Ideal solutions (liquid or solid)
Definition of ideal solution:
(whether there is a vapor phase or not)
From this definition, we get:
etc., etc. for other thermodynamic variables
Spring 2006
Chem312: Class 12
February 21, 2006
Ideal solutions (liquid or solid)
Definition of ideal solution:
(whether there is a vapor phase or not)
From this definition, we get:
etc., etc. for other thermodynamic variables
When there is a vapor phase: Equilibrium vapor pressure of ideal solution
Raoult's law
For ideal solution this is valid for the whole range of composition, from x = 0 to x = 1.
Phase diagrams for binary ideal solutions:
(From phase rule: F= 3 for 1 phase, F=2 for 2 phase, etc. If we fix T, this uses up one degree of freedom...)
P vs. x for fixed T (for non-ideal soln. P not linear with x)
Lever Rule (ideal or non-ideal)
Two components: 1&2
Numbers of moles: n1and n2
Overall composition given by mole fractions z1and z 2
Two phases: liquid (nliq) and vapor (nvap)
Do two different accounts on the amount of component 2
Based on overall composition: n2= z2(nliq+ nvap)
Based on composition of each phase:
n2= nliq x2liq+ nvap x2vap
Combine both to get lever rule:
nliq/nvap = (x2vap- z2) /(z2 - x2liq)
T vs. x for fixed P (non-linear for both ideal and non-ideal)
(Lever rule works for this kind of diagram also)
Fractional distillation ("theoretical plates")
"Dilute-ideal" solutions: Ideal solutions have simple behavior for entire composition range. Non-ideal solutions behave simply when they are extremely dilute.
Look in the neigborhood of x2= 0 (just use x without subscript):
Just keep linear term in x...
Henry's Law for solute.
"Dilute-ideal" solutions: Ideal solutions have simple behavior for entire composition range. Non-ideal solutions behave simply when they are extremely dilute.
What does this mean in terms of chemical potentials?
For the solute (substance 2)
What about the solvent (substance 1)?
Gibbs-Duhem equation:
Chemical potential of solvent in "dilute-ideal" soln:
Henry's Law for solute implies Raoult's Law for solvent.
All this applicable only when x2<<x1.
The dilute relationships
are useful even when there is no vapor phase.
In that case, some other method is needed for determining the value of the reference m for the solute.
Concentration units––we've been using mole fractions
Molality: m = number of moles of solute per kg of solvent
Calculate mole fractions in terms of molality
The molality is rougly linear in mole fraction for a very dilute solution.
We will stick with mole fractions for simplicity.
Colligative properties (useful for determination of molecular weights):
Vapor pressure lowering
Boiling point elevation
Freezing point depression
Osmotic pressure
"Ligare" = Latin "to bind."
Colligative properties are bound together on the basis of simple behavior of the chemical potential of the solvent in a dilute solution.
Vapor pressure lowering: assumes non-volatile solute
Neglect higher terms...
Osmotic pressure
On the solution side of the membrane, the chemical potential of the solvent is lower than that of the pure solvent.
This is a case where we need to take into account the pressure dependence of the chemical potential of a liquid.
The difference in chemical potential will cause solvent to flow from the pure solvent side (high chemical potential) into the solution side (lower chemical potential), building up a pressure head P on the solution side.
When this process reaches equil., the chemical potential of the solvent must be the same on both sides of the membrane.
van t'Hof equation
For treatment of boiling point elevation and freezing point depression, see handout on Colligative Properties .
