chemistry-ch10_solutions and solubility

1010 Solutions Solutions and solubilityand solubility

10.1 Introduction to solutions 10.1 Introduction to solutions and solubilityand solubility

• Solution– Homogeneous mixture of two or more

pure substance – May be gaseous, liquid or solid

• Solvent– Liquid of a liquid solution

• Solute– Dissolved substance in liquid solution

10.1 Introduction to solutions 10.1 Introduction to solutions and solubilityand solubility

• Solubility– Maximum amount of solute that dissolves

completely in a given amount of solvent at a particular temperature, T

• Saturated solution– Solution in which no more solute will

dissolve

• Dissolution– Process of dissolving a solute in a solvent to

give a homogeneous solution

10.2 Gaseous solutions10.2 Gaseous solutions

• All gases mix completely with all other gases in all proportions

• Gases mix spontaneously hence ΔG for mixing process negative


• Enthalpy change when two gases are mixed is usually small

• Large positive ΔmixS term ensures ΔmixG negative

• Intermolecular forces between individual gas molecules are tiny, and gas molecules are far apart

• No impediment to the mixing of gases


• The magnitude of interatomic and intermolecular attractions in the condensed phase can determine whether or not two substances can mix

10.3 Liquid solutions10.3 Liquid solutions

• Gas–liquid solutions

– For a gas to dissolve in a liquid, the gas molecules must be able to disperse themselves evenly throughout the solvent



– Intramolecular forces between the solvent molecules are not negligible

– Neither therefore is the value of ΔsolH, the enthalpy of solution

• Gas–liquid solutions– Solubility of gases vary significantly with

temperature– Solubility of gases vary significantly with

pressure



• Gas–liquid solutions– For gases that do not react with the solvent,

Henry’s law gives the relationship between gas pressure and gas solubility

– cgas is the concentration of the gas

– pgas is the partial pressure of the gas above the solution

– kH is called the Henry’s law constant and is unique to each gas

Tpkc constantgasHgas


• Gas–liquid solutions– Equation is only true at low

concentrations and pressures– An alternative expression of Henry’s law

is:

– c1 and p1 refer to initial conditions

– c2 and p2 refer to final conditions

2

2

1

1pc

pc


• Liquid–liquid solutions

– Formation of a liquid–liquid solution requires that the attractive forces present between the molecules of the two pure liquids is overcome

– Two substances are MISCIBLE when they mix completely in all proportions

– Two substances are IMMISCIBLE when they form two layers upon the addition of one to the other


• Liquid–liquid solutions

C C O

H

HH

H

H H

Like–dissolves–like

Ethanol Benzenehydrogen bond

C

CC

C

CC

H

H

H

HH

H

H O

H

H O

C2H5

H

OC2H5

H O

H

O

H

H


• Liquid–solid solutions– Basic principles remain

the same– Solvation is when a solute

molecule is surrounded by solvent molecules

– Hydration occurs when solutes become surrounded by water molecules

• Liquid–solid solutions– Like-dissolves-like– When intermolecular attractive forces within

solute and solvent are sufficiently different,the two do not form a solution


• Liquid–solid solutions


• Liquid–solid solutions– Temperature can

have a significant effect on the solubility of a solid solute in a liquid


10.4 Quantification of 10.4 Quantification of solubility: the solubility solubility: the solubility

productproduct• Ionic salts are generally classified as

being either soluble or insoluble in waterAgNO3(aq) + NaCl(aq) AgCl(s) + NaNO3(aq)

AgCl(s) Ag+(aq) + Cl–(aq)

Ksp = [Ag+][Cl–]

• Ksp is called the solubility product

MaXb(s) aMc+(aq) + bXd–(aq)

Ksp = [Mc+]a[Xd–]b


productproduct• The relationship between Ksp and

solubility

– Molar solubility (s)molar concentration of a salt in its saturated solution

– Molar solubility can be used to calculate Ksp, assuming that all of the salt that dissolves is 100% dissociated into its ions


productproductThe solubility of AgBr in water is 1.3 × 10–4 g L–1 at 25 °C. Calculate Ksp for AgBr at this temperature

AgBr(s) Ag+(aq) + Br–(aq)

Ksp = [Ag+][Br–]

[Ag+] = [Br–] = 6.9 × 10–7 mol L–1

Ksp = [Ag+][Br–] = (6.9 × 10–7 mol L–1)(6.9 × 10–7 mol L–1)

Ksp = 4.8 × 10–13 at 25 °C

mol109.6gmol77.187

g103.1 71

4

Mm

n


productproductCalculate the molar solubility of lead iodide, PbI2, given that Ksp(PbI2) = 7.9 × 10–9

PbI2(s) Pb2+(aq) + 2I–(aq)

Ksp = [Pb2+][I–]2

Define the molar solubility of PbI2(s) as s mol L–1

[Pb2+] = s mol L–1

[I–] = 2s mol L–1

Ksp = (s)(2s)2 = (s)(4s2) = 4s3 = 7.9 × 10–9

s = 1.3 × 10–3

The molar solubility of PbI2(s) in water at 25 °C is 1.3 × 10–3 mol L–1

4109.7 9

3s


productproduct• The common ion effect

– Any ionic salt is less soluble in the presence of a common ion, an ion that is in the salt

PbCl2(s) Pb2+(aq) + 2Cl–(aq)

Ksp = [Pb2+][Cl–]2

Add Pb(NO3)2(aq) to saturated solution of PbCl2 instantaneously increases [Pb2+] and therefore Qsp (ionic product).

Qsp > Ksp

PbCl2 is precipitated


productproductWhat is the molar solubility of PbI2 in a 0.10 M NaI solution?

PbCl2(s) Pb2+(aq) + 2Cl–(aq)

Ksp = [Pb2+][Cl–]2 = 7.9 × 10–9

Ksp = s(0.10 + 2s)2 = 7.9 × 10–9

Ksp = s(0.10)2 = 7.9 × 10–9

Molar solubility of PbI2 in 0.10 M NaI solution is 7.9 × 10–7 M (s)

PbI2(s) Pb2+(aq) + 2I–(aq)

Initial concentration (M) 0 0.10

Change in concentration (M) +s +2s

Equilibrium concentration (M) s 0.10 + 2s


productproduct• Prediction of precipitation

– Qsp > Ksp precipitate will form

– Qsp < Ksp no precipitate will form

AgCl(s) Ag+(aq) + Cl–(aq)

Ksp = [Ag+][Cl–] = 1.8 × 10–10

[Ag+] = 5.0 × 10–7 mol L–1

[Cl–] = 5.0 × 10–5 mol L–1

Qsp = 2.5 × 10–11

Qsp < Ksp no precipitate will form

10.5 Colligative properties of 10.5 Colligative properties of solutionssolutions

• Nonvolatile solutes– Solutes that can’t evaporate from solution– Vapour pressure of a solution of

nonvolatile solutes is lower than the pure solvent

• Colligative properties– Depend on number of solute particles in

solution rather than chemical identities


• Molarity– Amount of substance in a particular

volume of solution

– Solutions (usually) increase in volume with increasing temperature

– The molarity of a solution changes as the temperature changes

amount of solute (mol)

molarity ( )volume of solution (L)

c


• Molality– Preferred method of expressing solution

composition when colligative properties involved

– Amount of solute per kilogram of solvent

– Temperature independent

amount of solute (mol)

molality ( )mass of solvent (kg)

b


• Mole fraction– The number of moles of a particular

component divided by the total number of moles of material in the solution

– The mole fraction of A, XA, in a solution containing substances A, B and C

– Temperature independent

AA

A B C

nX

n n n


• Raoult’s law

– Boiling point of a solution containing a nonvolatile solute is higher than that of the pure solvent

– Boiling point of a solvent is the temperature at which the vapour pressure of the solvent is equal to the atmospheric pressure


• Raoult’s lawpsolution = Xsolvent p*

solvent

– psolution – vapour pressure of the solution

– Xsolvent – mole fraction or solvent in the solution

– p*solvent – vapour pressure of pure solvent

– For a simple two component system– Provided the solution is sufficiently dilute

10.5 Colligative properties 10.5 Colligative properties of solutionsof solutions

• Raoult’s law psolution = Xsolvent p*

solvent

Xsolvent = 1 – Xsolute

psolution = (1 – Xsolute)p*solvent

psolution = p*solvent – Xsolutep*

solvent

Δp = Xsolutep*solvent

Δp = p*solvent – psolution

• Raoult’s law– A solution that obeys Raoult’s law is called an ideal

solution– These solutions

are generally dilute and have only small interactions between their constituent molecules


• Solutions containing more than one volatile component– For component A

pA = XAp*A

– For component BpB = XBp*

B

– Total pressureptotal = XAp*

A + XBp*B


• Boiling point elevation and freezing point depression– boiling point elevation

ΔTb

ΔTb = Kbb

– freezing point depression

ΔTf

ΔTf = Kfb



• Boiling point elevation and freezing point depression– Molal boiling point elevation constant

• Kb

• Units – K mol–1 kg

– Molal freezing point depression constant• Kf

• Units – K mol–1 kg


• Boiling point elevation and freezing point depression– Molality of the solution

• b

• Units – mol kg–1

– Kbb and Kf b are properties of the solvent only and independent of the identity of the solute


• Osmosis and osmotic pressure– A membrane keeps mixtures and solutions

organised and separated.– Semipermeable membranes allow selective

substances to pass through– Dialysis occurs when a dialysing membrane

allows both water and small solute particles through

– Osmosis is a net shift of only solvent through an osmotic membrane


• Osmosis and osmotic pressure


• Osmosis and osmotic pressure– Osmotic pressure

• Π

– In dilute aqueous solution

Π = cRT

ΠV = nRT

– This is the van’t Hoff equation for osmotic pressure

Vn

c

• Osmosis and osmotic pressure

Osmometer

Isotonic HypotonicHypertonic



• Measurement of solute dissociation– Molal freezing point depression constant

for water is 1.86 K mol–1

– 1.00 mol kg–1 NaCl freezes at about –3.37 °C

– NaCl(s) Na+(aq) + Cl–(aq)– Solution has a a total molality of dissolved

solute particles of 2 mol kg–1

– Theoretically, a 1.00 mol kg–1 NaCl solution should freeze at –3.72 °C


• Measurement of solute dissociation– With increasing dilution solutes behave

more and more as if they were 100 % dissociated

– Compare degrees of dissociation by quantity called the van’t Hoff factor (i)

f

f

Ti

Tmeasured

calculatedasnonelectrolyte

• Measurement of solute dissociation



• Measurement of solute dissociationCH3COOH(aq) + H2O(l) H3O+(aq) + CH3COO–(aq)

– 1.00 mol kg–1 aqueous acetic acid solution freezes at –1.90 °C

– Only a little lower than expected if no ionisation occurred

1

1

kgmol02.1

kgmolK86.1

K90.1

b

KT

bf

f

%2ionisation%

%10000.102.0

ionisation%

100%availableacidofmol

ionisedofmolionisation%


• Measurement of solute dissociation– Some molecular solutes produce smaller

colligative effects than their molal concentrations would lead us to predict

– Often evidence of solute molecules clustering or undergoing association in solution

C6H5 C O HO

C6H5 CO H

OC6H5C

OH

O2

benzoic acid benzoic acid dimer

chemistry-ch10_solutions and solubility

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