at different
a
b
T. Thus m m only if T is uniform.]
A
A
12.5 TWO-COMPONENT PHASE DIAGRAMS
Phase diagrams for one-component systems were discussed in Chapter 7. Phase dia-
grams for two-component systems are discussed in Secs. 12.5 to 12.10 and for three-
component systems in Sec. 12.12.
With c ind 2, the phase rule f c ind p 2 becomes f 4 p. For a one-phase,
two-component system, f 3. The three independent intensive variables are P, T, and
one mole fraction. For convenience, we usually keep P or T constant and plot a two-
dimensional phase diagram, which is a cross section of a three-dimensional plot. The
restriction of constant T or P in the two-dimensional plot reduces f by 1 in this plot. A
two-component system is called a binary system.
Multicomponent phase equilibria have important applications in chemistry, geol-
ogy, and materials science. Materials science studies the structure, properties, and
applications of scientific and industrial materials. The main classes of materials are
metals, semiconductors, polymers, ceramics, and composites. Traditionally, the term
“ceramic” referred to materials produced by baking moist clay to form hard solids.
Nowadays, the term is broadened to include all inorganic, nonmetallic materials
processed or used at high temperature. Most ceramics are compounds of one or more
metals with a nonmetal (commonly oxygen) and are mechanically strong and resistant