Chapter 4 Phases and Solutions. 4.1 Phase Recognition 4.2 Physical transformations of pure substances 4.3 Simple mixtures 4.4 Raoult’s and Henry’s Laws 4.5 The chemical potentials of liquids 4.6 The properties of solutions. New Words and Expressions. Homogeneous 均相，同相
A single phase is uniform throughout both in chemical composition and physical state, and it is said to be homogeneous. In contrast to this, a heterogeneous system consists of more than one phase.
A phase transition, the spontaneous conversion of one phase into another phase, occurs at a characteristic temperature for a given pressure.
The transition temperature is the temperature at which the two phases are in equilibrium and the Gibbs energy is minimized at the given pressure.
Phase Equilibrium in a one-Component System: The change in Gibbs energy between the two equilibrium phase is zero under given conditions of temperature and pressure.
G(s)=G (l) (4.1)
and when there is equilibrium between water and steam
G(l)=G (g) (4.2)
We begin with the statement of phase equilibrium, written for a pure substance in the liquid and vapor states. If the pressure and temperature are changed infinitesimally in such a way that equilibrium is maintained,
the two phases are in equilibrium and the Gibbs energy is minimized at the given pressure.Sm(v)dT+Vm(v)dP= Sm(l)dT+Vm(l)dP
or dP/dT= [Sm(v) Sm(l)]/ [Vm(v) Vm(l)]
When one of the phases in equilibrium is a vapor phase, we assume that Vm(v) is so much larger than Vm(l) that we may neglect Vm(l) in comparison to Vm(v) when the pressure is near 1 bar. The second assumption is to replace Vm(v) by its equivalent from the ideal gas law RT/P. then,
Example 4.1 Benzene has a normal boiling point at 760 Torr of 353.25K and vapH=30.76kJmol-1, if benzene is to be boiled at 30.000C in a vacuum distillation, to what value of P must the pressure be lowered?
Solution: Using Eq.4.10 , we have
lnP2/760.0=30760/8.3145(1/353.25 - 1/303.15)
The entropies of vaporization vapSm of most non-hydrogen-bonded compounds have values of vapSm in the neighborhood of 88 JK-1mol-1. This generalization is known as Trouton’s rule and was pointed out in 1884:
100cm3 water + 100cm3 ethanol 192cm3
150cm3 water + 50cm3 ethanol 195cm3
50cm3 water + 150cm3 ethanol 193cm3
按偏摩尔量定义, of 353.25K and
The increase in volume per mole of component 1 is known as the partial molar volume of component 1. It is given the symbol V1 and is written as
V1 (V/n1)T,P,n,n, (4.9)
In either case, the definition for the partial molar volume, may be used to rewrite as
dV=Vdn1 + Vdn2 + (4.10)
则 equilibrium is that the chemical potential of the substance i is the same in the two phases.
l=g =0(g) +RTlnPl*/p0
s=g =0(g) +RTlnPs*/p0
P* is Saturated vapor pressureof pure liquid or pure solid.
A solution is any homogeneous phase that contains more than one component. We call the component that constitutes the larger proportion of the solution the solvent; the component in lesser proportion is called the solute.
Mixtures that obey the law throughout the composition range from pure A to pure B are called ideal solutions.
The solution is considered to be ideal when there is a complete uniformity of intermolecular forces, arising from similarity in molecular size and structure.
Where k is the Henry’s law constant, which is an empirical constant. Mixtures for which the solute obeys Henry’s law and the solvent obeys Raoult’s law are called ideal-dilute solutions.
where the superscript * represents the value for the pure material.
=p*A xB (4.31)
fusT=Tf* - Tf M1RTf*2/fusHm m2 (4.32)
is needed to be put into 1 dm3 aqueous solution then the osmotic pressure be the same as blood.
for a dilute solution, mB =cB
(2)M C12H22O11 =342.99g/mol