Acid-Base Equilibria

Chapter 16

Hw and suggested work:

Material in the lectures is to be used for educational purposes only. The media material is used from the accompanying book “Chemistry the Central Science” –Prentice Hall. The syllabus is based on the CHEM 1202 program at the Department of Chemistry, LSU. The lecture notes are prepared by Dr. Kresimir Rupnik, Chrupn@lsu.edu and Rupnik@intelion.com

Acids & Bases 2

Acids and Bases: A Brief Review

• Acid: taste sour and cause dyes to change color.

• Bases: taste bitter and feel soapy.

• Arrhenius: acids increase [H+] bases increase [OH-] in solution.

• Arrhenius: acid + base ® salt + water.

• Problem: the definition confines us to aqueous solution.

IMPORTANT: Acid and Base Definitions

Arrhenius

Acid increases H+ concentration

Base increases OH- concentration

Brønsted-Lowry (1923)

Acid donates a H+

Base combines with or accepts H+

Lewis Acid electron acceptor

Base electron donor

Brønsted-Lowry Acids and Bases: PROTON H+

The H+ Ion (PROTON) in Water

• The H+(aq) ion is simply a proton with no electrons. (H has one proton, one electron, and no neutrons.)

• In water, the H+(aq) form clusters.

• The simplest cluster is H3O+(aq). Larger clusters are H5O2

+ and H9O4+.

• Generally we use H+(aq) and H3O+(aq) interchangeably.

• Consider HCl(aq) + H2O(l) ® H3O+(aq) + Cl-(aq):

– HCl donates a proton to water. Therefore, HCl is an acid.

– H2O accepts a proton from HCl. Therefore, H2O is a base.

• Water can behave as either an acid or a base.

• Amphoteric substances can behave as acids and bases.

Conjugate Acid-Base Pairs

• Whatever is left of the acid after the proton is donated is called its conjugate base.

• Similarly, whatever remains of the base after it accepts a proton is called a conjugate acid.

• Consider

– After HA (acid) loses its proton it is converted into A- (base). Therefore HA and A- are conjugate acid-base pairs.

– After H2O (base) gains a proton it is converted into H3O+ (acid). Therefore, H2O and H3O+ are conjugate acid-base pairs.

• Conjugate acid-base pairs differ by only one proton.

Brønsted-Lowry Acids and BasesRelative Strengths of Acids and Bases

• The stronger the acid, the weaker the conjugate base.

• H+ is the strongest acid that can exist in equilibrium in aqueous solution.

• OH- is the strongest base that can exist in equilibrium in aqueous solution.

Acids & Bases 8

ch Water, pure liquid, itself has some ionic character:

H2O(l) H+(aq) + OHaq)

This is called self-ionization. Although most chemists simply write H+, it is important to realize that H+ by itself represents a naked proton. In water the H+ is hydrated, that is, it forms ionic-diople interactions with 4 water molecules. Although this is perhaps the most accurate way of describing a H+ in water, a common way of representing the fact that it is actually hydrated (interacting with water molecules) is to write H3O+.

Acids & Bases 9

H2O(l) H+(aq) + OH(aq)

H2O is a pure liquid and its concentration is constant. [H2O] = 55.6 M, so:

[H+] [OH] = 1 1014 M2

[H+] = [OH] = 1 107 M

So the H+ concentration in water is 1 107 M

Acids & Bases 10

Because of the often very small nature of H+ concentrations, chemists (and others) have devised a logarithmic scale to simplify expressing these values:

pH = log [H+] The negative sign in front of the log makes sure that most small concentrations of acid are given by positive values.

[H+] = 1 107 M

pH = log(1 107) = 7.0

The greater the [H+] concentration, the LOWER the pH value!!!

pH < 7.0 AcidicpH = 7.0 NeutralpH > 7.0 Basic (Alkaline)

Acids & Bases 12

Substance pH10 M HCl 1.01 M HCl 0.0Stomach Acid (HCl) 1.4Lemon Juice 2.1Orange Juice 2.8Wine 3.5Black Coffee 5.0Urine 6.0Pure Water 7.0Blood 7.4Baking Soda Solution 8.5Ammonia Solution 11.91 M NaOH 14.010 M NaOH 15.0

Acids & Bases 13

We can also define:

pOH = log [OH] Although most chemists mainly use pH, pOH can be useful in base equilibrium numerical problems that we will run into later.

Another definition we use is:

pKw = log Kw = 14So, for a given water solution:

pOH + pH  = pKw = 14or:

pOH = 14 pHpH = 14 pOH

Acids & Bases 14

Examples: The pH of wine is 3.5. What is the [H+]? What is the [OH]? What is the pOH?

pH = log[H+] = 3.5

[H+] = antilog(3.5) = 103.5 = 3.16 104 M

[OH] = = 3.1 1011 M

pOH = log[OH] = log(3.1 1011) = 10.5

---- or ----

pOH = pKw pH = 14 3.5 = 10.5

Problem: The pH in your stomach is around 1. What is the [H+]? What is the [OH]? What is the pOH?

Acids & Bases 15

Dissociation Equilibrium Constants

An acid is a compound that will ionize in solution (usually water) to form a H+(aq) and a counter-anion. This can be writen in a general fashion as:

HA(aq) H+(aq) + A(aq)

The equilibrium expression for this reaction is:

The equilibrium constant, Keq, is often given a special name for acids: Ka or the acid dissociation constant. The larger the Ka value the more H+ is being produced (the lower the corresponding pH), therefore, the stronger the acid!!!!

Just as with pH we can also define pKa as:

pKa = log Ka The smaller the pKa the stronger the acid!!!!

Acids & Bases 16

Acid Dissociation Constants and pKa ValuesAcid HA A- Ka pKahydroiodic HI I 10 -10hydrobromic HBr Br 10 -10perchoric HClO4 ClO4 10 -8

hydrochoric HCl Cl 10 -8sulfuric H2SO4 HSO4 10 -8

nitric HNO3 NO3 10 -8

trichloroacetic Cl3COOH Cl3COO 2 10 0.7

oxalic HOOCCOOH HOOCCOO 5.9 10 1.2sulfurous H2SO3 SO3 1.5 10 1.8

sulfuric (2nd H+) HSO4- SO4 1.2 10 1.9

phosphoric H3PO4 H2PO4 7.5 10 2.1

nitrous HNO2 NO2 4.6 10 3.3

hydrofluoric HF F 3.5 10 3.5formic HCOOH HCOO 1.8 10 3.8benzoic C6H5COOH C6H5COO 6.5 10 4.2

oxalic (2nd H+) HOOCCH2COO OOCCH2COO 6.4 10 4.2

acetic CH3COOH CH3COO 1.7 10 4.7

carbonic H2CO3 HCO3 4.3 10 6.4

hydrogen sulfide H2S HS- 9.1 10 7.1

phosphoric (2nd) H2PO4 HPO4 6.2 10 7.2

ammonium ion NH4 NH3 5.6 10 9.2

hydrocyanic HCN CN- 4.9 10 9.3

Acids & Bases 17

Note HClO3 is also STRONG

Acids & Bases 18

Strong AcidsThese are acids that are essentially completely dissociated in solution (usually water).

HCl(aq) H+(aq) + Cl(aq)

In general, Ka > 1 for a strong acid (although there is no firm dividing line!)

The common strong acids that you are expected to know are:

HCl, HBr, HI (the hydrohalic acids)H2SO4 (sulfuric acid) HNO3 (nitric acid)

HClO4 (perchloric acid) HClO3

HCl, H2SO4, and HNO3 are also referred to as mineral acids.

Acids & Bases 19

Problem: What are the pH's of the following solutions?

a) 0.001 M HCl

b) 0.1 M HNO3

c) 1 105 M H2SO4

d) 10 M HBr

e) 1 M HI

f) 0.1 M HF

g) 0.01 M HCl

h) 1 104 M HNO3

i) 1 M acetic acid

j) 1 1014 M HCl

Acids & Bases 20

Explaination for j) on the last page:

The actual proton concentration for any acid dissolved in water is more precisely defined as:

[H+]total = [H+]acid + [H+]water

Normally, [H+]water is 1 107 M and is much less than [H+]acid, so that we almost always ignore it.

BUT, in this example, [H+]acid turns out to be only 1 1014 M, which is much, much less than the [H+]water.

So in this example we actually ignore the tiny amount of H+ contributed from the strong acid and only consider the H+ naturally present in water:

Acids & Bases 21

This will work for acid concentrations of 1 108 M and lower, although it technically (and mathematically) gets complicated right around 1 107 M.

Strong & Weak vs. pH

A common mistake is to confuse pH with strong or weak acids/bases. For example, if I tell you a solution has a pH of 5.0, most of you would incorrectly assume that it is a weak acid. Maybe, maybe not.

A pH of 5.0 tells you that it is a weakly acidic solution. This solution might have been made from a medium to considerable amount of a weak acid, or a very small amount of a strong acid. Without knowing the concentration (or amount and nature) of the acid used (not just the resulting H+ concentration or pH), you can’t tell whether it is composed of a strong or weak acid.

It is true that solutions with very low pH’s (for example, 1.0) can pretty much only be composed of strong acids.

Acids & Bases 22

So you need to be very careful with your language in dealing with strong & weak acids and solutions that are strongly or weakly acidic.

Acids & Bases 23

Strong Bases

These are usually (and most commonly) alkali metal hydroxides that dissociate completely in solution:

NaOH(aq) Na+(aq) + OH(aq)

The common strong bases that you are expected to know are:

LiOH, NaOH, KOH, RbOH, & CsOH

The alkaline earth hydroxides Ca(OH)2, Sr(OH)2, Ba(OH)2 are medium strong bases.

Be(OH)2 & Mg(OH)2 are considered to be weak bases since they only partially dissociate in water. The smaller ionic radius of Be2+ and Mg2+ cations polarize coordinated H2O enough to promote hydrolysis (that is, loss of H+ from H2O).

Acids & Bases 24

It is very important to remember that there are almost always two steps in converting from [OH] to pH:1) convert [OH] to [H+]:

[H+] =

2) then convert [H+] to pH.---- or ----

1) convert [OH] to pOH2) then convert pOH to pH:

pH = 14 pOH

Acids & Bases 25

Problem: What are the pH's of the following solutions? What are the pOH's?

a) 0.001 M NaOH

b) 0.1 M CsOH

c) 1 105 M KOH

d) 10 M RbOH

e) 1 M NaOH

f) 0.1 M Be(OH)2

g) 0.01 M LiOH

h) 1 104 M NaOH

i) 1 M ammonia

j) 1 1014 M KOH

Acids & Bases 26

Explaination for j) on the last page:

The actual hydroxide concentration for any base dissolved in water is more precisely defined as:

[OH]total = [OH]base + [OH]water

Normally, [OH]water is 1 107 M and is much less than [OH]base, thus we can usually ignore it.

BUT, in this example, [OH]base turns out to be only 1 1014 M, much less than the [OH]water.

So in this example we actually ignore the tiny amount of OH contributed from the acid and only consider the OH naturally present in water:

This will work for base concentrations of 1 108 M and lower, although it technically (and mathematically) gets complicated right around 1 107 M.

Acids & Bases 27

Conjugate Acid-Base Pairs

Bronsted-Lowry Definition of a Base: a substance that combines or accepts a H+.

Consider the dissociation of an acid:

HA(aq) + H2O H3O+(aq) + A(aq)

Because this is an equilibrium, A(aq) is back reacting with H+(aq) to produce undissociated acid HA(aq). Therefore, A(aq) is acting like a base! Since it was originally part of an acidic compound (HA), there’s a special name for it: conjugate base.

Strong acids have weak conjugate bases.Weak acids have strong conjugate bases.To indicate that an equilibrium favors one side of a rxn chemists sometimes use the double equilibrium arrows where one arrow is shorter. For a strong acid (weak conjugate base) one could write:

HA(aq) H+(aq) + A(aq)

Acids & Bases 28

Bronsted-Lowry Definition of a Acid: a substance that donates a H+.

Consider the reaction of a weak base with water:

NH3(aq) + H2O NH4+(aq) + OH(aq)

Because this is an equilibrium, NH4+(aq) donates a H+(aq) that reacts with OH(aq) to produce the original NH3 (and water). Therefore, NH4+(aq) is acting like an acid! Since it started as a weak base (NH3), we call NH4+ a conjugate acid.

Strong bases have weak conjugate acids.Weak bases have strong conjugate acids.In the two reactions shown on this page and the previous, water is acting as either an acid or a base. Any chemical that can act as either an acid or base is called amphoteric.

Note that in the following reaction, Na+ would more accurately be called a conjugate Lewis Acid (it is not a proton donor).

Acids & Bases 29

NaOH(aq) Na+(aq) + OH(aq)

Acids & Bases 30

Weak Acids

These are acids that only dissociate to produce a small amount of H+ in solution:

HF(aq) H+(aq) + F(aq)

Most of a weak acid is dissolved in solution in its undissociated, neutral form. An acid is weak because its conjugate base (counter-anion) is a good base and likes to bond to H+.

A weak acid typically has Ka < 1 103

Most weak acids are organic acids based on the carboxylic group:

Acids & Bases 31

Some of the more common weak acids that we run into on a daily basis include:

Acids & Bases 33

Example: What is the pH of a 0.1 M solution of acetic acid? Ka 1 105

Abbreviation for acetic acid: HOAcInitial Cond: 0.1 M 0 M 0 M

HOAc(aq) H+(aq) + OAc(aq)

@ Equilib: 0.1 - x x x

Substitute our x values into the equilibrium expression and solve for x:

But, this will be a quadratic expression and we'll have to use the quadratic formula to solve for x (ugh!).

There is, however, a very good approximation we can make to dramatically simplify the algebra.

Acids & Bases 34

Because Ka is pretty small (105) we know that acetic acid is a weak acid and that we are only going to make small quantities of H+. That means that x will be a pretty small number. This in turn means that 0.1 - x will be approximately 0.1.

Our assumption, therefore, will be that x will be much less than 0.1 M (initial concentration of acid). This now really simplifies our algebra:

x2 = 1 x 10-6 } take square root of each side

x = [H+] = [OAc] = 1 x 10-3 MpH = log(1 x 10-3) = 3.0So when can I drop x?? When is it a good

approximation??

Approximation!!

Acids & Bases 35

Problem: What is the pH of a 10 M solution of hydrogen sulfide? Ka 1 107

H2S(aq) H+(aq) + HS(aq)

Acids & Bases 36

Problem: A new organic acid was prepared. A 0.015 M solution has the pH = 4.01. What is the Ka for this new acid?

HA(aq) H+(aq) + A(aq)

Acids & Bases 37

Effect of Structure on Acid/Base Behavior

Hydrohalic AcidsA combination of factors affects the acid strength of hydrohalic acids:

1) Polarity of the H-X bond

2) Strength of the H-X bond

) Stability of the conjugate base, X

Thus, HF is a weak acid because the rather small fluoride ion (F) has a concentrated negative charge that very effectively and strongly attracts the Hcation, not allowing it to dissociate and become a strong acid (like HCl, HBr, or HI).

OxyacidsOxyacids are those acids in which the central atom (most commonly N, Cl, S or P) is bonded to at least one, and usually more, oxygen atoms. The resulting negative charge on this unit is balanced by the proper # of H+ that associate with the oxygen atoms (one per oxygen atom).

Electrostatic attraction!!

Acids & Bases 38

A list of common oxyacids and their names:HNO2 HNO3

Nitrous Nitric

HClO HClO2 HClO3 HClO4

Hypochlorous Chlorous Chloric Percloric

H2SO3 H2SO4

Sulfurous Sulfuric

H3PO2 H3PO3 H3PO4

Hypophosphorous Phosphorus Phosphoric

The acid strength of oxyacids increases for a series of compounds as follows:

1) given the same central atom, the more oxygens present the stronger the acid

Reasoning: the more electronegative oxygens present, the more the negative charge on the anion is spread out over a larger volume. This means that there will be less concentrated negative charge on any single oxygen atom. Thus, there will be a lower electrostatic attraction to the H+

cations, allowing them to dissociate more easily.

Acids & Bases 39

2) given the same # of oxygen atoms, the more electronegative the central atom, the stronger the acidReasoning: the more electronegative the central atom, the more the negative charge on the anion will be pulled towards the central atom and away from the outlying oxygens. Thus, there will be a lower electrostatic attraction to H+ cations, allowing easier dissociation.

Example:HClO HClO2 HClO3 HClO4

Hypochlorous Chlorous Chloric Percloric

Ka = 3 x 10 Ka = 1 x 10 Ka = 5 x 10 Ka = 1 x 10

Shown above are electrostatic potential surface plots for ClO through ClO4 anions (no H+). The red color (dark) indicates more negative charge and a stronger electrstatic attraction to the H+ cation (weaker acid). Postive charge is indicated by the blue color (darker color on center atom).

Acids & Bases 40

Problem: Which one of the following is the stronger acid of the pair?

a) H2SO4 or H3PO4

b) HNO2 or HNO3

c) HOBr or HOI

d) H2SeO4 or H2SeO3

e) HI or HF

f) H2SO3 or H2SO4

g)

Acids & Bases 41

Weak BasesThese are bases that only react to a relatively small extent with H+ in solution:

:NH3(aq) + H+(aq) NH4+(aq)

The convention, however, for writing equilibria for weak bases is to react the base with water, which generates a small quantity of OH-:

:NH3(aq) + H2O NH4+(aq) + OH(aq)

This is the equilibrium we use to define our base equilibrium constant, Kb:

In this equilibrium NH4+(aq) is called the conjugate acid (it acts like a weak acid).

Acids & Bases 42

Some weak bases are shown in the table below:

Base Formula Structure Kb

methylamine NH2CH3 4.4 x 10-4

carbonate ion CO32- 1.8 x 10-4

ammonia NH3 1.8 x 10-5

hydrosulfide ion HS- 1.8 x 10-7

nicotine C10H14N2 7 x 10-7

1.4 x 10-11

hydroxylamine NH2OH 1.1 x 10-8

pyridine C5H5N 1.9 x 10-9

Note that all bases have atoms with lone pairs of electrons that can interact with a H+. Remember that a H+ doesn't have any electrons and has a positive charge. It will be attracted to atoms with negative charges or lone pairs of electrons.

Acids & Bases 43

Example: What is the pH of a 0.1 M solution of ammonia? Kb 1 105

Init: 0.1 M 0 M 0 M

:NH3(aq) + H2O NH4+(aq) + OH(aq)

@ Eq: 0.1 - x x x

Substitute our x values into the equilibrium expression and solve for x:

But, this will be a quadradic expression and we'll have to use the quadradic formula to solve for x (ugh!).

There is, however, a very good approximation we can make that will dramatically simplify the algebra.

Acids & Bases 44

Because Kb is pretty small (105) we know that ammonia is a weak base and that we are only going to make small quantities of OH. That means that x will be a pretty small number. This in turn means that 0.1 - x will be 0.1.

Our assumption, therefore, will be that x will be much less than 0.1 M (initial concentration of acid). This now really simplifies our algebra:

x2 = 1 x 10-6 } take square root of each side

x = [OH] = [NH4+] = 1 x 10-3 M

pOH = log(1 x 10-3) = 3.0

pH = 14 pOH = 11

DANGER!!

VERY Common mistake!!

Approximation!

Acids & Bases 45

Problem: What is the pH of a 1 M solution of sodium carbonate? Kb 1 104

CO32(aq) + H2O HCO3(aq) + OH(aq)

Acids & Bases 46

Relationship Between Ka and Kb

Consider our ammonia equilibrium:

:NH3(aq) + H2O NH4+(aq) + OH(aq)

This expression now corresponds to the following equilibrium multiplied times Kw:

:NH3(aq) + H+(aq) NH4+(aq)

Acids & Bases 47

The reverse of this reaction, however, is the "acid" equilibrium:

NH4+(aq) :NH3(aq) + H+(aq)

Writing the reaction this way means that we can now set-up a Ka equilibrium expression:

Acids & Bases 48

Knowing the mathematical relationship between Ka and Kb is very important. Many references only list Ka values for bases and not the Kb values that you would expect.

One reason that references often list Ka values for bases is that they can then put acids and bases on the same scale and table.

If a reference gives a Ka value for the base you are looking up, you'll have to convert it to a Kb value in order to calculate the [OH], and then the pH.

You must, therefore, pay close attention to what data the problem is giving you and what you need to use. READ CAREFULLY!!

DANGER!!

VERY Common mistake!!

Acids & Bases 49

Problem: What is the pH of a 0.1 M solution of the weak base triethyl amine (NEt3)? Ka = 1 1011

Acids & Bases 50

Salts of Weak Acids and BasesWhen a weak acid (e.g., acetic acid) reacts with a strong base (e.g., an alkali hydroxide like NaOH) water and the salt of the weak acid is formed:

Note that the acetate anion formed in the reaction is itself a weak base. Thus it can react with water to produce a small amount of [OH].

Therefore, dissolving sodium acetate (the salt of acetic acid) in water will make a basic solution.

Acids & Bases 51

Similarly, the reaction of a weak base with a strong acid will produce the salt of a weak base, which will act as a weak acid. Shown below we have the reaction of ammonia with HCl to produce ammonium chloride (the salt of a weak base):

Dissolving ammonium chloride in water, therefore, produces an acidic solution (NH4+ is a weak acid).

Acids & Bases 52

The big question is “How the heck do I tell whether a salt will produce an acidic, basic, or neutral solution??”

The KEY is to remember the strong acids and bases:

Strong Acids:HCl(aq) H(aq) + Cl(aq)

HBr(aq) H(aq) + Br(aq)

HI(aq) H(aq) + I(aq)

HNO3(aq) H(aq) + NO3(aq)

H2SO4(aq) 2H(aq) + SO4(aq) *

HClO4(aq) H(aq) + ClO4(aq)

Strong Bases:LiOH(aq) Li(aq) + OH(aq)

NaOH(aq) Na(aq) + OH(aq)

KOH(aq) K(aq) + OH(aq)

RbOH(aq) Rb(aq) + OH(aq)

CsOH(aq) Cs(aq) + OH(aq)

These are extremely weak conjugate bases -- Neutral Anions!

These are extremely weak conjugate acids -- Neutral Cations!

Acids & Bases 53

Putting these Neutral (neutral here refers to their acid-base properties, NOT their charges!!) anions and cations together generates Neutral (not acidic or basic) salts (Ca, Sr, Ba salts not shown):

NeutralCation

NeutralAnion Neutral Salts

Li Cl LiCl, LiBr, LiI, LiNO3, Li2SO4,

Na Br NaCl, NaBr, NaI, NaNO3, Na2SO4,

K I KCl, KBr, KI, KNO3, K2SO4,

Rb NO3 RbCl, RbBr, RbI, RbNO3, Rb2SO4,

Cs SO4 CsCl, CsBr, CsI, CsNO3, Cs2SO4,

ClO4 Perchlorate salts are explosive !!!

Solutions of these Neutral Salts are neither acidic nor basic, but rather have a pH = 7 (Neutral!).

A simple set of guidelines, therefore, are:

CATIONS other than Li, Na, K, Rb, Cs (& Ca2, Sr2, Ba2)-negligible- will generate ACIDIC solutions (that is, the cation is a good conjugate acid). Example, Fe3+ is a good Lewis acid!

ANIONS other than Cl, Br, I, NO3, SO4

-negligible- will generate a BASIC solution (that is, the anion is a good conjugate base). Example , F-

Acids & Bases 54

Acids & Bases 55

Problem: Will the following salts make an acidic, basic or neutral solution when dissolved in water?

a) NaF Ka (HF) = 3.5 10-4

b) NaCl Ka (HCl) = 1 108

c) Ka (pyridineH+) = 5 10-6

d) C6H5COONa Ka (C6H5COOH) = 6.5 10-5

e) RbBr Ka (HBr) = 1 1010

f) CH3COOCs Ka (CH3COOH) = 1.7 10-5

g) Cs2S Ka (H2S) = 9.1 10-8

h) NH4NO3 Ka (NH4+) = 5.6 10-10

Acids & Bases 56

i) KCN Ka (HCN) = 4.9 10-10

j) KNO3

Acids & Bases 57

Example: What is the pH of 1 M NaF? Ka (HF) = 1 x 104.

Initial: 1 M 0 0

F(aq) + H2O HF(aq) + OH(aq)

@ Eq: 1 - x x x

This is a basic equilibrium, so we need to convert Ka into Kb:

Our equilibrium expression, therefore, is:

NeutralCation

BasicAnion

DANGER!!VERY

Common mistake!!

Acids & Bases 58

take the square-root of each side:

x = [OH] = [HF] = 1 105 M

So the [OH] = 1 105 M. The pOH is:

pOH = -log(1 105) = 5

The pH, then, is given by:

pH = 14 - pOH = 14 - 5 = 9

DANGER!!VERY

Common mistake!!

Acids & Bases 59

Example: What is the pH of a 0.1 M solution of NH4Cl. Ka (NH4

+) = 1 x 109.

Acids & Bases 60

Polyprotic AcidsSulfuric Acid:

H2SO4(aq) H+(aq) + HSO4(aq) Ka1 108

HSO4(aq) H+(aq) + SO4

2(aq) Ka2 10-2

Phosphoric Acid:

H3PO4(aq) H+(aq) + H2PO4(aq) Ka1 10-3

H2PO4(aq) H+(aq) + HPO4

2(aq) Ka2 10-8

HPO42(aq) H+(aq) + PO4

3(aq) Ka3 10-13

Carbonic Acid:

H2CO3(aq) H+(aq) + HCO3(aq) Ka1 10-7

HCO3(aq) H+(aq) + CO3

2(aq)Ka2 10-11

Note that for polyprotic acids only the first dissociation (the first H+) is likely to occur. The second (or third) dissociation process is far less likely, so the contribution of these subsequent dissociations to the overall [H+]total .

Acids & Bases 61

So, generally we only have to worry about the first proton and the first dissociation constant!!

Acids & Bases 62

Reactions of Acids & Bases

Strong Acids and Strong Bases:

The reaction of a strong acid and strong base is the simplest type of acid-base reaction.

Consider the rxn of NaOH and HCl:

Na+(aq) + OH(aq) + H+(aq) + Cl(aq) H2O + Na+(aq) + Cl(aq)

The rxn above shows all the aqueous species. Note that NaCl(aq) is one of the products. When acids react with bases, water and the salt of the acid/base are formed (the base provides the cation and acid the anion).

The net ionic equation version of the above reaction is shown below:

OH(aq) + H+(aq) H2O

A key point to remember is that when we react acids and bases we are usually reacting solutions of acids and bases. When one mixes two solutions together the overall volume increases and the concentrations of all species will decrease! DANGER!!

VERY Common mistake!!

Acids & Bases 63

Because of the change in volume due to the mixing together of two solutions one has to take this into account.

We do this by dealing directly with MOLES and not Molarity. So you have to:

convert molarity into moles, do your calculations, then convert back to molarity using the

NEW total (combined) solution volume

EXAMPLE: What is the pH if we mix 100 mL of 0.1 M HCl with 50 mL of 0.1 M NaOH?

First, convert concentrations into moles:

(100 mL)(0.1 M) = 10 mmol HCl (50 mL)(0.1 M) = 5 mmol NaOH

Now for the reaction: 5 mmol NaOH will react with only 5 mmol HCl, leaving behind 5 mmol HCl. But now we have 150 mL of solution, so [H+] is: DANGER!! VERY Common mistake!!

Acids & Bases 64

PROBLEM: What will be the pH when 100 mL of 0.1 M HNO3 is mixed with 300 mL of 0.2 M KOH?

Acids & Bases 65

PROBLEM: What will be the pH when 100 mL of 0.1 M HNO3 is mixed with 200 mL of 0.05 M KOH?

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Strong Acids and Weak Bases:

Strong Bases and Weak Acids:

Things get more complicated (well, not too bad) when you react a strong acid with a weak base or a strong base with a weak acid.

For this case, however, we will simplify things a little by only using equivalent amounts of the acid and base.

The key thing to remember when you react a weak acid or base with a strong base or acid is that one ends up with the SALT of that weak acid or base. Remember that the SALT of a weak acid is actually a weak base and gives a basic solution. Similarly, the SALT of a weak base generates an acidic solution.

DANGER!!VERY Common mistake!!

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EXAMPLE: What is the pH if 150 mL of 0.5 M acetic acid is mixed with 150 mL of 0.5 M NaOH? Ka (HOAc) 1 105.

HOAc(aq) + OH(aq) H2O + OAc(aq)

The OAc produced is a weak base and will produce a weakly basic solution:

H2O + OAc(aq) HOAc(aq) + OH(aq)

Since this is a base equilibrium, we need to use Kb:

Calculate the concentration of OAc :(150 mL)(0.5 M) = 75 mmol HOAc (150 mL)(0.5 M) = 75 mmol OH

Not realizing this - DANGER!! VERY Common mistake!!

Not realizing this - DANGER!! VERY Common mistake!!

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Thus, we will produce 75 mmol of OAc. The concentration of OAc, therefore, will be:

Now we can set-up our initial and equilibrium conditions:

Initial: 0.25 M 0 0

H2O + OAc(aq) HOAc(aq) + OH(aq)

@ Eq: 0.25 - x x x

pOH = 4.6 } so the pH = 14 - 4.6 = 9.4

Volume Change - DANGER!!

VERY Common mistake!!

Forgetting to convert pOH to pH - DANGER!! VERY Common

mistake!!

Approximation!

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PROBLEM: What is the pH of the reaction of 500 mL of 2 M NH3 and 500 mL of 2 M HCl? Ka (NH4+) 1 1010.

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Titrations

A titration is the careful measured addition of a known concentration of one substance that will react with another unknown material in order to determine the concentration of the unknown material. Determining the concentrations of unknown materials is a routine procedure in chemistry. Titrations are commonly used to determine the concentrations of acids and bases in solution, as well as many other chemicals. Titrations are also often the simplest and least expensive way of determining concentrations of unknown materials.

If we are titrating an unknown acid with a known amount of base with a known concentration, we can use the (M1)(V1) = (M2)(V2) relationship to find the unknown's concentration at the equivalence point (the point at which we've added just enough base to react with all the acid).

In order to determine when we have reached the equivalence point in an acid base reaction, we generally use an indicator.

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Indicators

An indicator is a weak organic acid or base that has sharply different colors in its associated and dissociated forms:

HIn(aq) H+(aq) + In(aq)

red acidic blue basicIndicators usually have very intense colors so one only has to use a very small amount (a few drops) so it will not affect the titration of the solution. Remember that the indicator is an acid or base so if you add a lot it will affect the titration!!

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Some Common Acid-Base Indicators

NamepH color change

region Acid color Base Color

Methyl violet 0 - 2 yellow violet

methyl yellow 1.2 - 2.3 red yellow

methyl orange 2.9 - 4.0 red yellow

methyl red 4.2 - 6.3 red yellow

bromthymol blue 6.0 - 7.6 yellow blue

thymol blue 8.0 - 9.6 yellow blue

phenolphthalein 8.3 - 10 colorless pink

Alizarin yellow 10.1 - 12 yellow red

HIn(aq) H+(aq) + In(aq)

At the color change [H+] = [In] = [HIn], so:

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Titrating an unknown strong acid with a known amount of strong base:

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Titrating an unknown strong base with a known amount of strong acid:

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Titrating an unknown weak base with a known amount of strong acid:

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Titrating an unknown weak acid with a known amount of strong base:

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Buffer Solutions

Consider an acetic acid solution:

HOAc(aq) H+(aq) + OAc(aq)If we add enough NaOAc (the salt of acetic acid) to increase the OAc concentration roughly equal to HOAc, we now form the following mixture:

HOAc(aq) H+(aq) + OAc(aq)

The added OAc, which is a weak base, will consume some of the free H+ causing the pH to rise (become less acidic).

Note that if we add H+ to this solution, it will react with the large pool of weak base OAc to form HOAc. The H+ concentration, therefore, will stay about the same.

Similarly, if we add some OH it will react with the H+ present. Since we have an equilibrium, however, some HOAc will, in turn, dissociate to replace the missing H+, keeping it about the same.

A solution of a weak acid and the salt (conjugate base) of a weak acid – or – a weak base and the salt

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(conjugate acid) of a weak base is called a BUFFER!

If the concentration of the two components is high enough and you don’t add too much acid or base, the buffer solution will be very resistant to changes in the pH due to added acid or base.

Buffer solutions are critically important to biological systems (i.e., keeping us alive!).

For a solution of a weak acid or base and their salt, one can write the following equations for calculating the [H+] and [OH] of the buffer solution generated:

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If the acid/base concentration is the same as the salt concentration, then we can write:

[OH] = Kb [H+] = Ka

–– or ––

pOH = pKb pH = pKa

By varying the weak acid or base and the salt being used to make the buffer solution, as well as their concentration ratio, one can set the pH of the buffer to almost anything you want.

The more concentrated the buffer components, the more effective the buffer solution will be at resisting pH changes. But remember that you can always overload a buffer by adding too much acid or base to it.

One of the trickiest things for you to determine is just what salts will work to make a buffer. The salts of strong acids and bases (i.e., NaCl, KBr, Na2SO4, CsNO3) do NOT make buffers, nor do mixtures of strong acids and bases with their salts!

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Note, however, that reacting ½ equivalent of a strong base with a weak acid, generates a buffer solution!

This is the region where we have a buffer solution present

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Problems: Which of the following solutions is a buffer? Which will be the most effective buffer solution?

a) 0.1 M NaOH + 0.1 M NaOAc

b) 0.01 M HCl + 0.01 M NaCl

c) 0.5 M NH4Cl + 0.5 M NH3

d) 2 M NaOAc + 2 M HOAc

e) 0.01 M citric acid + 0.01 M sodium citrate

f) 0.3 M H3PO4 + 0.3 M NaH2PO4

g) 2 M HNO3 + 2 M NaNO3

h) 0.05 M H2CO3 + 0.05 M KHCO3

i) 0.5 M HI + 0.5 M CsI

j) 0.2 M benzoic acid + 0.2 M cesium benzoate

k) 1 M NaOAc + 1 M KBr

l) 0.001 M HCl + 0.001 M KOH

m) 0.1 M KOAc + 0.1 M NH3

n) 0.2 M HOAc + 0.2 M KHCO3