Chemistry 232. Properties of Solutions. Concentration Terms. Dilute - not a lot of solute. Concentrated - a large amount of solute. Concentration can be expressed quantitatively is many ways: Molarity Molality Percentage Mole fraction. Molarity and Molality.
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Chemistry 232
Properties of Solutions
Define a partial molar thermodynamic property as
Euler’s Theorem
We define the chemical potential of a substance as
Shows how all the extensive thermodynamic properties depend on system composition
TmixS/n
kJ/mol
TmixH/n
0
TmixG/n
XA
For an ideal solution
Consider the following system
The chemical potential expressions
VP of solution relates to VP of pure solvent
PA = XAP*A
Solutions that obey Raoult’s law are called ideal solutions.
The total vapour pressure and partial vapour pressures of an ideal binary mixture
Dependence of the vp on mole fractions of the components.
Benzene and toluene behave almost ideally
Follow Raoult’s Law over the entire composition range.
Henry’s law relates the vapour pressure of the solute above an ideally dilute solution to composition.
The chemical potential expressions
The Standard State Chemical potential for Henry’s Law
When the system is in equilibrium
The chemical potential expressions reduce to Henry’s Law
The Standard State Chemical potential for Henry’s Law
When the system is in equilibrium
The chemical potential expressions reduce to Henry’s Law in terms of molalities
The chemical potential expressions
oJ,m = chemical potential of the solute in an
ideal 1 molal solution
The Gibbs-Duhem gives us an interrelationship amongst all partial molar quantities in a mixture
Examine the chemical potential expressions involved
The boiling point elevation
Examine the chemical potential expressions involved
Define the freezing point depression
- the osmotic pressure
Equilibrium is established across membrane under isothermal conditions
The osmotic pressure is related to the solutions molarity as follows
Isotonic: having the same osmotic pressure
Hypertonic: having a higher osmotic pressure
Hypotonic: having a lower osmotic pressure
Hemolysis: the process that ruptures a cell placed in a solution that is hypotonic to the cell’s fluid
Crenation: the opposite effect
In a multicomponent system
The partial molar volume of a substance
slope of the variation of the total sample volume plotted against composition.
PMV’s vary with solution composition
The partial molar volumes of water and ethanol at 25C.
Note the position of the maxima and minima!!
Obtain the densities of systems as a function of composition
Inverse of density – specific volume of solution
Plot volumes vs. mole fraction of component A or B
Draw a tangent line to the plot of volume vs. mole fraction.
Where the tangent line intersects the axis – partial molar volume of the components at that composition
Define the mean mixing molar volume as
V*J – the molar volume of the pure liquid
Vm = V/nT
VB-VB*
VA-VA*
The value of a partial molar thermodynamic property in the limit of zero volume is its infinite dilution value
E.g., for the volumes
For any real system, the chemical potential for the solute (or solvent) is given by
The chemical potential is essentially invariant with pressure for condensed phases
or aJ = 1
For a pure solid or a pure liquid at standard to moderately high pressures
The chemical potential of a real gas is written in terms of its fugacity
The activity coefficient (J) relates the activity to the concentration terms of interest.
In gaseous systems, we relate the fugacity (or activity) to the ideal pressure of the gas via
We substitute the activity of the solute and solvent into our expressions for Raoult’s Law
Note – as XJ 1
JI 1 and PJ PJid
Vapour pressure above real solutions is related to its liquid phase mole fraction and the activity coefficient
The solvent is treated in the same manner as for Convention I
For the solute, substitute the solute activity into our Henry’s Law expression
Note – as XJ 0
JII 1 and PJ PJid
Vapour pressure above real dilute solutions is related to its liquid phase mole fraction and activity coefficient
Note – as mJ 0
J(m) 1 and aJ(m) mJ
For the solute, we use the molality as our concentration scale