Summary: Ionic Equilibria

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As applied to:

H+ concentration pH = -log10[H+]

Ka pKa = -log10KaKb pKb = -log10Kb

Kw pKw = -log10Kw

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Bronsted-Lowry definition proton donor

must have a hydrogen atom that can be lost

proton acceptor

must have a lone pair of electrons which can form acoordinate bond with a hydrogen ion

Weak acids / bases dissociate partially insolution

An acid works in tandem with a base one to proton, the other to .

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Conjugate acid-base pairs

This equation may be simplified as:

HA A- + H+

HA + H2O A- + H3O

+

acid base conjugate

base

conjugate

acid

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Conjugate acid-base pairs

B + H2O BH+ + OH-

base acid conjugateacid

conjugatebase

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Acid Dissociation Constant

In dilute aqueous solutions, amount of H2O thatreacts with HA is compared to the total

amount of water present. [H2O] remains , and is left out of

the Ka expression.

HA + H2O A- + H3O

+

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Ka

[A][H3O ]

[HA]


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To calculate pH of weak acid, HA

where [HA]i is the initial concentration of HA, beforexof it dissociates to form A- and H3O

+ ions

HA A- + H3O+

Initial conc / mol dm-3 [HA]i 0 0

Change in conc/ mol dm-3

-x +x+x

Eqm conc / mol dm-3 [HA]i - x x x

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To calculate pH of weak acid Assuming degree of acid dissociation is small such

that [HA]i >> x, and [HA]ix [HA]i

Ka [A

][H3O

][HA]

x

2

[HA]i x x

2

[HA]i

x [H ] Ka {[HA]i x} Ka [HA]i

pH lg Ka [HA]

pH

lgKa

[HA]i

or

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equals to [HA]at equilibrium


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Base Dissociation Constant

Kb is derived similarly.

B + H2O BH+ + OH-

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Kb

[BH ][OH ]

[B]


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To calculate pH of weak base, B

where [B]i is the initial concentration of B, before xof it dissociates to form BH+ and OH ions

B + H2O BH+ +

OH-

Initial conc/ mol dm-3

[B]i - 0 0


-x - +x+x

Eqm conc/ mol dm-3

[B]i - x - x x

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To calculate pOH of weak base Assuming degree of base dissociation is small such

that [B]i >> x, and [B]ix [B]i

Kb [BH

][OH

][B]

x

2

[B]i x x

2

[B]i

x [OH ] Kb {[B]i x} Kb [B]i

pOH lg Kb [B]

pOH

lgKb

[B]i

or

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equals to [B]at equilibrium


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Ionic Product of Water, Kw

2H2O H3O+ + OH-

Kw = [H3O+][OH-]

pKw = pH + pOH

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Temperature dependence ofKw

pH + pOH = 14 is applicable at 25 C! pH of pure water decreases with temperature as

[H+] increases. Is water becoming more acidic?

Temperature/ C

Kw/ x 10-14

mol2 dm-6pKw

[H+]/ 10-7

mol dm-3

[OH-]/ 10-7

mol dm-3pH

0 0.114 14.9 0.338 0.338 7.47

25 1.01 14.0 1.00 1.00 7.00

50 5.48 13.3 2.34 2.34 6.63

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Relationship between Kw, Ka and Kb Consider a weak acid HA,

Its conjugate base, A-, undergoes salt hydrolysis as

follows:A- + H2O HA + OH

-

Ka [A][H3O

]

[HA]

Kb [HA][OH ]

[A ]

HA + H2O A- + H3O

+acid conjugate

base

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Relationship between Kw, Ka and Kb

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Ka Kb [A ][H3O

]

[HA][HA][OH]

[A ]

Ka Kb [H3O][OH ] Kw



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pH Titration Curves Source: catalog.flatworldknowledge.com

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Choice of Indicator pH transition range of chosen indicator should fall

within the region where a sharp change in pH isobserved on the titration curve.

E.g. Source: www.chemguide.co.uk

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Buffers Acidic buffer: weak acid HA + conjugate base A-

HA H+ + A-

MA M+ + A-

Alkaline buffer: weak base B + conjugate acid BH+

B + H2O BH+ + OH-

BH+Cl- BH+ +Cl-

i.e. salt of weak acid HA

i.e. salt of strongmineral acid, e.g. HCl

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How do buffers work? Consider an acidic buffer, an equimolar mixture of

CH3CO2H and CH3CO2-Na+,

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CH3CO2H CH3CO2-

OH-

CH3CO2-

H+

CH3CO2H

CH3CO2H + OH-

CH3CO2- + H2O

CH3CO2- + H+

CH3CO2H


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CH3CO2H CH3CO2-

CH3CO2H CH3CO2-

CH3CO2H CH3CO2-

+H+

+OH-

pH of bufferdecreases only slightly

pH of bufferincreases only

slightly

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To calculate pH of an acidic buffer

where [HA]i and [A-]i are initial concentrations of HA

and A- respectively, before xof HA dissociates toform ions.

HA + H2O A- + H3O

+

Initial conc/ mol dm-3

[HA]i - 0


-x - +x+x

Eqm conc/ mol dm-3

[HA]i - x - x

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To calculate pH of an acidic buffer

Ka [A ][H3O

]

[HA] [H3O

] [A ]

[HA]

lgKa lg[H ] lg

[A ]

[HA]

lg[H ] lgKa

lg[A ]

[HA]

pH pKa lg[A ]

[HA]23



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To calculate pH of an acidic buffer Assuming [HA]ix [HA]i and [A

-]i + x [A-]i

pH pKa lg{[A ]i x}

{[HA]i x}(where x= [H+])

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pH pKa lg[A ]i[HA]i

pH

pKa

lg

[A]

[HA]


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Similarly, expressions to calculate pOH ofalkaline buffers may be derived.

pOH pKb lg[BH]

[B]

pOH pKb

lg[BH ]i

[B]i

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An indicator is a weak acid whose conjugatebase is of a different colour. or a weak base whose conjugate acid is of a

different colour.


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HIn + H2O In- + H3O

+

acidColour A

conjugatebase

Colour B


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The is the sudden colour changeseen in a titration.

A colour change is typically detected when


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KInd [H3O ]

[Ind ]

[HInd]

[Ind

][HInd]

110

or 101


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Difference between end pointandequivalence point The of the titration is reached

when moles of acid react with moles of

base. If indicator is chosen correctly, the end point will be

very closeto the equivalence point.


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Solubility Product, Ksp Consider a sparingly soluble salt, MX2

MX2(s) M2+(aq) + 2X-(aq)

Since MX2 is a solid, its concentration is taken to be

its density, and is a constant. Thus Ksp does not contain [MX2(s)] in its expression.

Ksp = [M2+][X-]2

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To predict occurrence of precipitation Calculate ionic product (IP), and compare with Ksp.

IP = Ksp saturated solution

On the brink of precipitation

Precipitate forms immediately if seed crystal is added. IP < Ksp unsaturated solution

No precipitation

IP > Ksp over-saturated solution

Precipitate forms.

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Solubility Product, Ksp Ionic Product (IP)

IP expression is exactly the as Ksp expression

Only used with ionicconcentrations in asolution

Applicable to all types ofsolutions (unsaturated orsaturated) of

At constant temperature,Ksp value is IP value keeps with ionic concentration,even at constanttemperature

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Common Ion Effect Consider a sparingly soluble salt, MX2,

MX2(s) M2+(aq) + 2X-(aq)

When a common ion (i.e. M2+ or X-) is added to a

solution of MX2, by Le Chateliers Principle, equilibrium shifts left to decrease concentration of

common ion.

MX(s) is precipitated.

of MX(s) is .

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Summary


Summary: Ionic Equilibria

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