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5-1

Topic 5

Acid and Bases

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Acid and Bases

• Arrhenius and Ostwald: Theory of electrolyte dissociation

acid + base salt + water

• Brønsted and Lowry (1923): Protontransfer reactions– Acid is proton donor, base is proton acceptor

• Lewis (1923): Generalization of previous theories– Acid is electron pair acceptor, base is electron pair donor

–> Neutralization: formation of a covalent bond between acid and base

There are a number definitions for aicd and bases, depending on whatis convenient to use in a particular situation:

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Brønsted-Lowry Acid and Bases

A Brønsted-Lowry acid is a substance that can donate a hydrogen ionA Brønsted-Lowry base is a substance that can accept a hydrogen ion

HCl + NH3 NH4+ + Cl–

acid base conjugate acid conjugate base

Note: Water can act as base or an acid = amphoteric behavior:

–> H2O is the conjugate acid of OH– and the conjugate base of H3O+ –> H3O+ is the conjugate acid, OH– the conjugate base of H2O

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Brønsted-Lowry Acid and Bases

• The Brønsted-Lowry definition includes also acid-base reactions inthe gas phase, or in solvents other than water, e.g. liquid ammonia:

2 NH3 NH4+ + NH2

–

Note: In any solvent, the direction of the reaction is always such, that theproducts are weaker acids or bases than the reactants

2 H2O H3O+ + OH–

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5-5

Solvent Dissociation Theory

• The Brønsted-Lowry theory is limited to proton transfer reactions(and mostly aqueous systems), therefore, aprotic nonaqueoussystems require a different definition of acid and base:

The cation resulting from autodissociation of a solvent is the acidThe anion resulting from autodissociation of a solvent is the base

2 H2O H3O+ + OH–

acid base

Other solvent dissociation equilibria:

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Properties of Solvents

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5-7

Dissociation of Pure WaterThe autodissociation of water proceeds only to a slight extent, but isresponsible for a small but measurable presence of H3O+ and OH–

ions: 2 H2O H3O+ + OH–

K

Pure water contains no other ions than H3O+ and OH– and thenegative charges must be equal the positive:

[H3O+ ] = [HO- ] = 10-7 M neutral solution

[H3O+ ] > [HO-]

[H3O+ ] < [HO-]

acidic solution

basic solution

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The pH FunctionIn aqueous solution the concentration of hydronium ions can rangefrom 10 M to 10–15 M. It is convenient to express this large range by alogarithmic scale, the pH scale:

Neutral pH: [H3O+] = 10–7 M –> pH = 7Acidic range [H3O+] > 10–7 M –> pH < 7

Basic range [H3O+] < 10–7 M –> pH > 7

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The Strength of Acids and BasesAcids are classified as strong or weak depending on whether theirreaction with water to give H3O+ (aq) go to completion or reach anequilibrium:

HA + H2O H3O+ + A–

The acidity constant Ka (also called acid dissociation constant oracid ionization constant) is a quantitative measure of the strength ofthe acid in a given solvent (in this case water)–> the larger Ka the stronger the acid

Note: Acidity constants are typically written as pKa values:

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Acidity Constants in Water

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Base StrengthThe strength of a base is inversely related to the strength of itsconjugated acid: the weaker the acid, the stronger the conjugatedbase and vice versa.

B + H2O HB+ + OH–Kb

Kb is the basicity constant. Since Kw = [H3O+][HO- ] = 10–14M2

we can also write:

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Multiple EquilibriaIf two bases compete for hydrogen ions, the stronger base “wins” andwill hold the larger portion of hydrogen ions:

HF + CN– HCN + F–K

K =[HCN][F -][HF][CN– ]

We can calculate K from the tabulated values for the two individualchemical equilibria involved:

HF + H2O H3O+ + F–Ka

Ka =[H3O+ ][F -]

[HF]= 6.6 ⋅10-4

HCN + H2O H3O+ + CN–K’a

Ka =[H3O+ ][CN-]

[HCN]= 6.2 ⋅10-10

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5-13

Acid vs. Conjugate Base Strengths

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IndicatorsAn indicator is a soluble compound, generally an organic dye, thatchanges its color noticeably over a fairly short range of pH:

HInd + H2O H3O+ + Ind–Ka

Ka =[H3O+ ][Ind -]

[HInd]

[H3O+ ]Ka

=[HInd][Ind- ]

and

If [H3O+] is much larger than Ka, then [HInd] > [Ind–] –> most of the indicator is protonated, and the color of the acid formis predominant (and vice versa)

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5-15

Indicator Color Change as Function of pH

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Color Change of Phenolphtalein

The red color of the deprotonated indicator (pH > 8) is due to theextended and delocalized pi-system (resonance structures)–> the HOMO-LUMO energy difference is smaller in the conjugated pi-system, which shifts the absorption wavelength into the visible range

O

O

redcolorless

Ka

OH

OH

OO

OO

acidic solut ion basic solut ion

H3O+

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5-17

pH Indicators in BiologySNARF is a pH sensitive fluorescent probe, which can be used tomeasure the pH value inside a living cell using fluorescence microscopy:

Human neutrophils loadedwith SNARF

OMe2N

O

COO

OMe2N

OH

COO

Ka

H3O+

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pH Range in Various Solvents

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5-19

Equilibria of Weak Acid and Bases

• Weak acid and bases react only partially with water to form H3O+ orOH–

–> pH calculations must be performed based on Ka or Kb and theinvolved thermodynamic equilibrium

HA + H2O H3O+ + A–Ka

Ka =[H3O+ ][A- ]

[HA]Solve equation for [H3O+]–> calculate pH

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pH Calculations

Example: pH of 1.0 M acetic acid (Ka = 1.8E-5):

CH3COOH + H2O H3O+ + CH3COO–Ka

Since acetic acid is a weak acid, we can approximate above quadratic equation with1.00–y ≈ 1.00, thus

And the fraction of ionized acetic acid is calculated to be:

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pH Calculations: Diluted Solutions

If water is added to further dilute acetic acid, the concentration of H3O+

decreases (moving towards 10–7 M), and the fraction of the ionized acidCH3COO– increases.

†

Ka =[H3O

+][CH3COO-][CH3COOH]

Example: pH of 0.0001 M acetic acid:

Solving above equation with the same approximation as before gives a 42%fraction of ionized acid –> the approximation is not valid anymore, and thequadratic equation must be solved accurately:

†

[H3O+] = [CH3COO-]

†

f =[CH3COO– ][CH3COOH]

⋅100ionized fraction:

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Weak BasesExample: pH of 0.01 M ammonia (Kb = 1.8E-5):

†

Kb =[NH4

+][OH-][NH3]

NH3 + H2O NH4+ + OH–

Ka

Above quadratic equation is solved again for y:

†

[NH4+] = [OH-]

The hydronium ion concentration (and pH) of the solution is then obtained via Kw:

†

[H3O+] = Kw

[OH-]

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Hydrolysis Reactions

• Some anionic or cationic species react with water to give an acidicor basic solution

• For example, the ammonium cation NH4+ is hydrolyzed to give an

acidic solution:

NH4+ + H2O H3O+ + NH3

Ka

†

Ka =[H3O

+][NH3][NH4

+]

• Similarly, hydrolysis of F– ion increases the OH– concentration andso raises the pH:

F– + H2O OH– + HFKa

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Hydrolysis

• Most ionic species hydrolyze to a detectable extent:–> the hydrolysis of anions typically raises the pH–> the hydrolysis of cations typically lowers the pH

• Metal cations with a large charge/size ratio undergo extensivehydrolysis reactions:

Al(H2O)63+ + H2O

• +1 metal cations and large +2 cations do not undergo hydrolysis(pKa > 7) (Li+, Na+, K+, Rb+, Cs+, Mg2+, Ca2+, Sr2+, Ba2+)

• The conjugate bases of very strong acids are nonhydrolyzinganions: ClO4

–, Cl–, Br–, I–, HSO4–, NO3

–

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5-25Hydrolysis Constants of Cations

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Buffer Solutions

Example: Calculate the pH of a mixture of 1M HCOOH and 0.5 M NaHCOO Ka (formic acid) = 1.8E–4:

HCOOH + H2O H3O+ + HCOO–Ka

Since acetic acid is a weak acid, we can approximate above quadratic equation with1.00–y ≈ 1.00 (and 0.5+y ≈ 0.5):

Buffer solution = any solution that maintains an approximately constant pHdespite small additions of acid or base–> typically a buffer solution contains a weak acid and a weak base that areconjugate to one another

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How Buffer Solutions Work

• In a buffer solution the concentration of [HA] and [A–] are similar,and therefore the addition of small amounts of acid or base will notaffect the [H3O+] concentration substantially:

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Designing Buffers

• Assuming that the equilibrium concentrations of [HA] and [A–] arevery close to the initial total concentrations ([HA]0 and [A–]0), we canwrite:

Ka =[H3O+][A -]

[HA]ª

[H3O+][A-]0

[HA]0

• Solving for [H3O+] and using the definitions for pK and pH gives:

Henderson-HasselbalchEquation

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Concentration Dependence

• Continuos dilution of buffer solutions will gradually change the pHtowards 7, since the initial assumption of [HA]0 ≈ [HA] and [A–]0 ≈[A–] does not apply at low buffer concentrations

pH vs. conc. plots for various buffersystems:

1: Sodium phosphate2: Ammonia3: 2,4-dichlorophenol4: Uric Acid5: Acetic acid6: H2B4O77: Phosphoric acid

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Acid-Base Titration Curves

• A graph of pH versus the volume of titrating solution is called titrationcurve:

–> the exact shape of an acid-basetitration curve can be calculated based onthe ionization constants of the acid andbase and their concentrations

–> the titration curve can be used tocalculate an unknown ionization constantof an acid or base (by titration with aknown base or acid)

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Titration of a Strong Acid with a Strong Base

• Simplest type of titration, the chemical reaction corresponds to aneutralization reaction:

The pH at each point of the titrationcurve can be calculated (ormeasured) assuming completereaction of the added base and acidpresent

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Concentration Dependence

• Since the measured pH reflects the total [H3O+] concentration, theshape of the titration curve depends on the concentration of theacid (and added base):

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Titration of a Weak Acid with a Strong Base

Example: Titration of acetic acid with NaOH: The titration curve has four distinct ranges:

1) Before NaOH addition:pH given by ionization of a weak acid

2) Less than 1 molar equivalent of NaOH added:OH– is a much stronger base than acetate,, and therefore substracts the protonfrom acetic acid to form NaOAc–> the pH can be calculated using the Henderson-Hasselbalch equation(buffered region of the titration curve)Note: At the half equivalence point (V=Ve/2) pH ≈ pKa = 4.74

3) Equivalence point (VNaOH = VHOAc):All the protons of acetic acid are neutralized –> the pH is identical with the pH ofa solution of NaOAc of identical concentration

4) After addition of more than 1 molar equivalent of NaOH:Beyond the equivalence point, all the acetic acid has been neutralized. The pHof the solution is approximately identical with the pH observed in the titration ofa strong acid and strong base.

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Titration of HOAc with NaOH

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Polyprotic Acids

• Polyprotic acids donate two or more hydrogen ions in stages (e.g.H2CO3, oxalic acid, phosphoric acid)Note: Even though acetic acid (CH3COOH) has a total of four hydrogen atoms, itis a monoprotic acid (only one of the four hydrogen atoms is acidic!)

• The titration of a diprotic weak acid involves two simultaneousequilibria:

H2CO3 + H2O H3O+ + HCO3–

Ka1

†

Ka1 =

HCO3– + H2O H3O+ + CO3

2–Ka2

†

Ka2 =

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Titration of Polyprotic Acids

• As shown for monoprotic acids, the titration points can becalculated according to the involved equilibria with thecorresponding ionization constants

If the pKa values reasonably apart fromeach other, the inflection points of thetitration curve directly reflect theequilibrium positions where pH ≈ pKa

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Effect of pH on Solution Composition

• Changing the pH shifts the positions of all acid-base equilibria ina solution, and therefore the overall composition with respect tothe involved species

Solution composition for thecarbonate equilibrium as afunction of pH

H2CO3 + H2O H3O+ + HCO3–

HCO3– + H2O H3O+ + CO3

2–

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The pH of Blood

• Human blood has a pH near 7.4 that is maintained by a combinationof carbonate, phosphate and protein buffers (a blood pH below 7.0or above 7.8 leads quickly to death)

The blood pH is depended on pCO2, thepartial pressure of CO2 –> in order to get the non-respiratory pH,the pH is measured at two different CO2partial pressures, the intersection at 40mmHg CO2 gives then the (standardized)non-respiratory blood pH

Deviations from pH 7.4 are indicative ofvarious disease conditions(respiratory or metabolic acidosis oralkalosis)

Actual pH

Non-respiratory pH

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Potentiometry

• The accurate measurement of [H3O+] concentration with a pHelectrode allows to solve complicated equilibrium systems withmany species, including metal complexes:

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Lewis Acid and Bases

A Lewis base is any species that donates electrons through coordinationto its lone pairs, a Lewis acid is any species that accept such electronpairs.

–> In addition to the reactions previously discussed, the Lewis definition ismuch broader and includes reactions such as:

Ag+ + 2 NH3 [H3N-Ag-NH3 ]+

acid base adduct

BF3 + NH3 H3N-BF3

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Donor Acceptor Bonding

energyempty p orbital(LUMO)

filled orbital(lone pair, HOMO)

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Acidity and Basicity of Binary Hydrides

• Binary hydrogen compounds range from strong acids (HCl) toweak bases (NH3), or non-acidic molecules (CH4)

• Acidity is greatest with lowest electronegativity in each group–> larger molecules have lower charge density and form less stablebonds to hydrogen–> larger molecules form more stable conjugate bases (betterstabilization of negative charge)

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Inductive Effects

• Substitution of electronegative groups such as fluorine or chlorinein place of hydrogen results in weaker bases–> the central atom lone pair is less readily donated to an acid(e.g. PF3 is a much weaker base than PH3)

• Substitution with alkyl groups results stronger bases–> the central atom lone pair is more electron rich

Example: Gas phase basicity is decreasing in the order:

NMe3 > NHMe2 > NH2Me > NH3

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The Strength of Oxyacids

• In the series of oxyacids of chlorine, the acid strength in aqueoussolution is decreasing in the order

With increasing number of electronegative substituents on Cl, the O–Hbond is weakened due to the increasing positive charge on Cl. At the sametime the negative charge of the conjugate base is further stabilized.–> Both effects result in an increasing acidity

HClO4 > HClO3 > HClO2 > HOCl

pKa:

• For oxyacids with more than one ionizable hydrogen, the pKavalues increase by about 5 units with each successive removal:

H3PO4 > H2PO4 – > HPO4

2–

pKa:

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Super Acids• Any acid solution which is more acidic than sulfuric acid is called

a super acid–> super acid systems are necessarily nonaqueous, since the acidity ofany aqueous system is limited by the fact that the strongest acid that canexist in the presence of water is H3O+

• The acidity is measured by the Hammett acidity function (B/BH+is an indicator and its conjugate base):

H0 ª pKBH + - log[BH+][B]