general chemistry academic journal (sample)

Learning Outcomes: Pages: 1. Definitions of acids and bases 1 – 5

2. pH and ionization constants 5 – 9

3. Acid–base reactions to form salts 9 – 10

4. Buffer solutions 10 – 12

5. Acid–base titrations 12 – 15

1. Definitions of acids and bases Arrhenius definition:

o Svante Arrhenius proposed that:

1. Acids ionize in water to produce anions and H+ ions (or protons) as its

only +vely–charged ion

2. Bases ionize to produce cations and [OH]− as its only –vely–charged ion

(ammonia, despite not having hydroxide, produces the hydroxide ion by

reacting with water (i.e. NH3 (𝑎𝑞) + H2O (𝑙) ⇌ [NH4]+ (𝑎𝑞) +

[OH]− (𝑎𝑞)))

o Hydrogen ions can exist in vacuum but otherwise are bonded with water

molecules via dative bonds to form (hydronium) / (hydroxonium) / (oxonium)

ions because of the small sizes and high charge densities of “bare” protons:

H+ (𝑎𝑞) + H2O (𝑙) → [H3O]+ (𝑎𝑞)

Hydrogen bonding also exists among the hydronium ions, with 1

hydronium ion being hydrogen bonded to a max. of 3 water molecules

Thus, the 𝐎 − 𝐇 bond in hydronium ions is stronger than that in water

o Arrhenius base is any metal oxide/hydroxide containing either O2− ion or

[OH]− ion but Arrhenius alkali is a soluble Arrhenius base that dissociates in

water to produce aqueous solutions containing [OH]− ions and cations

o The Arrhenius definition, however, is unable to describe acidic / basic

behavior in non–aqueous media

o Common properties of acids:

Sour taste

Often corrosive when concentrated or hot

Δs the color of a damp blue litmus paper to colors ranging from red

(strong acids) to yellow (weak acids)

pH ranges from 0 − 7

Conducts electricity and electrical conductivity s as acid strength s

Strong acids react with metals which are higher than

hydrogen in the reactivity series to form metal salts and

hydrogen gas:

full eqn. : H2SO4 (𝑎𝑞) + Mg (𝑠) → MgSO4 (𝑎𝑞) + H2 (𝑔)

net ionic eqn. : 2 H+ (𝑎𝑞) + Mg (𝑠) → Mg2+ (𝑎𝑞) + H2 (𝑔)

When water–insoluble metal salts are formed, the rxn. stops

halfway because an insoluble layer of the metal oxide that is

formed then coats the metal surface

Some acid–metal rxns. do not produce hydrogen gas (e.g. rxn.

of copper with nitric acid)

Strong acids react with strong metal hydroxides to form

metal salts and water:

full eqn. : H2SO4 (𝑎𝑞) + Mg(OH)2 (𝑎𝑞)

→ MgSO4 (𝑎𝑞) + 2 H2O (𝑙)

net ionic eqn. : 2 H+ (𝑎𝑞) + 2 [OH]− (𝑎𝑞) → 2 H2O (𝑙)

Strong acids react with strong metal oxides to form metal

salts and water:

full eqn. : H2SO4 (𝑎𝑞) + MgO (𝑠) → MgSO4 (𝑎𝑞) + H2O (𝑙)

net ionic eqn. : 2 H+ (𝑎𝑞) + O2− (𝑠) → H2O (𝑙)

E.g. MnO2 (s) + 4 HCl (aq) → MnCl2 (aq) + 2 H2O (l) + Cl2 (g)

is not a neutralization rxn. since a product other than metal salt

and water is produced

Strong acids react with metal carbonates to form metal salts,

water and carbon dioxide:

full eqn. : H2SO4 (𝑎𝑞) + MgCO3 (𝑠)

→ MgSO4 (𝑠) + H2O (𝑙) + CO2 (𝑔)

net ionic eqn. : 2 H+ (𝑎𝑞) + MgCO3 (𝑠)

→ Mg2+ (𝑎𝑞) + H2O (𝑙) + CO2 (𝑔)

Initially, carbonic acid is formed but it is rapidly converted to

water and carbon dioxide

There are also other exchange rxns. with metal sulfites and sulfides:

H2SO4 (𝑎𝑞) + MgSO3 (𝑠) → MgSO4 (𝑠) + H2O (𝑙) + SO2 (𝑔)

H2SO4 (𝑎𝑞) + MgS (𝑠) → MgSO4 (𝑠) + H2S (𝑔)

o Common properties of bases:

Bitter taste & soapy feel

Δs the color of a damp red litmus paper to colors ranging from blue

(strong acids) to purple (weak acids)

pH ranges from 8 − 14

Alkali can react with ammonium salts when heated to give

off ammonia gas, metal salt and water:

full eqn. : NaOH (𝑎𝑞) + NH4Cl (𝑎𝑞)

→ NaCl (𝑎𝑞) + NH3 (𝑔) + H2O (𝑙)

ionic eqn. : [OH]− (𝑎𝑞) + [NH4]+ (𝑎𝑞) → NH3 (𝑔) + H2O (𝑙)

Alkali can react with a solution of a metal salt to give metal

hydroxide and another metal salt (the metal hydroxide

appears as a ppt. if it is water–insoluble):

2 NaOH (𝑎𝑞) + FeSO4 (𝑎𝑞) → Fe(OH)2 (𝑠) + Na2SO4 (𝑎𝑞)

BrØnsted–Lowry definition:

o Johannes BrØnsted and Thomas Lowry proposed that:

1. Acids are proton donors (e.g. the proton bound to the oxygen atom of a

carboxylic acid group is sufficiently +vely–charged to be donated as a

proton since the 2 oxygen atoms of the carboxylic acid group actually

pull electron density away from proton)

2. Bases are proton acceptors (e.g. the lone pair of an amine can accept a

proton from water)

o All acids contain hydrogen atoms but only compounds containing acidic

hydrogen atoms, which are often attached to a highly–electronegative atom,

are acids

o In acid–base rxns., acids donate protons to bases

o This definition does not require:

1. An acid to form [𝐇𝟑𝐎]+ ions

2. A base to contain 𝐎𝟐− ion or [𝐎𝐇]− ion (however, it must have a highly

electronegative atom and ±𝟏 lone pair that can form a coordinate

covalent bond with proton)

o Unlike the Arrhenius definition, this definition extends to acid–base rxns. in

gaseous states and non-aqueous solvents or under anhydrous conditions

Lewis definition provides the most general definition because they are based on

sharing of electron pairs rather than proton transfers:

o Gilbert N. Lewis proposed that:

1. A Lewis acid can accept a pair of electrons (often a lone pair or a pair

of phi electrons on a multiple bond) to form a new bond

2. A Lewis base can donate a pair of electrons (often a lone pair or a pair

of phi electrons on a multiple bond) to form a new bond

o An acid–base rxn. occurs when a Lewis base with a lone pair reacts with a

Lewis acid that accepts the electron pair to form a coordinate covalent bond

o +vely–charged metal ions are potential Lewis acids since they have ±𝟏 empty

orbital which can accommodate the electron pair from the base, thereby

forming the coordinate covalent bond in often highly–colored complexes:

Possible Lewis bases include water molecules, ammonia molecules,

hydroxide ions etc:

Radicals, which have only 1 unpaired electron, are unable to act

as Lewis bases

When a metal ion is hydrated with water, a lone pair on the oxygen

atom in water forms a coordinate covalent bond to the metal ion – these

hydrated metal ions, esp. those of transition cations, are weak acids:

An aluminium ion has a large enough charge and a small

enough size to attract the shared pair of the 𝐌 − 𝐎 bond to it

This weakens the 𝐎 − 𝐇 bond, making the hydrogen atom of the

M – O – H bond more acidic than it would be in a water molecule

that is not bonded to the metal ion:

[M(H2O)6]n+ (𝑎𝑞) + H2O (𝑙)

⇌ [M(H2O)5(OH)]n−1 (𝑎𝑞) + [H3O]+ (𝑎𝑞)

When a metal ion is bonded with hydroxide ions, amphoterism is often

observed – for instance, aluminium hydroxide is amphoteric:

Al(OH)3 (𝑠) + [OH]− (𝑎𝑞) ⇌ [Al(OH)4]− (𝑎𝑞) (as an acid)

Al(OH)3 (𝑠) + 3 [H3O]+ (𝑎𝑞) ⇌ Al3+ (𝑎𝑞) + 6 H2O (𝑙) (as a base)

o Neutral molecules like the oxides of non–metals can behave as acids:

In CO2 or SO2, since oxygen is highly electronegative, electrons are

attracted away from the central atom (i.e. carbon or sulfur)

The central atom becomes slightly +vely–charged and becomes a likely

site to attract a pair of electrons

o Lewis definition is impt. in explaining chemistry in aprotic solvents, acid /

base catalysis etc

o Nucleophiles & electrophiles:

Nucleophile is a Lewis base that donates a lone pair to an atom other

than an acidic hydrogen atom

BrØnsted–Lowry base is a Lewis base that donates a lone pair to an

acidic hydrogen atom

Lewis base

Nucleophile

BrØnsted–Lowry base

Lewis acid Electrophile BrØnsted–Lowry acid

Acidic molecules other than acidic hydrogen

atoms (e.g. CO2, SO2, [M(H2O)6]n+ etc)

Electrophile is a Lewis acid

♣! A conjugate acid–base pair is a pair of molecules or ions related to each

other by the loss or gain of a proton:

o If one member of the pair is a reactant, the other member is a product

o The conjugate acid can be derived from the conjugate base by adding a proton

to the conjugate base and then ing the charge by +1:

conjugate acid → conjugate base + H+

o In any BrØnsted–Lowry acid–base rxn., there are 2 conjugate acid–base rxns.

Electrolytes:

o An ionic substance that dissolves in water is a strong electrolyte

o A strong acid is also a strong electrolyte since it ionizes completely in water

o By measuring the extent to which various acids donate protons to water,

chemists can compare the relative strengths of acids and their conjugate bases:

Strong acids are better proton donors than weak acids and strong bases

are better proton acceptors than weak bases

Thus, stronger acids have weaker conjugate bases and weaker acids

have stronger conjugate bases

o Acid–base rxns. favor going from the stronger member to the weaker member

of each conjugate acid–base pair

o Nonelectrolytes are often molecular compounds that do not ionize in aqueous

solutions, although they may still be water–soluble

Amphoteric substances can act as either an acid or base, depending on the chem. env.:

o Water is an amphoteric substance:

HA + H2O ⇌ [H3O]+ + A−

B + H2O ⇌ [BH]+ + [OH]−

2. pH and ionization constants

The auto–ionization or auto–protolysis of water is an unfavorable rxn.

whose equilibrium constant at 25℃ is Kw = [H3O+][OH−] = 10−14 M2:

2 H2O (𝑙) ⇌ [H3O]+ (𝑎𝑞) + [OH]− (𝑎𝑞)

o These conc. can be measured by its electrical conductivity since hydronium

ions migrates toward the cathode and hydroxide ions toward the anode (thus,

even pure water conducts a small electrical current)

o For pure water and all aqueous solutions, the product of the hydronium ion

conc. times the hydroxide ion conc. is constant at a given temperature

o If an acid or base is added to a neutral solution, the auto–ionization

equilibrium is disturbed and the final solution becomes acidic or basic

respectively, but Kw = 10−14 M2 is maintained (e.g. when acid is added,

[H3O+]𝑓 > [H3O+]0 but since Kw is constant, [OH−]𝑓 < [OH−]0)

The pH of a solution is the –ve of the common logarithm of the

hydronium ion conc., measured in M:

pH ≡ − lg(a[H3O]+) ≡ − lg([H3O+]γ[H3O]+) ≈ − lg[H3O+] − eqn. (2a)

o The relative conc. of [H3O]+ and [OH]− indicate the acidic, neutral or basic

nature of an aqueous solution – at 25℃:

[H3O+] and [OH−] at 25℃ pH at 25℃ Neutral solution [H3O+] = [OH−] = 1.0 × 10−7 M pH = 7.00 = pOH

Acidic solution [H3O+] > 1.0 × 10−7 M and [OH−] < 1.0 × 10−7 M pH < 7.00

Basic solution [H3O+] < 1.0 × 10−7 M and [OH−] > 1.0 × 10−7 M pH > 7.00

o A change of 1 pH unit represents a ten–fold Δ in [H3O+]

The pOH of a solution is the –ve of the common logarithm of the

hydroxide ion conc., measured in M:

pOH ≡ − lg(a[OH]−) ≡ − lg([OH−]γ[OH]−) ≈ − lg[OH−] − eqn. (2b)

Since [H3O+] and [OH−] are related by Kw, for all aqueous solutions at

25℃,:

pKw ≡ pH + pOH = 14.00 − eqn. (2c)

The approximations, a[H3O]+ ≈ [H3O+] and a[OH]− ≈ [OH−], are valid only when

[H3O+] or [OH−] is small since non–covalent interactions among the constituent ions

are significant when [H3O+] or [OH−] is large:

o If pH = −3.6, this implies that a[H3O]+ = 103.6 and not [H3O]+ = 103.6

o For pure water, the activity coefficients of both ions are unity since the ionic

strength of pure water is small:

Kw = 1.0 × 10−14 = [H3O+]γ[H3O]+[OH−]γ[OH]− ≈ [H3O+][OH−]

o For aqueous salts, ionic strength of the salt is non–negligible:

Kw = 1.0 × 10−14 = [H3O+]γ[H3O]+[OH−]γ[OH]−

Thus, pH of water may Δ when we add neutral salts since activities of

the hydronium & hydroxide ions, via their activity coefficients, are

affected

pH measurements:

o pH is measured using a pH meter, which has a pair of electrodes that detect the

hydronium ion conc. of the test solution and display it as the pH value

o Acid–base indicators are weak organic acids that Δ color within a narrow pH

range of 𝟏 − 𝟐 pH units due to deprotonation of the acid:

HIn (𝑎𝑞) + H2O (𝑙) ⇌ [H3O]+ (𝑎𝑞) + [In]− (𝑎𝑞)

The observed color depends on the ratio, [HIn]

[In−],:

1. When [HIn]

[In−]≥ 10, the indicator solution is the acid color

2. When [HIn]

[In−]≤ 0.1, the indicator solution is the base color

3. When [HIn]

[In−]≈ 0.1, the indicator solution color is intermediate

btw. the acid & base colors

E.g. litmus is a purple dye indicator which can be used as a solution or

on paper to check whether a substance is acidic or alkaline

o Strips of paper impregnated with acid–base indicators are also used to

approximate pH and the color of the paper after it has been dampened by the

solution to be tested is compared with a set of colors at known pH

Ionization constants can be used to evaluate the extent of ionization or dissociation of

an acid or a base in water based on the BrØnsted–Lowry definition:

o When performing these calculations, the contribution of [H3O]+ and [OH]−

from the auto–ionization of water can be ignored as long as the initial conc. of

the acid or base is > 10−7 M

o % ionization of an acid or a base is the ratio of the equilibrium

conc. of hydronium ions or hydroxide ions to the initial conc. of the

acid or the base:

% ionization

=[H3O+] or [OH−] at equilibrium

initial acid or base conc.× 100%

− eqn. (2d(i))

Concentrated acids / bases only slightly dissociate because there is

insufficient water molecules to solvate the free ions

o Acid (ionization) / (dissociation) constants are the equilibrium

constant for the ionization of an acid, HA, in water:

HA (𝑎𝑞) + H2O (𝑙) ⇌ [H3O]+ (𝑎𝑞) + A− (𝑎𝑞)

Ka ≡a[H3O]+aA−

aHA≈

[H3O+][A−]

[HA]

For strong acids, Ka ≫ 1, and for weak acids, 0 < Ka < 1

Strong acids are acids that give up protons more easily than hydronium

ions – these include HCl, HBr, HI, HNO3, H2SO4 and HClO4

HF is a weak acid because fluorine, being the most electronegative

element, forms the strongest hydrogen bond of any ion, and the

hydronium ions remain tightly associated with 𝐅− ions through a

hydrogen bond as an ion pair:

Ion pairs are also common in aqueous solutions of any ion

whose charge is > 1

Partial ionization of weak acids is shown by measuring their pH, which

shows that [H3O+] is very low:

In an aqueous solution of a weak acid, 2 different bases compete

for hydronium ions that can be donated from 2 different acids

E.g. the ionization of acetic acid to acetate ions is reactant–

favored because hydronium ion is a stronger acid than acetic

acid and because acetate ion is a stronger base than base:

CH3COOH + H2O ⇌ [CH3COO]− + [H3O]+

o Base ionization constants are the equilibrium constant for the

ionization of a base, B, in water:

B (𝑎𝑞) + H2O (𝑙) ⇌ [BH]+ (𝑎𝑞) + [OH]− (𝑎𝑞)

Kb ≡a[BH]+a[OH]−

aB≈

[BH+][OH−]

[B]

For strong bases, Kb ≫ 1, and for weak bases, 0 < Kb < 1

Strong bases are bases that accept protons more easily than hydroxide

ions – these include group IA metal hydroxides / oxides, group IIA

metal hydroxides / oxides, quaternary ammonium hydroxides

([NR4]+[OH]−), sulfides (containing S2−), alkoxides (containing [RO]−),

oxides (containing O2−), hydrides (containing H−) and carbanions

o Thus, the chem. equilibrium eqn. for the ionization of an acid or a base is the

basis for the ionization constant expression

o In a conjugate acid–base pair, Ka of a conjugate acid, HA, is

inversely–related to Kb of its conjugate base, A−,:

KaKb = 10−14 = ([H3O+][A−]

[HA]) (

[HA][OH−]

[A−])

= Kw − eqn. (2d(ii))

If Ka > Kb, the conjugate acid is stronger than its conjugate base, and

vice–versa

o As Ka or Kb is d:

1. The acid–base rxn. speed is d

2. The electrical conductivity of the aqueous acid or aqueous base is d

o Monoprotic species can only exchange a single proton per molecule while

polyprotic ones can exchange > 𝟏 protons per molecule in a stepwise fashion

and, thus, have > 𝟏 ionization constants:

♣! Basicity of an acid is the no. of hydronium ions produced per

molecule of the acid:

An acid equivalent is equal to 1 mol of [H3O]+ ions

A (monoprotic) / (monobasic) acid can produce 1 mol of [H3O]+

ions per mol of acid if dissociation is complete

♣! Acidity of a base is the no. of hydronium ions received per

molecule of the base:

A base equivalent is equal to 1 mol of [OH]− ions

A (monoprotic) / (monoacidic) base can accept 1 mol of [H3O]+

ions per mol of base

When all acidic protons have been donated by a polyprotic acid, the

result is a polyprotic base

Each ionization step occurs to a lesser extent than the preceding

ionization because, for instance, it is more difficult to remove a proton

from a –vely–charged molecule (e.g. [HA]−) than from a neutral

molecule (e.g. H2A)

3. Acid–base reactions to form salts

In these exchange rxns., an acid and a base react to produce a salt plus

water:

HX (𝑎𝑞) + MOH (𝑎𝑞) → MX (𝑎𝑞) + H2O (𝑙)

Strong acids react with stoichiometric amounts of strong bases to form neutral salts

and the rxn. goes into completion since [H3O]+ is a strong acid and [OH]− is a strong

base, while water is a weak acid / base:

o The net ionic eqn. is:

[H3O]+ (𝑎𝑞) + [OH]− (𝑎𝑞) → 2 H2O (𝑙)

o Properties of the salt solution are the same as if it had been prepared by

dissolving the neutral salt in water

o Neutralization rxns. have the greatest energy Δ when a strong acid is reacted

with a strong base

o The salt solution has a neutral pH since it contains no significant conc. of acids

or bases; it only contains the metal & non–metal ions, with a few more water

molecules than before:

1. The cation does not react as either an acid or base with water

2. The anion, being the conjugate base of a strong acid, is a weak base

which does not react with water

Strong bases react with stoichiometric amounts of weak acids to form basic salts,

which react with water to form hydroxide ions, leading to pH > 7.00:


HA (𝑎𝑞) + [OH]− (𝑎𝑞) → A− (𝑎𝑞) + H2O (𝑙)

o The basic 𝐀− ions then react with water in a hydrolysis rxn. and the Kb of A−

ions can be used for calculations:

A− (𝑎𝑞) + H2O (𝑙) ⇌ HA (𝑎𝑞) + [OH]− (𝑎𝑞)

Strong acids react with stoichiometric amounts of weak bases to form acidic salts,

which react with water to form hydronium ions, leading to pH < 7.00:


B (𝑎𝑞) + [H3O]+ (𝑎𝑞) → [BH]+ (𝑎𝑞) + H2O (𝑙)

o The acidic [𝐁𝐇]+ ions then react with water and the Ka of [BH]+ ions can be

used for calculations:

[BH]+ (𝑎𝑞) + H2O (𝑙) ⇌ B (𝑎𝑞) + [H3O]+ (𝑎𝑞)

Salts of weak bases and weak acids have pH that are determined by the relative

strengths of the conjugate base and conjugate acid formed:

o There are 2 rxns. that can determine the pH of BHA, a salt formed by weak

bases and weak acids:

1. Formation of [H3O]+ ions by proton transfer from the cation:

[BH]+ (𝑎𝑞) + H2O (𝑙) ⇌ B (𝑎𝑞) + [H3O]+ (𝑎𝑞)

2. Formation of [OH]− ions by hydrolysis of the anion:

A− (𝑎𝑞) + H2O (𝑙) ⇌ HA (𝑎𝑞) + [OH]− (𝑎𝑞)

o If Ka(BH+) > Kb(A−), the 1st rxn. is more favorable and the resulting solution

is slightly acidic and vice–versa

The direction of an acid–base rxn., HA + B− ⇌ A− + BH, can be determined by the

relative pKa of the acid in the reactant (i.e. HA) and the acid in the product (BH):

pKa(HA) < pKa(BH) or Ka(HA) > Ka(BH) → rxn. is product − favored

pKa(HA) > pKa(BH) or Ka(HA) < Ka(BH) → rxn. is reactant − favored

Acid–base properties of typical ions in aqueous solutions:

Neutral Basic Acidic

Anions

Cl−, Br−, I−

[NO3]−

[ClO4]−

F−

S2− [SO4]2−, [SO3]2−

[CO3]2−

[PO4]3− [CN]− Carboxylate ions

[HSO4]−, [HSO3]−

[H2PO4]−

Cations Li+, Na+, K+

Mg2+, Ca2+, Ba2+ None

Al3+

[NH4]+ Transition metal ions

4. Buffer solutions

♣! A buffer solution is a solution consisting of a weak acid and its weak

conjugate base that are in equilibrium with each other

Since the acid & base components are conjugates which do not react with one

another, to form a buffer, both the conjugate acid and conjugate base must be present

in approximately equal conc.

pH of a buffer solution consisting of a 𝐇𝐀/𝐀− system can be calculated

by setting the equilibrium table and solving using the known 𝐊𝐚

expression or by using the Henderson–Hasselbalch eqn., which is a

shortcut that solves for [H3O]+ in the table:

pH = pKa(HA + H2O ⇌ A− + [H3O]+) + lg ([A−]

[HA])

= pKa(HA + H2O ⇌ A− + [H3O]+) + lg (nA−

nHA) − eqn. (4a)

o Since 0.1 <[A−]

[HA]< 10, the pH range of the buffer, known as the buffer region,

is constrained to pKa ± 1.00

o When the conc. of conjugate base and conjugate acid are equal, [A−]

[HA]= 1 and

pH = pKa

o Stronger acids have higher 𝐊𝐚 and lower 𝐩𝐊𝐚 than weaker acids

o When selecting an appropriate conjugate acid–base buffer pair, we choose a

pair whose conjugate acid has a pKa near the desired 𝐩𝐇

o While pH is a measure of proton conc. and is an experimentally alterable

property of a solution, pKa is a fixed property of an acid (similarly, conc. can

be Δd but strength is a constant property)

o Direct 𝐩𝐊𝐚 determination of an acid in aqueous solution is limited to acids

that are less acidic than [H3O]+ and more acidic than H2O:

Since [H3O]+ is the strongest acid that can exist in water, if we dissolve

an acid that is stronger than water in water, it ionizes to [H3O]+

Thus, pKa for very strong & very weak acids are estimated using other

solvents, esp. in many organic rxns.

pKb of the conjugate base is related to the pKa of the conjugate acid:

pKb + pKa = pKw = 14 − eqn. (4b)

o This emphasizes the fact that the greater the pKa of an acid, the weaker that

acid is but the stronger its conjugate base is

Buffers maintain a relatively–constant pH when limited amounts of base or acid are

added to them because a buffer has a:

1. Weak acid that can react with added base to form the conjugate base:

HA (𝑎𝑞) + [OH]− (𝑎𝑞) → A− (𝑎𝑞) + H2O (𝑙)

2. Weak base that can react with added acid to form the conjugate acid:

A− (𝑎𝑞) + [H3O]+ (𝑎𝑞) → HA (𝑎𝑞) + H2O (𝑙)

pH is carefully controlled in cells because many enzymes are sensitive to pH:

o The pH of blood plasma is ~7.4

o 2 impt. buffers in blood are dihydrogen phosphate ([H2PO4]−) and

bicarbonate ([HCO3]−):

Ionization of phosphate has a pKa ≈ 6.86 and thus the phosphate /

dihydrogen phosphate system is a decent buffer when pH = 6.86 ± 1

Bicarbonate is impt. as it involves an equilibrium with CO2 (𝑔):

The extent of pH change depends on the amount of acid or base that is added and on

the buffer capacity (the relative amounts of conjugate acid & conjugate base):

o Buffers are most pH–resistant at the 𝐩𝐊𝐚 pts.

o When nearly all of the conjugate acid in a buffer has reacted with the added

base, adding just a little more base can the pH since the buffer capacity has

been exceeded

o Procedures:

1. Calc. the moles of [H3O]+ or [OH]− added (since these are strong acids /

bases, they are consumed by the conjugate base / conjugate acid in the

buffer system in a rxn. that goes into completion)

2. Calc. the no. of moles of conjugate acid after the addition, nHA

𝑡𝑓

3. Calc. the no. of moles of conjugate base after the addition, nA−

𝑡𝑓

4. If 0.1 <nA−

tf

nHA

tf< 10, use the Henderson–Hasselbalch eqn. to calc. the pH;

otherwise, follow the steps provided in the titration section of this

chapter

5. Acid–base titrations In volumetric analysis, the titrant, a solution whose conc. is known, is added to the

analyte and Vtitrant∗ , the required volume of the titrant required to neutralize the

analyte is used to determine the initial conc. of the titrant

We assume that:

1. The final volume is the sum of the volumes of the titrant and the analyte

2. Activities can be used to approximate concentrations

♣! The equivalence pt. is the pH when a stoichiometric amount of titrant has

been added to exactly neutralize the analyte

♣! The end pt. is the pH at which the indicator Δs color and this is used to

approximate the equivalence pt.:

o Thus, an indicator must give an endpt. that is very close to the equivalence pt.

For the titration of a monoprotic strong acid, HA, using a monoprotic strong base:

𝑡 Vtitrant pH calculations

Initial, 𝑡0 Vtitrant = 0

pH is determined by the initial conc. of hydronium ions formed from the

complete dissociation of the acid:

pH ≈ − lg[H3O+]0 = − lg[HA]0 − eqn. (5a(i))

Intermediate, 𝑡int 0 < Vtitrant

< Vtitrant∗

pH is determined by the conc. of the remaining hydronium ions after

some of the hydronium ions are consumed by the added base:

pH ≈ − lg[H3O+]int = − lg (nHA

𝑡0 − ntitrant

VHA𝑡0 + Vtitrant

) − eqn. (5a(ii))

Equivalent, 𝑡∗ Vtitrant = Vtitrant∗

The equivalence pt. is pH = 7.00 since a neutral salt is produced at the

equivalence pt.:

pH = 7.00 − eqn. (5a(iii))

Final, 𝑡𝑓 Vtitrant > Vtitrant∗

pH is determined by the conc. of the excess hydroxide ions:

pH ≈ 14.00 + lg[OH−]𝑓 = 14.00 + lg (ntitrant − nHA

𝑡0

VHA𝑡0 + Vtitrant

) − eqn. (5a(iv))

For the titration of a monoprotic weak acid, HA, using a monoprotic strong base, the

equivalence pt. is pH > 7.00 since a basic salt is produced at the equivalence pt.:




partial dissociation of the acid:

pH ≈ − lg[H3O+]0 − eqn. (5b(iα))

[H3O+]02

[HA]0 − [H3O+]0= Ka(HA + H2O ⇌ A− + [H3O]+) − eqn. (5b(iβ))

Buffer, 𝑡buffer 0 < Vtitrant

< Vtitrant∗

pH is determined by the conc. of the hydronium ions formed by the partial

dissociation of the remaining acid:

pH ≈ pKa + lg (nA−

𝑡buffer

nHA

𝑡buffer) = pKa + lg (

ntitrant

nHA𝑡0 − ntitrant

) − eqn. (5b(ii))

*The pKa = pH pt. is reached when ntitrant =1

2nHA

𝑡0

Equivalent, 𝑡∗ Vtitrant = Vtitrant∗

pH is determined by the conc. of hydroxide ions formed from the partial

dissociation of the conjugate base of the acid:

pH ≡ 14.00 − pOH ≈ 14.00 + lg[OH−]∗ − eqn. (5a(iiiα))

[OH−]∗2

nHA𝑡0

VHA𝑡0 + Vtitrant

∗− [OH−]∗

= Kb(A− + H2O ⇌ HA + [OH]−) − eqn. (5b(iiiβ))

Final, 𝑡𝑓 Vtitrant > Vtitrant∗

pH is determined by the conc. of the excess hydroxide ions (ignoring the

small contribution of hydroxide ions from the conjugate base of the acid):

pH ≈ 14.00 + lg[OH−]𝑓 = 14.00 + lg (ntitrant − nHA

𝑡0

VHA𝑡0 + Vtitrant

) − eqn. (5b(iv))

o The rapidly rising portion of the curve near the equivalence pt. is shorter than

it is for the titration of a strong acid with a strong base, thus limiting which

indicators can be used

o In fact, near the equivalence pt., the weaker the acid:

1. The higher the initial pH

2. The shorter the rise in pH at the rapid rise of the curve

For the titration of a monoprotic weak base, B, using a monoprotic strong acid, the

equivalence pt. is pH < 7.00 since an acidic salt is produced at the equivalence pt.:



pH is determined by the initial conc. of hydroxide ions formed from the

partial dissociation of the base:

pH ≈ − lg[OH−]0 − eqn. (5c(iα))

[OH−]02

[B]0 − [OH−]0= Kb(B + H2O ⇌ [BH]+ + [OH]−) − eqn. (5c(iβ))

Buffer, 𝑡buffer 0 < Vtitrant

< Vtitrant∗

pH is determined by the conc. of hydroxide ions formed by the partial

dissociation of the remaining base:

pH ≈ pKa + lg (nB

𝑡buffer

nBH+𝑡buffer

) = pKa + lg (nB

𝑡0 − ntitrant

ntitrant) − eqn. (5c(ii))

*The pKa = pH pt. is reached when ntitrant =1

2nB

𝑡0

Equivalent, 𝑡∗ Vtitrant

= Vtitrant∗

pH is determined by the conc. of hydronium ions formed from the partial

dissociation of the conjugate acid of the base:

pH ≈ − lg[H3O+]∗ − eqn. (5c(iiiα))

[H3O+]∗2

nB𝑡0

VB𝑡0 + Vtitrant

∗− [H3O+]∗

= Ka([BH]+ + H2O ⇌ B + [H3O]+) − eqn. (5c(iiiβ))

Final, 𝑡𝑓 Vtitrant

> Vtitrant∗

pH is determined by the conc. of the excess hydronium ions (ignoring the

small contribution of hydronium ions from the conjugate acid of the base):

pH ≈ − lg[H3O+]𝑓 = 14.00 + lg (ntitrant − nB

t0

VBt0 + Vtitrant

) − eqn. (5c(iv))

For the titration of a diprotic weak acid, H2A, using a monoprotic strong base:




partial dissociation of H2A:

pH ≈ − lg[H3O+]0 − eqn. (5d(iα))

[H3O+]02

[H2A]0 − [H3O+]0= Ka1(H2A + H2O ⇌ [HA]− + [H3O]+) − eqn. (5d(iβ))

Buffer 1,

𝑡1buffer

0 < Vtitrant

< Vtitrant∗,1


dissociation of the remaining H2A:

pH ≈ pKa1 + lg (ntitrant

nH2A𝑡0 − ntitrant

) − eqn. (5d(ii))

*The 1st pKa1 = pH pt. is reached when ntitrant =1

2nH2A

𝑡0

Equivalent 1,

𝑡1∗

Vtitrant = Vtitrant∗,1


dissociation of [HA]−:

pH ≡ 14.00 − pOH ≈ 14.00 + lg[OH−]∗ − eqn. (5d(iiiα))

[OH−]∗2

nHA𝑡0

VHA𝑡0 + Vtitrant

∗− [OH−]∗

= Kb1([HA]− + H2O ⇌ H2A + [OH]−) − eqn. (5d(iiiβ))

Buffer 2,

𝑡2buffer

Vtitrant∗,1 < Vtitrant

< Vtitrant∗,2


dissociation of the remaining [HA]−:

pH ≈ pKa2 + lg (ntitrant − n[HA]−

𝑡0

2nH2A𝑡0 − ntitrant

) − eqn. (5d(iv))

*The 1st pKa2 = pH pt. is reached when ntitrant =3

2nH2A

𝑡0

Equivalent 2,

𝑡2∗

Vtitrant = Vtitrant∗,2


dissociation of A−:

pH ≡ 14.00 − pOH ≈ 14.00 + lg[OH−]∗,2 − eqn. (5d(vα))

[OH−]∗,22

nHA𝑡0

VHA𝑡0 + Vtitrant

∗,2 − [OH−]∗,2

= Kb2(A2− + H2O ⇌ [HA]− + [OH]−) − eqn. (5d(vβ))

Final, 𝑡𝑓 Vtitrant < Vtitrant∗,2

pH is determined by the conc. of the excess hydroxide ions (ignoring the

small contribution of hydroxide ions from the conjugate base of the acid):

pH ≈ 14.00 + lg[OH−]𝑓 = 14.00 + lg (ntitrant − 2nHA

𝑡0

VHA𝑡0 + Vtitrant

) − eqn. (5d(vi))

Reference:

1. Moore, J., & Stanitski, C. (2014). Chemistry: The molecular science, Cengage Learning,

Chapter 16

general chemistry academic journal (sample)

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