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The Nature of Acid-Base Equilibria

BrØnsted-Lowry Theory

a substance that donates a proton (H+) is a BrØnsted-Lowry acid,

while a substance that accepts a proton (H+) is a BrØnsted-Lowry

base

e.g. (1)

e.g (2)

a substance that acts as a BrØnsted-Lowry acid in some reactions

and as a BrØnsted-Lowry base in others is called amphoteric

(amphiprotic)

the BrØnsted-Lowry is useful in that we can define acids and

bases in terms of chemical reactions in various states and not

solely in aqueous solutions

Reversible Acid-Base Reactions

these reactions at equilibrium can proceed in both forward &

reverse directions, having both an acid and a base on both sides

of the reaction arrow

e.g.

when a pair of substances differ by a single H+ ion (a proton) the

substances are called a conjugate acid-base pair

i.e. HC2H3O(aq) and C2H3O2-(aq) and H2O(l) and H3O+(aq)

the BrØnsted-Lowry model lets us view acid-base reactions as a

competition for protons between 2 bases i.e. between C2H3O2-(aq)

and H2O(l)

in this reaction only about 1.3% of a 0.1 mol/LHC2H3O(aq) have

reacted at SATP…this explains why the equilibrium lies far to the

left and why we call acetic acid, a weak acid

similarly, when HCl(aq) reacts with H2O(l), Cl in HCl has a much

weaker affinity for the proton than the H2O(l) does so that

H3O+(aq) results

this results in a reaction whose equilibrium lies far to the right and

explains why HCL is a strong acid

we can generalize the relationship between an acid and its

conjugate base as follows:

The Autoionization of Water

water sometimes will react with itself to produce hydronium ions

and hydroxide ions as in:

as the conductivity is slight there are many more water molecules

than ions

when the right energy and orientation are present then the above

reaction can occur

this process is called the autoionization of water

it can also be written without showing the water molecules that

are not reacting:

this reaction is very rare, occurring with less than 2 water

molecules out of every billion at SATP

water equilibrium obeys the equilibrium law and therefore the

equilibrium law expression for water is:

the concentration of water molecules in pure water & dilute

aqueous solutions is constant at 55.6 mol/L(using density &MH2O)

i.e.

a new constant, taking into account the constant value of [H2O(l)]

and the equilibrium can be calculated and is called the:

ion product constant for water, KW

in pure water the concentrations of hydrogen & hydroxide ions are

equal and measurements have shown that the conc. is 1.0 x 10-7

at SATP, therefore,

the numerical value for KW is valid at SATP but NOT at

temperatures that are much higher or lower

for higher temperatures KW is greater so products are favoured

we can use KW to calculate either the [H+] or [OH-] if the

concentrations are known

Strong Acids

strong acids ionize greater than 99% but assuming 100%

we would see

so in looking at a bottle of HCl(aq)that has a molar concentration

1.0mol/L , we would assume that the bottle contained 1.0mol/L of

H+(aq) and 1.0mol/L of Cl-(aq)

there are only a few strong acids e.g. HCl(aq), HBr(aq), H2SO4(aq),

HNO3(aq) and H3PO4(aq) to name some familiar ones

monoprotic acids contain only 1 “ionizable” H atom

(see sample problem on pages 535-536)

Strong Bases

according to Arrhenius, a base is a substance that dissociates to

produce [OH-] and increase the hydroxide concentration of a

solution

ionic hydroxides are all strong bases as are all of the hydroxides of

Group I elements i.e. LiOH, NaOH, etc.

e.g.

Group II elements also form strong bases, which dissociate to

produce 2 moles of OH- for every mole of metal hydroxide.

e.g.

(see Sample Problems on pages 538-540)

Hydrogen Ion Concentration and pH

A Danish chemist Soren Sorenson(1909) expressed [H+] using a

scale without units….the pH scale

Mathematically expressed as:

See examples on page 541&542 and look at sidebar “Learning Tips” to remember how to use your calculator to find pH and [H+]

pOH and pKW

the [OH-] is very small in dilute bases and we can use a similar formula to calculate the [OH-]

(see example on page 542)

using mathematics of logarithms we can show a relationship between pK and pOH…to do this we need to define pKW

the numerical value of pKW is always 1x10-14 at SATP

Measuring pH

can use acid-base indicators, litmus paper, pH meters

The pH of Strong Acids

strong acids ionize >99%, a 0.1mol/L HCl(aq) solution has almost

no HCl molecules in it

we can assume it has 0.1mol/L H+(aq) and 0.1mol/L Cl-(aq), giving a pH of 1

pH of solutions of strong monoprotic acids is found from the [H+]

(see sample problem on page 545

The pH of Strong Bases

Ba(OH)2 has a higher conductivity and pH compared to NaOH

Ba(OH)2 is more basic because when it dissociates it produces 2 OH- per formula unit

Like strong acids the pH and pOH of strong bases are determined by the [OH-] contributed by the dissociation of the ionic hydroxide

(see sample problem on pages 547-548)

WEAK ACIDS & BASES

a weak acid is an electrolyte that does not completely ionize in water e.g. ‘s HF(aq),H2CO3(aq), H2S(aq), H3BO3(aq)

weak basesare compounds other than ionic hydroxides that when they dissolve produce basic solutions, they are not as basic as ionic hydroxides

Arrhenius’ theory is not useful in explaining this and therefore we would use Bronsted Lowry theory of bases being proton acceptors

Percent Ionizationof Weak Acids

weak acids ionize less than 50% and have pH’s closer to 7

acetic acid,HC2H3O2(aq) ,ionized only 1.3% in solution at 25C and 0.10 mol/L

i.e.

Percent Ionization,p, is defined as

P=concentration of acid ionized x 100%

concentration of acid solute

therefore in a 0.10 mol/L HCl solution, almost all the HCl molecules ionize so the [H+] is equal to the initial concentration of the solute i.e.

but in a 0.10mol/L solution of acetic acid only 1.3% of the molecules will ionize to form H ions

see sample problem on page 553-556

Ionization Constants for Weak Acids

the equilibrium constant for a weak acid is known as the acid ionization constant and is represented as Ka where “a” means that the constant applies to the equilibrium of an acid (see sample problem on pages 554-556)

Percent Ionization and Concentration

Ka values give us a means of comparing the strengths of weak acids, percent ionization can be used but only when comparing solutions that have equal initial concentrations

generally, the more dilute the solution, the greater the degree of ionization

in general, the more dilute a weak acid solution, the greater the percent ionization, and vice versa.

Ionization Constants for Weak Bases

weak bases like ammonia also can form dynamic equilibria in solution

as water is a pure liquid this is a heterogeneous equilibrium and its concentration can’t change by increasing or decreasing its amount in solution

that makes [H2O(l)] a constant, and its concentration value is incorporated into the value of K, yielding a new constant, Kb, the base ionization constant

(see Table 3 on page 558) for Kb values)

Organic Bases

include bases like methylamine and urea, these molecules can be viewed as substituted ammonia molecules where one of the H atoms is replaced with a methyl group

pyridine is similar to benzene with one of the C rings replaces with a N atom

alkaloids are nitrogen-containing organic bases that have powerful stimulating effects on animal nervous systems

e.g.’s ephedrine, codeine, novocaine, morphine, quinine, cocaine, etc

nitrogeneous bases are generally weak Bronsted-Lowry bases that undergo the same type of ionization reaction with water as ammonia

Relationship Between Ka and Kb

(see sample problem on page 561)

in KaKb=KW, for any conjugate acid-base pair the product KaKb is a constant

therefore the larger the value of Ka , the smaller the value of Kb

i.e. the weaker the acid the stronger its conjugate base and vice versa

The pH of Weak Acid Solutions

since the value of Ka is constant over a range of acid concentrations, it can be used to calculate [H+] and pH of weak acid solutions

(see sample problems on pages 563-570)

The pH of Weak Base Solutions

we can use Kb to predict pH, pOH, etc.

to calculate the Kb value we must;

(see example in text on page 571 & sample problems on pages 571-574)

Polyprotic Acids

some acids like H2SO4, and boric acid, H3BO3 have more than 1 ionizable protons and so are called polyprotic acids

polyprotic acids do not donate all their protons simultaneously but rather one at a time

in each step the reaction has its own acid ionization constant

e.g. the ionization of arsenic acid, H2AsO4(aq)

in general, for a polyprotic acid, Ka1>Ka2>Ka3…

(see sample problems on pages 575-578)

ACID-BASE TITRATIONS

Titration

a chemical analysis involving the progressive addition of a solution of a known solute concentration (titrant) into a sample of solution of unknown concentration (sample)

  • titrant or sample may be either acid or base
  • Purpose: to determine the amount of a specified chemical in the sample (mass and concentration) using stoichiometric relationships

Standardizing the Titrant

titrant is usually standardized using primary standards that are available in a pure & stable form (with accurate stated concentration)- include sodium carbonate, Na2CO3(s) and potassium hydrogen phthalate, KHC7H4O4(s)

HCl and NaOH are not primary standards as HCl gas vaporizes and NaOH is hygroscopic (gains mass by absorbing water from the air)

Equivalence Point

The point where the amount of reactant in the sample is just consumed by the reactant in the titrant

Acid-Base Indicator

this signals the end of a titration by sharply and permanently changing clour at the equivalence point

common indicators include bromothymol blue, phenolphthalein and methyl orange (see text)

End Point

  • point where indicator changes colour

ideal situation is where end point occurs at equivalence point; unfortunately not easy to achieve

  • phenolthalein changes pH at 8.2 to 10.0 and not at a pH of 7.0
  • however, slope of titration curve is quite steep at endpoint, such that the volume of titrant at the endpoint is very close in value to the volume of titrant at the equivalence point

Strong Acid-Strong Base Titrations

consider the reaction between HCl(aq) and NaOH(aq);

resulting product: Acid + Base  Salt + Water

since a strong acid and base fully ionize (>99%) once the equivalence point is reached the solution is neutral with a pH of 7.0 and all the H3O+ and OH- = reacted

remember that the conjugates of a strong acid and base are a very weak conjugate base and a very weak conjugate acid which cannot hydrolyze, therefore the pH is 7.00

if we plotted the pH of the solution flask in the sample problem we would get a curve that is typical for the titration of a strong acid with a strong base

Weak Acid-Strong Base Titration

titrant: strong base

sample: weak acid

Before Titration

  • must realize that sample achieves an equilibrium before the titration begins
  • can determine the pH by using the Ka and knowing the initial concentration of the weak acid
  • Ka of a weak acid is very small as dissociation is small – may be able to use the hundred rule approximation method

During Titration to the Equivalence Point

  • strong base will neutralize weak acid – weak acid will continue to ionize during titration
  • all of the H+ from the weak acid will be reacted when the equivalence point is reached
  • can calculate the concentration of the salt (weak conjugate base) of the weak acid at the equivalence point by using the new volume – original volume of weak acid + volume of titrant (strong base) added

Equilibrium of Weak Acid at the Equivalence Point

  • NO more titrant (strong base) added
  • salt (weak conjugate base) ofa weak acid will now hydrolyze and form a new equilibrium
  • set up equilibrium equation with the salt of the weak acid (weak conjugate base) on reactant side
  • now looking at a basic reaction – use Kb to determine new pH
  • initial concentration of the salt is a new concentration as determined above at the equivalence point
  • the final equivalence point of the acid-base titration will be this new pH

titrating acetic acid with NaOH is an example of a weak acid-strong base titration

the low Ka indicates that the acetic acid exists as acetic acid particles in solution and as NaOH is added, the OH- ions react with the acetic acid as,

Weak Base-Strong Acid Titration

titrant: strong acid

sample: weak base

the analysis of the titration follows format as laid out in the titration of a weak acid with a strong base

1.Determine the pH before the titration – use Kb and initial concentration of weak base

2.During the titration to the equivalence point – strong acid will neutralize the weak base until all OH- of weak base is consumed; salt (weak conjugate acid) of weak base now has a new concentration based on original volume of the weak base and volume of titrant (strong acid) added

3.Equilibrium at the equivalence point – salt (weak conjugate acid) of the weak base will now hydrolyze and form new equilibrium; pH can be calculated using Ka of salt (weak conjugate acid)

  • the pH at the equivalence point will be this new pH

titrating NH3(aq) with HCl(aq) is an example

Acid-Base Indicators

behaviour depends on Bronsted-Lowry concept and the equilibrium concept

an indicator is a conjugate weak acid-base pair formed by dissolving it in water

e.g.

  • using Le Chatelier’s Principle, an increase in the [H3O+] shifts the equilibrium to the left
  • in acidic solutions, the primary form of the indicator is its un-ionized (HIn(aq)) form, eg. when litmus is added to an acidic solution
  • in basic solutions, the OH- ions remove the H3O+ ions and the equilibrium shifts to the right, than the base colour predominates (In-(aq))
  • different indicators have different acid strengths so the acidity or pH can vary (see p.609, Table 7)

in acid-base titrations, the pH changes sharply near the equivalence point

  • this change occurs over a small range of pH but in a titration the change occurs very quickly so that all we see is a very quick colour change at the indicator’s transition point
  • when selecting an indicator, the pH at the equivalence point must be known

  • the equilibrium constant equation for the indicator equilibrium is:
  • since KIn , [H3O+(aq)] , or [H+(aq)] are very small we can convert them by taking the negative logarithm of each value
  • an indicator works best when its pKIn equals the pH at the equivalence point of that particular titration

Titrations of Polyprotic Acids and Bases

polyprotic acids include: H2SO4(aq), H3PO4(aq), H2CO3(aq)

  • the titration of H3PO4 with a strong base follows the following multiple ionizing steps

1.H3PO4(aq) + NaOH(aq)  H2PO4-(aq) + H2O(l) + Na+(aq)

2.H2PO4-(aq) + NaOH(aq)  HPO42-(aq) + H2O(l) + Na+(aq)

3.HPO42-(aq) + NaOH(aq)  PO43-(aq) + H2O(l) + Na+(aq)

  • each ionizing step occurs in succession
  • the titration curve of the polyprotic acid, H3PO4, with a strong base also shows multiple endpoints as follows (p. 613, Figure 9)
  • the curves show two endpoints requiring equal volumes of base
  • the third endpoint does not register as the third ionizing step because HPO42- is an extremely weak acid (Ka = 4.2 x 10-13) and apparently does not quantitatively lose its proton – only quantitative reactions produce detectable endpoints in an acid-base titration

bases can also be considered polyprotic, such as:CO32-, PO43-, S2-

  • consider a titration of NaCO3 solution: the salt will dissociate into an anion (conjugate base), CO32-,of a weak acid - as a result it can hydrolyze first to HCO3- and then to H2CO3
  • in a titration with a strong acid the carbonate and bicarbonate anions will act as a base and accept a proton from the acid in two steps:

1.CO32-(aq) + HCl(aq)  HCO3-(aq) + Cl-(aq)

2.HCO3-(aq) + HCl(aq)  H2CO3(aq) + Cl-(aq)

  • The titration curve will appear with two endpoints representing both reactions (p. 611, Figure 8)
  • the volume to reach each endpoint will be the same

BUFFERS

Buffer Solution

pH curves involving a weak acid or weak base have at least one region where the pH changes very little, despite the addition of an appreciable amount of acid or base (buffering action)

  • the pH curve in this region is most nearly horizontal (flat) at a volume of titrant that is one-half the volume of the equivalence point
  • mixture in buffering region contains approximately equal amounts of unreacted weak acid and its conjugate base
  • prepared by mixing weak acid with a soluble salt of its conjugate base (may also use weak base with a soluble salt of its conjugate acid)

examples include blood

buffering action works with addition of a small amount of a strong acid or strong base

Capacity of a Buffer

buffers have a certain capacity,i.e. addition of a strong acid or strong base beyond a certain point will result in a dramatic changein pH