Thermodynamics and Chemistry

CHAPTER 2 SYSTEMS AND THEIR PROPERTIES

2.4 THESTATE OF THESYSTEM 46

Table 2.4 Values of state functions of an aqueous su-

crose solution (A = water, B = sucrose)

temperature TD293:15K

pressure pD1:01bar

amount of water nAD39:18mol

amount of sucrose nBD1:375mol

volume VD 1000 cm^3

mass mD1176:5g

density D1:1765g cm^3

mole fraction of sucrose xBD0:03390

osmotic pressure D58:2bar

refractive index, sodium D line nDD1:400

Various conditions determine what states of a system are physically possible. If a uni-
form phase has an equation of state, property values must be consistent with this equation.
The system may have certain built-in or externally-imposed conditions or constraints that
keep some properties from changing with time. For instance, a closed system has constant
mass; a system with a rigid boundary has constant volume. We may know about other
conditions that affect the properties during the time the system is under observation.
We can define the state of the system with the values of a certain minimum number of
state functions which we treat as theindependent variables. Once we have selected a set of
independent variables, consistent with the physical nature of the system and any conditions
or constraints, we can treat all other state functions asdependent variableswhose values
depend on the independent variables.
Whenever we adjust the independent variables to particular values, every other state
function is a dependent variable that can have only one definite, reproducible value. For
example, in a single-phase system of a pure substance withT,p, andnas the independent
variables, the volume is determined by an equation of state in terms ofT,p, andn; the
mass is equal tonM; the molar volume is given byVmDV=n; and the density is given by
DnM=V.

2.4.2 An example: state functions of a mixture

Table2.4lists the values of ten state functions of an aqueous sucrose solution in a particular
state. The first four properties (T,p,nA,nB) are ones that we can vary independently, and
their values suffice to define the state for most purposes. Experimental measurements will
convince us that, whenever these four properties have these particular values, each of the
other properties has the one definite value listed—we cannot alter any of the other properties
without changing one or more of the first four variables. Thus we can takeT,p,nA, and
nBas the independent variables, and the six other properties as dependent variables. The
other properties include one (V) that is determined by an equation of state; three (m,,
andxB) that can be calculated from the independent variables and the equation of state;
a solution property () treated by thermodynamics (Sec.12.4.4); and an optical property
(nD). In addition to these six dependent variables, this system has innumerable others:
energy, isothermal compressibility, heat capacity at constant pressure, and so on.