Solutions

Chapter 13Properties of Solutions

Solutions

Solutions

• Solutions are homogeneous mixtures of two or more pure substances.

• In a solution, the solute is dispersed uniformly throughout the solvent.

•The intermolecular forces between solute and solvent particles must be strong enough to compete with those between solute particles and those between solvent particles.

Solutions

How Does a Solution Form?• As a solution forms, the solvent pulls solute

particles apart and surrounds, or solvates, them.• If an ionic salt is soluble in water, it is because the

ion-dipole interactions are strong enough to overcome the lattice energy of the salt crystal.

•Side note - Just because a substance disappears when it comes in contact with a solvent, it doesn’t mean the substance dissolved.•Dissolution is a physical change—you can get back the original solute by evaporating the solvent.•If you can’t, the substance didn’t dissolve, it reacted.

Solutions

Energy Changes in Solution• Three processes affect the

energetics of the process:Separation of solute particlesSeparation of solvent particlesNew interactions between solute

and solvent

The enthalpy change of the overall process depends on H for each of these steps.

Solutions

Why Do Endothermic Processes Occur?

• Things do not tend to occur spontaneously (i.e., without outside intervention) unless the energy of the system is lowered.

• Yet we know that in some processes, like the dissolution of NH4NO3 in water, heat is absorbed, not released.

Solutions

Enthalpy Is Only Part of the Picture

• The reason is that increasing the disorder or randomness (known as entropy) of a system tends to lower the energy of the system.

• So even though enthalpy may increase, the overall energy of the system can still decrease if the system becomes more disordered.

Solutions

Types of Solutions• Saturated

Solvent holds as much solute as is possible at that temperature.

Dissolved solute is in dynamic equilibrium with solid solute particles.

• UnsaturatedLess than the maximum

amount of solute for that temperature is dissolved in the solvent.

Solutions

Types of Solutions

• SupersaturatedSolvent holds more solute than is normally possible at

that temperature.These solutions are unstable; crystallization can

usually be stimulated by adding a “seed crystal” or scratching the side of the flask.

Solutions

Factors Affecting Solubility• Chemists use the axiom

“like dissolves like”: Polar substances tend to

dissolve in polar solvents. Nonpolar substances tend to

dissolve in nonpolar solvents.

• The more similar the intermolecular attractions, the more likely one substance is to be soluble in another.

Solutions

Factors Affecting SolubilityGlucose (which has hydrogen bonding) is very soluble in water, while cyclohexane (which only has dispersion forces) is not.

• Vitamin A is soluble in nonpolar compounds (like fats).

• Vitamin C is soluble in water.

Solutions

Gases in Solution

• In general, the solubility of gases in water increases with increasing mass.

• Larger molecules have stronger dispersion forces.

Solutions

Gases in Solution – Henry’s Law• The solubility of liquids and solids

does not change appreciably with pressure.

• The solubility of a gas in a liquid is directly proportional to its pressure.

Sg = kPg

whereSg is the solubility of the gas;

k is the Henry’s law constant for that gas in that solvent;

Pg is the partial pressure of the gas above the liquid.

Solutions

Temperature

Generally, the solubility of solid solutes in liquid solvents increases with increasing temperature.

Solutions

Temperature

• The opposite is true of gases:Carbonated soft

drinks are more “bubbly” if stored in the refrigerator.

Warm lakes have less O2 dissolved in them than cool lakes.

Solutions

Ways of Expressing

Concentrations of Solutions

Solutions

Mass Percentage

Mass % of A =mass of A in solutiontotal mass of solution

100

Solutions

Parts per Million andParts per Billion

ppm =mass of A in solutiontotal mass of solution

106

Parts per Million (ppm)

Parts per Billion (ppb)

ppb =mass of A in solutiontotal mass of solution

109

Solutions

moles of Atotal moles in solution

XA =

Mole Fraction (X)

• In some applications, one needs the mole fraction of solvent, not solute—make sure you find the quantity you need!

Solutions

mol of soluteL of solution

M =

Molarity (M)

• You will recall this concentration measure from Chapter 4.

• Because volume is temperature dependent, molarity can change with temperature.

Solutions

mol of solutekg of solvent

m =

Molality (m)

Because both moles and mass do not change with temperature, molality (unlike molarity) is not temperature dependent.

Solutions

Changing Molarity to Molality

If we know the density of the solution, we can calculate the molality from the molarity, and vice versa.

Solutions

Colligative Properties

• Changes in colligative properties depend only on the number of solute particles present, not on the identity of the solute particles.

• Among colligative properties areVapor pressure lowering Boiling point elevationMelting point depressionOsmotic pressure

Solutions

Vapor Pressure• Because of solute-solvent

intermolecular attraction, higher concentrations of nonvolatile solutes make it harder for solvent to escape to the vapor phase.

• Therefore, the vapor pressure of a solution is lower than that of the pure solvent.

Solutions

Raoult’s Law

PA = XAPAwhere• XA is the mole fraction of compound A

• PA is the normal vapor pressure of A at that temperature

NOTE: This is one of those times when you want to make sure you have the mole fraction of the solvent.

Solutions

Boiling Point Elevation and Freezing Point Depression

Nonvolatile solute-solvent interactions also cause solutions to have higher boiling points and lower freezing points than the pure solvent.

Solutions

Boiling Point ElevationThe change in boiling point is proportional to the molality of the solution:

Tb = Kb m

where Kb is the molal boiling point elevation constant, a property of the solvent.Tb is added to the normal

boiling point of the solvent.

Solutions

Freezing Point Depression• The change in freezing

point can be found similarly:

Tf = Kf m

• Here Kf is the molal freezing point depression constant of the solvent.

Tf is subtracted from the normal freezing point of the solvent.

Solutions

Boiling Point Elevation and Freezing Point Depression

Note that in both equations, T does not depend on what the solute is, but only on how many particles are dissolved.

Tb = Kb m

Tf = Kf m

Solutions

Colligative Properties of Electrolytes

Since colligative properties depend on the number of particles dissolved, solutions of electrolytes (which dissociate in solution) should show greater changes than those of nonelectrolytes.

Solutions

Colligative Properties of Electrolytes

However, a 1 M solution of NaCl does not show twice the change in freezing point that a 1 M solution of methanol does.

Solutions

van’t Hoff Factor• One mole of NaCl in

water does not really give rise to two moles of ions.

• Some Na+ and Cl− reassociate for a short time, so the true concentration of particles is somewhat less than two times the concentration of NaCl.

Solutions

van’t Hoff Factor

• Reassociation is more likely at higher concentration.

• Therefore, the number of particles present is concentration dependent.

Solutions

The van’t Hoff FactorWe modify the previous equations by multiplying by the van’t Hoff factor, i

Tf = Kf m i

Solutions

Ex. Electrolyte (i = ?)

• IMPORTANT – the colligative properties of freezing point and boiling point are proportional to the number of particles present in the solution.

• van Hoft factor, i

• NaCl i = 2 moles Ie. 1m = 2m

• CaCl2 i = 3 moles Ie. 1m = 3m

• Al2(SO4)3 i = 5 moles Ie. 1m = 5m

Solutions

Osmosis• Some substances form semipermeable membranes, allowing

some smaller particles to pass through, but blocking other larger particles.

• In biological systems, most semipermeable membranes allow water to pass through, but solutes are not free to do so.

• In osmosis, there is net

movement of solvent

from the area of higher

solvent concentration

(lower solute concentration)

to the are of lower solvent

concentration (higher solute

concentration).

Solutions

Osmotic Pressure

• The pressure required to stop osmosis, known as osmotic pressure, , is

nV

= ( )RT = MRT

where M is the molarity of the solution

If the osmotic pressure is the same on both sides of a membrane (i.e., the concentrations are the same), the solutions are isotonic.

Solutions

Osmosis in Cells• If the solute concentration

outside the cell is greater than that inside the cell, the solution is hypertonic.

• Water will flow out of the cell, and crenation results.

• If the solute concentration outside the cell is less than that inside the cell, the solution is hypotonic.

• Water will flow into the cell, and hemolysis results.

Solutions

Molar Mass from Colligative Properties

We can use the effects of a colligative property such as osmotic pressure to determine the molar mass of a compound.

Solutions

Ideal Solutions

• Two types of molecules are randomly distributed

• Typically, molecules are similar in size and shape

• Intermolecular forces in pure liquids & mixture are similar

• Examples: benzene & toluene, hexane and heptane

(more precise thermodynamic definition coming)

In ideal solutions, the partial vapor pressure of componentA is simply given by Raoult’s Law:

*AAA PxP

vapor pressure of pure Amole fraction of A in solution

Solutions

Total VP of an ideal solution

BAtotal PPP

** ln

A

AAA P

PRT

*AAA PxP

AAA xRT ln*

This serves to define an idealsolution if true for all values of xA

The total vapor pressure of an ideal solution:

**BBAAtotal PxPxP

40 °C

)( ***ABBAtotal PPxPP

Solutions

Deviations from Raoult’s Law

Methanol, ethanol, propanolmixed with water. Which oneis which? (All show positive deviations from ideal behavior)

CS2 and dimethoxymethane: Positive deviation from ideal (Raoult’s Law) behavior.

trichloromethane/acetone: Negative deviation from ideal (Raoult’s Law) behavior.

Solutions

Raoult and Henry

1 as * AAAA xPxP

0 as , AAHAA xkxP

Raoult’s law

Henry’s law constant:*

, AAH Pk

The Henry’s law constant reflects the intermolecular interactions between the two components.

Solutions following both Raoult’s and Henry’s Laws are called ideal-dilute solutions.

Henry’s behavior:

Henry’s law(Raoult’s Law)

Solutions

The Vapor Pressure of Solutions

• Nonvolatile Solute/Solvent

0solventsolventsolution PxP Raoult’s Law

Solutions

Solutions

Solutions

Raoult’s Law with Multiple Volatile compounds

• Ideal solution: A solution, obeys Raoult’s law, formed with no accompanying energy change, when the intermolecular attractive forces between the molecules of the solvent are the same as those between the molecules in the separate components.

Solutions

Rauolt’s Law

e solutionvapor abov

d B in there of A anial pressu: the part and PP

B and pure of pure Ar pressure: the vapo and PP

of A and B fraction : the mole and xx

PxPxPPP

BA

BA

BA

BBAABAtotal

00

00

Solutions

1.What is the total vapor pressure in a mixture of

50.0 g CH3OH (P° = 93.3 torr) and 25.0 g H2O

(P° = 17.5 torr)?

2.In a mixture of 86.0 g C6H6 (P° = 93.96 torr)

and 90.0 g C2H4Cl2 (P° = 224.9 torr), what is

the total vapor pressure?

Solutions

Nonideal Solution

• Solutions that do not obey Raoult’s Law are called nonideal solutions.

• Solute-solvent interactions are significantly different from solute-solute and solvent-solvent interactions, the solution is likely to be a nonideal solution.

• Intermolecular forces between components in a dissolved solution can cause deviations from the calculated vapor pressure.

Solutions

Negative Deviation from Raoult’s Law

• Both components have a lower escaping tendency in the solution than in the pure liquids.

C O

H3C

O

H

H

H3C

Solutions

Positive Deviation from Raoult’s Law

• If two liquids mix endothermically, this indicates that the solute-solvent interactions are weaker than the interactions among the molecules in the pure liquids.

• More energy is required to expand the liquid than is released when the liquids are mixed. The molecules in the solution have a higher tendency to escape than expected.

CH3 CH2 OH CH3 CH2 CH2 CH2 CH2 CH3

Solutions

ideal system positive deviation negative deviation

Solutions

Solutions54

Ideal Solutions

A Solution is any homogeneous phase that contains more than one component. These components can’t be physically differentiated. A Solvent is the component with the larger proportion or quantity in the solution. A Solute is the component with the smaller proportion or quantity in the solution.The idea of Ideal Solutions is used to simplify the study of the phase equilibrium for solution. The solution is considered to be ideal when:

its components are assumed to have similar structures and sizes, and when it represents complete uniformity of molecular forces (basically attraction forces).

Solutions55

Ideal Solutions

When considering a binary system, we are often interested to study the behavior of that system in terms of the variables P, T and n.

Solutions56

Raoult’s Law

Recall that the vapor pressure is a measure of the tendency of the substance to escape from the liquid.

For an ideal solution composed of two components (binary systems) , Raoult’s law relates between the vapor pressure of each component in its pure state (P*) to the partial vapor pressure of that component when it is in the ideal solution (P).

Solutions57

Raoult’s Law

To know what partial vapor pressure a component in a solution has is important. This is because it gives you information about the cohesive forces in the system.

Solutions58

Raoult’s LawIf the solution has partial vapor pressures that follow:

*222

*111

PxP

PxP

then the system is said to obey Raoult’s law and to be ideal, taken into consideration T is fixed for the solvent and solution.Examples include:

Benzene – toluene. C2H5Cl – C2H5Br. CHCl3 – HClC=CCl2.

Solutions59

Application of Raoult’s Law

Problem 5.21:

Benzene and toluene form nearly ideal solutions. If at 300 K, P*(toluene) = 3.572 kPa and P*(benzene) = 9.657 kPa, compute the vapor pressure of a solution containing 0.60 mole fraction of toluene. What is the mole fraction of toluene in the vapor over this liquid?

Solutions60

Deviations from Raoult’s Law

Deviations from Raoult’s law occur for nonideal solutions.

Consider a binary system made of A and B molecules.Positive deviation occurs when the attraction forces between A-A and B-B pairs are stronger than between A-B. As a result, both A and B will have more tendency to escape to the vapor phase.Examples:

CCl4 – C2H5OH system.

n-C6H14 – C2H5OH system

Solutions61

Deviations from Raoult’s Law

For a binary system made of A and B molecules.Negative deviation occurs when the attraction force between A-B pairs is stronger than between A-A and B-B pairs. As a result, both A and B will have less tendency to escape to the vapor phase.Examples:

CCl4 – CH3CHO system.

H2O – CH3CHO system

Solutions62

Deviations from Raoult’s Law

Another important observation is that

at the limits of infinite dilution, the vapor pressure of the solvent obeys Raoult’s law.

Solutions63

Henry’s Law

The mass of a gas (m2) dissolved by a given volume of solvent at constant T is proportional to the pressure of the gas (P2) above and in equilibrium with the solution.

m2 = k2 P2

where k2 is the Henry’s law constant.

Solutions64

Henry’s Law

For a mixture of gases dissolved in a solution. Henry’s law can be applied for each gas independently. The more commonly used forms of Henry’s law are:

P2 = k’ x2

P2 = k” c2

Solutions65

Henry’s Law

The vapor pressure of a solute, P2 , in a solution in which the solute has a mole fraction of x2 is given by:

P2 = x2 P2*

where P2* is the vapor pressure of the solute in a pure liquefied state. It is also found that at the limits of infinite dilution, the vapor pressure of the solute obeys Henry’s law.

Solutions66

Application of Henry’s Law