Chapter 4: Physical Transformations Of Pure Substances
• Phase: form of matter that is uniform throughout in chemical composition and
• Phase Transition: the spontaneous conversion of one phase into another and
may be studied by techniques that include thermal analysis.
o Transition Temperature (Ttrs): the temperature at which the two
phases are in equilibrium and Gibbs energy of the system is minimized
at the prevailing pressure.
o Thermal Analysis: the transition is detected by noting that the
temperature does not change even though heat is being supplied or
removed from the sample.
o Metastable Phases: thermodynamically unstable phases that persist
because the transition is kinetically hindered.
• The thermodynamic analysis of phases is based on the fact that at
equilibrium, the chemical potential of a substance is the same throughout the
sample, regardless of how many phases are present.
o Chemical Potential (μ ): measure of the potential that a substance has
for undergoing change in a system and is synonyms with molar Gibbs
energy (μ = Gm).
o At equilibrium, μ 1 = μ 2 and then, there is no change in G.
• A susbtance characterized by a variety of parameters that can be identified on
its phase diagram.
o Phase Diagram: shows the regions of pressure and temperature at
which its various phases are thermodynamically stable.
o Phase Boundaries: the lines separating the regions that show the
values of p and T at which two phases coexist in equilibrium and their
chemical potentials are equal.
o Vapor Pressure: the pressure of a vapor in equilibrium with the liquid.
o Sublimation Vapor Pressure: the vapor pressure of the solid phase.
o The vapor pressure of a substance increases with temperature
because at higher temperatures, more molecules have enough energy
to escape from their neighbors.
o Boiling: the condition of free vaporization throughout the liquid.
o Boiling Temperature: the temperature at which the vapor pressure of a
liquid is equal to the external pressure.
At normal boiling point, temperature where external pressure is
At standard boiling point, temperature where vapor pressure is
o Critical Temperature (Tc): temperature at which the surface
o Critical Pressure (pc): vapor pressure at the critical temperature.
o Supercritical Fluid: a single uniform phase at and above the critical
o Melting Temperature: the temperature at which the liquid and solid
phases of a substance coexist in equilibrium.
o Freezing Temperature: because a substance melts at exactly the same
temperature as it freezes, melting temperature is the same as its
Normal Freezing Point (Tf): freezing temperature when pressure
is 1 atm. Standard Freezing Point (Ts): freezing point when pressure is 1
o Triple Point: a point at which the three phase boundaries meet; it
occurs at a single definite pressure and temperature characteristic of
o If the slope of the solid-liquid phase boundary is shown, then the triple
point also marks the lowest temperature at which the liquid can exist;
the critical temperature is the upper limit.
• The phase rule relates the number of variables that may be changed while the
phases of a system remain in mutual equilibrium.
o Phase Rule: F = C – P + 2, where F is the variance, C is the number of
components and P is the number of phases at equilibrium.
o Component: chemically independent constituent of a system; the
minimum number of types of independent species necessary to define
the composition of all the phases present in the system.
o Constituent: a chemical species that is present.
A mixture of ethanol and water has two constituents.
A solution of sodium chloride has three constituents; Na+, Cl-
o Variance: the number of intensive variables that can b