SolutionsPart I: Colligative Properties

(loosely from Jespersen Chap. 13 Sec 6 & 7

Dr. C. Yau

Fall 2013

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What are Solutions?

Quick reminder:

Solutions are homogeneous mixtures consisting of...

generally one solute

dissolved in a solvent.

(More than one solute is possible.)

Colligative PropertiesThe term "colligative" comes from a Greek word meaning "dependent on the number."

Colligative properties refer to the properties of the solvent that depends on the number of particles (of the solute) and not the nature of the particles. However, with the stipulation that...

These solutes must be nonvolatile (and therefore does not contribute to the vapor pressure of the solvent). 3

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Colligative Properties

Since the properties are NOT dependent on the "nature" of the solute, this means the IMF of the solute plays no part in this.

We will be studying how the concentration of the solute affects the properties of the solvent.

Raoult's Law

Psoln = Xsolvent Posolvent

Psoln = vp of the solution (only due to the solvent because the solute is nonvolatile)

Xsolvent = mole fraction of solvent

=

Posolvent = vp of the pure solvent

(without solute)

solutesolvent

solvent

n n

n

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Raoult's Law

Psoln = Xsolvent Posolvent

Vp of solution is a fraction of the vp of the pure solvent.

This means that the solute has lowered the vp of the solvent.

Why?

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VP Lowering

One way to explain it is to consider the entropy of the system (which will be covered in a later chapter).

Another way is to consider the solute particles at the surface of the solution.

Their presence decreases the number of solvent particles on the surface, thus decreasing the chances of them breaking off into the vapor phase.

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solvent alone solute + solvent

VP is lower here.

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Phase Diagram of a Pure SolventVP of solvent is lowered by the solute

What happens to the BP and FP when a solute is added?

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Effect of Solute on MP and BP

Again we are considering only solutes that are nonvolatile…

The BP is raised

and the FP is lowered by the presence of the solute.

These are referred to as…

BP elevation

and FP depression.

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The Unit of Molality (m)Before we begin to study the quantitative effect of solute on the certain physical properties of a solvent, we must consider a special unit of concentration:

which is not to be confused with

Take a moment to compare the two.

# mol solutem = molality

# kg solvent

# mol soluteM = molarity

# L solution

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Molality – not affected by T

# mol solutem = molality

# kg solvent

Can you see why m is not affected by T?

# mol soluteM = molarity

# L solution

Is molarity affected by T? Why?Learn the definitions of these units of concentration NOW!

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Colligative PropertiesThe change in freezing point ΔTf is

proportional to the molality:

ΔTf = Kf m

and change in boiling point ΔTb is

also proportional to the molality:

ΔTb = Kb m

Table 13.3 p.609 gives these constants for various solvents.

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page 609

ΔTb = Kb mΔTf = Kf m

NOTE: BP is NOT ΔTb

What is the difference between BP and ΔTb?This is a common mistake!!!What is the symbol for BP?

Tb

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Determination of fp of solutionExample 13.8 p. 609Estimate the fp of a solution made from 10.0

g of urea, CO(NH2)2, with MM 60.06 g mol-1, and 125 g of water.

Table 13.3 tells us

Kf for water = 1.86oC m-1 (or oC/m)

Do Practice Exercise 17 & 18 p.610.

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Determination of MM from Colligative Properties

Example 13.9 p.611

A solution made by dissolving 5.65 g of an unknown molecular compound in 110.0 g of benzene froze at 4.39oC. What is the molar mass of the solute?

Table 13.3 tells us

Kf for benzene = 5.07 oC/m

Fp for benzene = 5.45 oC

Do Practice Exercise 19 & 20 p.612.

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Colligative Properties:Osmotic Pressure

Osmosis is the movement of solvent molecules through a semipermeable membrane from a dilute soln to a more concentrated soln.

Fig. 13.19 p.614

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Fig. 13.18p.613Onlysolventcan passthru themembrane.

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Effect on Osmotic Pressure = MRT (Note: M not m)

where = osmotic pressureM = concentration in molarityR = gas constant = 0.08206 atm.L.mol-1.K-1)T = temperature in KExample 13.10 p.616A very dilute soln , 0.00100 M sugar in water, is

separated from pure water by an osmotic membrane. What osmotic pressure in torr develops at 25oC?

Do Practice Exercises 21 ans 22 p.617.

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Determination of MM from Osmotic Pressure

Example 13.11 p.617

An aqueous solution with a volume of 100. mL and containing 0.122 g of an unknown molecular compound has an osmotic pressure of 16.0 torr at 21.0oC. What is the molar mass of the solute?

Do Practice Exercises 23 & 24 p.618.

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When Solute is an Ionic Compound

When the solute is ionic, such as NaCl the effect is doubled. Why?

When the solute is (NH4)2SO4, the effect is tripled. Why?

What does NaCl do when it dissolves in water?

NaCl(s) Na+ (aq) + Cl- (aq)

One f.u. transforms into TWO particles, so the effect is doubled.

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Colligative Properties for Ionic Solutes

ΔTf = i Kf m

ΔTB = i KB m

= i MRT

i = number of particles into which the ionic solute breaks up.

i = 2 for NaCl (effect is doubled)

i = 3 for (NH4)2SO4 (effect is tripled)

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Effect of Ions in SolutionFP of a 0.10 m sucrose (C12H11O22) solution is

found to be -0.19C.

FP of a 0.10 m NaCl solution = -0.38C (lowered by twice as much).

Kb of water = 0.51 C/m

What do you expect the BP to be for…

a) 0.10 m sucrose?

b) 0.10 m NaCl?

Which do you expect to have the higher BP?

a) 0.1m NaCl or b) 0.05m Na2SO4Ans. (a)

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Nonelectrolyte: ΔTf = Kf m

(Solute is molecular.)

Electrolyte: ΔTf = i Kf m

(Solute is ionic.)If we don’t know whether a solute is ionic, we can identify it as such as follows:

Calc ΔTf as a nonelectrolyte.

Compare it with the observed ΔTf .

e.g. If calc ΔTf is 6oC and observed is 12oC, we know i = 2. (Effect is doubled.)

Effect of Ions in Solution

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Effect of Ions in SolutionExperimentally, the i value is determined thus:

Example: Experimentally we determined 0.10 m NaCl to have a Tf of 0.38C. We calculate the theoretical

Tf = kf m = (1.86C/m)(0.10m)=0.18C.

Calculate i.

f

f as nonelectrolyte

T

Tmeasured

calculated

i

f fT is some multiple of Tmeasured nonelectrolyte

0.38 C i = = 2.1

0.18 C

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Effect of concentration on i

• i value is affected by concentration!

• WHY?

• When the concentration increases, the ions are closer together and the attraction between them increases.

• They begin to act less freely as dissociated ions (less than 100% dissociated).

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p.622

As concentration increases, deviation increases.Dilution leads towards the theoretical i value.Compare NaCl with MgSO4. Both have theoretical i = 2.Why does MgSO4 deviate much more than NaCl?

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Effect on Colligative Properties can be LESS.

We see that the effect of ionic solute causes the effect to be GREATER than expected.

What kind of solute would cause the effect to be LESS than expected?

O

OH

O

OH O

OH

Benzoic acid forms a "dimer" in solution. Two molecules are not freely working as two particles, but working as ONE unit. Thus, i = ½ and effect is one half of expected.

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Vapor Pressure Lowering

We had previously begun with the explanations to why the vapor pressure of a solvent is lowered when a solute is added.

Let us now return to “vapor pressure lowering” and examine the implications.

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Posolvent is a constant, characteristic of the solvent

Psoln and Xsolvent are variables.If we rearrange the equation, we getPsoln = Po

solvent Xsolvent

y = m x If we plot Psoln vs Xsolvent ,

the slope is Posolvent.

Psoln = Xsolvent Posolvent

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Example 13.6 p. 604

Carbon tetrachloride has a vp of 155 torr at 20oC. This solvent can dissolve candle wax, which is essentially nonvolatile. Although candle wax is a mixture, we can take its molecular formula to be C22H46 (MM 311g mol-1).

What is the vapor pressure at 20oC of a solution prepared by dissolving 10.0 g of wax in 40.0 g of CCl4 (MM 154 g mol-1).

Do Practice Exercises 13 & 14 p.605

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By how much is the vp lowered?

P = change in vp due to solutes

= ?P = Xsolute P°solv

How do we get this equation?

(See lecture notes. This was derived in class. It is also in your textbook, more or less.)

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VP of soln if solute is volatileLet us now consider the case when the

solute is VOLATILE.Applying Dalton's Law of Partial Pressures

to a mixture of gases A + B,

PTotal = PA + PB

where PA is partial pressure of A = XAPoA

and PB is partial pressure of B = XBPoB

PTotal = XAPoA + XBPo

B

Raoult's equation is simply dropping off one term (such as XBPo

B because the solute is nonvolatile).

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Raoult's LawOne last point about Raoult's Law….

It is for the ideal solutions.

BUT, even deviations from the law gives us information on the IMF of the solute to the solvent and IMF of the solvent molecules to solvent molecules.

If the solute-solvent IMF is strong, vp of solution would be lowered more than expected.

If the solvent-solvent IMF is strong, vp of the solution would not be lowered as much as expected (adding solute disrupts the IMF of the solvent and allows more solvent to vaporize).