Topic 5. Acid and Bases

Topic 5

Acid and Bases

5-2

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

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

Brønsted-Lowry Acid and Bases

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

5-4

Brønsted-Lowry Acid and Bases

• The Brønsted-Lowry definition includes also acid-base reactions in the 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 the products are weaker acids or bases than the reactants

2 H₂O H₃O⁺ + OH^–

Solvent Dissociation Theory

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

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

2 H₂O H₃O⁺ + OH^– acid base Other solvent dissociation equilibria:

5-6

Properties of Solvents

Dissociation of Pure Water

The autodissociation of water proceeds only to a slight extent, but is responsible 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 the negative charges must be equal the positive:

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

[H₃O⁺] < [HO^-]

acidic solution basic solution

5-8

The pH Function

In aqueous solution the concentration of hydronium ions can range from 10 M to 10^–15 M. It is convenient to express this large range by a logarithmic scale, the pH scale:

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

The Strength of Acids and Bases

Acids are classified as strong or weak depending on whether their reaction with water to give H₃O⁺ (aq) go to completion or reach an equilibrium:

HA + H₂O H₃O⁺ + A^–

The acidity constant

K

_a (also called acid dissociation constant or acid ionization constant) is a quantitative measure of the strength of the acid in a given solvent (in this case water)

–> the larger

K

_a the stronger the acid

Note: Acidity constants are typically written as p

K

_a values:

5-10

Acidity Constants in Water

Base Strength

The strength of a base is inversely related to the strength of its conjugated acid: the weaker the acid, the stronger the conjugated base and vice versa.

B + H₂O HB⁺ + OH^–

K_b

K

_b is the basicity constant. Since K_w = [H₃O⁺][HO^-] = 10^{– 1 4}M² we can also write:

5-12

Multiple Equilibria

If two bases compete for hydrogen ions, the stronger base “wins” and will 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 individual chemical equilibria involved:

HF + H₂O H₃O⁺ + F^–

K_a

K_a =[H₃O⁺][F^-]

[HF] = 6.6⋅10^-4

HCN + H₂O H₃O⁺ + CN^–

K’_a

K_a =[H₃O⁺][CN^-]

[HCN] = 6.2 ⋅10^{-1 0}

Acid vs. Conjugate Base Strengths

5-14

Indicators

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

HInd + H₂O H₃O⁺ + Ind^–

K_a

K_a = [H₃O⁺][Ind^-] [HInd]

[H₃O⁺]

K_a = [HInd]

[Ind^-]

and

If [H₃O⁺] is much larger than K_a, then [HInd] > [Ind^–]

–> most of the indicator is protonated, and the color of the acid form is predominant (and vice versa)

Indicator Color Change as Function of pH

5-16

Color Change of Phenolphtalein

The red color of the deprotonated indicator (pH > 8) is due to the extended 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

red colorles s

Ka OH

OH O O

O O

acidic solut ion basic solut ion H₃O⁺

pH Indicators in Biology

SNARF is a pH sensitive fluorescent probe, which can be used to

measure the pH value inside a living cell using fluorescence microscopy:

Human neutrophils loaded with SNARF

O Me₂N

O

COO

O Me₂N

OH

COO K_a

H3O⁺

5-18

pH Range in Various Solvents

Equilibria of Weak Acid and Bases

• Weak acid and bases react only partially with water to form H₃O⁺ or OH^–

–> pH calculations must be performed based on

K

_aor

K

_b and the involved thermodynamic equilibrium

HA + H₂O H₃O⁺ + A^–

K_a

K_a =[H₃O⁺][A^-]

[HA] Solve equation for [H₃O⁺]

–> calculate pH

5-20

pH Calculations

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

CH₃COOH + H₂O H₃O⁺ + CH₃COO^–

K_a

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

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

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 acid CH₃COO^– increases.

†

K_a =[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 the quadratic equation must be solved accurately:

†

[H₃O⁺] = [CH3COO^-]

†

f = [CH₃COO^–] [CH₃COOH]⋅100 ionized fraction:

5-22

Weak Bases

Example: pH of 0.01 M ammonia (K_b = 1.8E-5):

†

K_b =[NH₄⁺][OH^-] [NH₃]

NH₃ + H₂O NH₄⁺ + OH^–

K_a

Above quadratic equation is solved again for y:

†

[NH₄⁺] = [OH^-]

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

+ K

Hydrolysis Reactions

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

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

NH₄⁺ + H₂O H₃O⁺ + NH₃

K_a

†

K_a =[H₃O⁺][NH₃] [NH₄⁺]

• Similarly, hydrolysis of F^– ion increases the OH^– concentration and so raises the pH:

F^– + H₂O OH^– + HF

K_a

5-24

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 extensive hydrolysis reactions:

Al(H₂O)₆³⁺ + H₂O

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

• The conjugate bases of very strong acids are nonhydrolyzing anions: ClO₄^–, Cl^–, Br^–, I^–, HSO₄^–, NO₃^–

Hydrolysis Constants of Cations

5-26

Buffer Solutions

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

HCOOH + H₂O H₃O⁺ + HCOO^–

K_a

Since acetic acid is a weak acid, we can approximate above quadratic equation with Buffer solution = any solution that maintains an approximately constant pH despite small additions of acid or base

–> typically a buffer solution contains a weak acid and a weak base that are conjugate to one another

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 not affect the [H₃O⁺] concentration substantially:

5-28

Designing Buffers

• Assuming that the equilibrium concentrations of [HA] and [A^–] are very close to the initial total concentrations ([HA]₀ and [A^–]₀), we can write:

K_a = [H₃O⁺][A^-]

[HA] ª [H₃O⁺][A^-]₀ [HA]₀

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

Henderson-Hasselbalch Equation

Concentration Dependence

• Continuos dilution of buffer solutions will gradually change the pH towards 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 buffer systems:

1: Sodium phosphate 2: Ammonia

3: 2,4-dichlorophenol 4: Uric Acid

5: Acetic acid 6: H₂B₄O₇

7: Phosphoric acid

5-30

Acid-Base Titration Curves

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

–> the exact shape of an acid-base

titration curve can be calculated based on the ionization constants of the acid and base and their concentrations

–> the titration curve can be used to calculate an unknown ionization constant of an acid or base (by titration with a known base or acid)

Titration of a Strong Acid with a Strong Base

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

The pH at each point of the titration curve can be calculated (or

measured) assuming complete reaction of the added base and acid present

5-32

Concentration Dependence

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

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 proton from 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=V_e/2) pH ≈ pK_a = 4.74 3) Equivalence point (V_NaOH = V_HOAc):

All the protons of acetic acid are neutralized –> the pH is identical with the pH of a 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 pH of the solution is approximately identical with the pH observed in the titration of a strong acid and strong base.

5-34

Titration of HOAc with NaOH

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, it is a monoprotic acid (only one of the four hydrogen atoms is acidic!)

• The titration of a diprotic weak acid involves two simultaneous equilibria:

H₂CO₃ + H₂O H₃O⁺ + HCO₃^–

K_a1

†

K_a1=

HCO₃^– + H₂O H₃O⁺ + CO₃^2–

K_a2

†

K_{a 2} =

5-36

Titration of Polyprotic Acids

• As shown for monoprotic acids, the titration points can be calculated according to the involved equilibria with the corresponding ionization constants

If the pK_a values reasonably apart from each other, the inflection points of the titration curve directly reflect the equilibrium positions where pH ≈ pK_a

Effect of pH on Solution Composition

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

Solution composition for the carbonate equilibrium as a function of pH

H₂CO₃ + H₂O H₃O⁺ + HCO₃^– HCO₃^– + H₂O H₃O⁺ + CO₃^2–

5-38

The pH of Blood

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

The blood pH is depended on pCO₂, the partial pressure of CO₂

–> in order to get the non-respiratory pH, the pH is measured at two different CO₂ partial pressures, the intersection at 40 mmHg CO₂ gives then the (standardized) non-respiratory blood pH

Deviations from pH 7.4 are indicative of various disease conditions

Actual pH

Non-respiratory pH

Potentiometry

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

5-40

Lewis Acid and Bases

A Lewis base is any species that donates electrons through coordination to its lone pairs, a Lewis acid is any species that accept such electron pairs.

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

Ag⁺ + 2 NH₃ [H₃N-Ag-NH₃ ]⁺

acid base adduct

BF₃ + NH₃ H₃N-BF₃

Donor Acceptor Bonding

energy

empty p orbital (LUMO)

filled orbital (lone pair, HOMO)

5-42

Acidity and Basicity of Binary Hydrides

• Binary hydrogen compounds range from strong acids (HCl) to weak 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 stable bonds to hydrogen

–> larger molecules form more stable conjugate bases (better stabilization of negative charge)

Inductive Effects

• Substitution of electronegative groups such as fluorine or chlorine in 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

5-44

The Strength of Oxyacids

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

With increasing number of electronegative substituents on Cl, the O–H bond is weakened due to the increasing positive charge on Cl. At the same time the negative charge of the conjugate base is further stabilized.

–> Both effects result in an increasing acidity

HClO₄ > HClO₃ > HClO₂ > HOCl pK_a:

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

H₃PO₄ > H₂PO₄ ^– > HPO₄ ^2–

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 of any aqueous system is limited by the fact that the strongest acid that can exist 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 pK_BH⁺ - log[BH⁺] [B]