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Chapter 17 Principles of Chemical Reactivity: The Chemistry of Acids and Bases. Acids & Bases: A Review. In Chapter 3, you were introduced to two definitions of acids and bases: the Arrhenius and the Brønsted–Lowry definition.

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acids bases a review
Acids & Bases: A Review
  • In Chapter 3, you were introduced to two definitions of acids and bases: the Arrhenius and the Brønsted–Lowry definition.
  • Arrhenius acid: Any substance that when dissolved in water increases the concentration of hydrogen ions, H+.
  • Arrhenius base: Any substance that increases the concentration of hydroxide ions, OH, when dissolved in water.
  • A Brønsted–Lowry acid is a proton (H+) donor.
  • A Brønsted–Lowry base is a proton acceptor.
strong weak acids bases
Strong & Weak Acids/Bases
  • Generally divide acids and bases into STRONG or WEAK ones.

STRONG ACID:

HNO3(aq) + H2O(liq)  H3O+(aq) + NO3-(aq)

HNO3 is about 100% dissociated in water.

strong weak acids bases1
Strong & Weak Acids/Bases

HNO3, HCl, H2SO4 and HClO4 are classified as strong acids.

strong weak acids bases2
Strong & Weak Acids/Bases

CaO

  • Strong Base: 100% dissociated in water.

NaOH(aq)  Na+(aq) + OH-(aq)

Other common strong bases include KOH and Ca(OH)2.

CaO (lime) + H2O 

Ca(OH)2 (slaked lime)

strong weak acids bases3
Strong & Weak Acids/Bases
  • Weak base: less than 100% ionized in water

An example of a weak base is ammonia

NH3(aq) + H2O(liq)  NH4+(aq) + OH-(aq)

strong weak acids bases4
Strong & Weak Acids/Bases

Weak acids are much less than 100% ionized in water.

Example: acetic acid = CH3CO2H

the br nsted lowry concept of acids bases extended
The Brønsted–Lowry Concept of Acids & Bases Extended
  • Proton donors may be molecular compounds, cations or anions.
the br nsted lowry concept of acids bases extended1
The Brønsted–Lowry Concept of Acids & Bases Extended
  • Proton acceptors may be molecular compounds, cations or anions.
the br nsted lowry concept of acids bases extended2
The Brønsted–Lowry Concept of Acids & Bases Extended

Using the Brønsted definition, NH3 is a BASE in water and water is itself an ACID

Proton acceptor

Proton donor

the br nsted lowry concept of acids bases extended3
The Brønsted–Lowry Concept of Acids & Bases Extended
  • Acids such as HF, HCl, HNO3, and CH3CO2H (acetic acid) are all capable of donating one proton and so are called monoprotic acids.
  • Other acids, called polyprotic acids are capable of donating two or more protons.
conjugate acid base pairs
Conjugate Acid–Base Pairs
  • A conjugate acid–base pair consists of two species that differ from each other by the presence of one hydrogen ion.
  • Every reaction between a Brønsted acid and a Brønsted base involves two conjugate acid–base pairs
water the ph scale
Water & the pH Scale

Water Autoionization and the Water Ionization Constant, Kw:

The water autoionization equilibrium lies far to the left side. In fact, in pure water at 25 °C, only about two out of a billion (109) water molecules are ionized at any instant.

Even in pure water, there is a small concentration of ions present at all times. [H3O+] = [OH] = 1.00  107

water the ph scale1
Water & the pH Scale

H2O can function as both an ACID and a BASE.

In pure water there can be AUTOIONIZATION.

Equilibrium constant for autoionization = Kw

Kw = [H3O+] [OH-] = 1.00 x 10-14at 25 °C

water the ph scale2
Water & the pH Scale
  • In a neutral solution, [H3O+] = [OH]
  • Both are equal to 1.00  10 7 M
  • In an acidic solution, [H3O+] > [OH]
  • [H3O+] > 1.00  10 7 M and [OH] < 1.00  10 7 M
  • In a basic solution, [H3O+] < [OH]
  • [H3O+] < 1.00  10 7 M and [OH] > 1.00  10 7 M
the ph scale1
The pH Scale
  • The pH of a solution is defined as the negative of the base (10) logarithm (log) of the hydronium ion concentration.

pH =  log[H3O+]

  • In a similar way, we can define the pOH of a solution as the negative of the base - 10 logarithm of the hydroxide ion concentration.

pOH =  log[OH]

pH + pOH = pKw = 14

the ph scale2
The pH Scale
  • The concentration of acid, [H3O+] is found by taking the antilog of the solutions pH.
  • In a similar way, [OH] can be found from:
the ph scale3
The pH Scale

Once [H3O+] is known, [OH] can be found from:

And vice versa.

equilibrium constants for acids bases
Equilibrium Constants for Acids & Bases
  • In Chapter 3, it was stated that acids and bases can be divided roughly into those that are strong electrolytes (such as HCl, HNO3, and NaOH) and those that are weak electrolytes (such as CH3CO2H and NH3)
  • In this chapter we will discuss the quantitative aspects of dissociation of weak acids and bases.
  • The relative strengths of weak acids and bases can be ranked based on the magnitude of individual equilibrium constants.
equilibrium constants for acids bases1
Equilibrium Constants for Acids & Bases
  • Strong acids and bases almost completely ionize in water (~100%):

Kstrong >> 1

(product favored)

  • Weak acids and bases almost completely ionize in water (<<100%):

Kweak << 1

(Reactant favored)

equilibrium constants for acids bases2
Equilibrium Constants for Acids & Bases
  • The relative strength of an acid or base can also be expressed quantitatively with an equilibrium constant, often called an ionization constant. For the general acid HA, we can write:

Conjugate

acid

Conjugate

base

equilibrium constants for acids bases3
Equilibrium Constants for Acids & Bases
  • The relative strength of an acid or base can also be expressed quantitatively with an equilibrium constant, often called an ionization constant. For the general base B, we can write:

Conjugate

base

Conjugate

Acid

ionization constants for acids bases
Ionization Constants for Acids/Bases

Increase strength

Increase strength

Conjugate

Bases

Acids

equilibrium constants for acids bases4
Equilibrium Constants for Acids & Bases
  • The strongest acids are at the upper left. They have the largest Ka values.
  • Ka values become smaller on descending the chart as the acid strength declines.
  • The strongest bases are at the lower right. They have the largest Kb values.
  • Kb values become larger on descending the chart as base strength increases.
equilibrium constants for acids bases5
Equilibrium Constants for Acids & Bases
  • The weaker the acid, the stronger its conjugate base: The smaller the value of Ka, the larger the value of Kb.
  • Aqueous acids that are stronger than H3O+ are completely ionized.
  • Their conjugate bases (such as NO3) do not produce meaningful concentrations of OH ions, their Kb values are “very small.”
  • Similar arguments follow for strong bases and their conjugate acids.
equilibrium constants for acids bases8
Equilibrium Constants for Acids & Bases

Ka Values for Polyprotic Acids

In general, each successive dissociation produces a weaker acid.

equilibrium constants for acids bases9
Equilibrium Constants for Acids & Bases

Logarithmic Scale of Relative Acid Strength, pKa

  • Many chemists use a logarithmic scale to report and compare relative acid strengths.

pKa =  log(Ka)

The lower the pKa, the stronger the acid.

equilibrium constants for acids bases10
Equilibrium Constants for Acids & Bases

Relating the Ionization Constants for an Acid and Its Conjugate Base

equilibrium constants for acids bases11
Equilibrium Constants for Acids & Bases

Relating the Ionization Constants for an Acid and Its Conjugate Base

equilibrium constants for acids bases12
Equilibrium Constants for Acids & Bases

Relating the Ionization Constants for an Acid and Its Conjugate Base

equilibrium constants for acids bases13
Equilibrium Constants for Acids & Bases

Relating the Ionization Constants for an Acid and Its Conjugate Base

equilibrium constants for acids bases14
Equilibrium Constants for Acids & Bases

Relating the Ionization Constants for an Acid and Its Conjugate Base

When adding equilibria, multiply the K values.

acid base properties of salts1
Acid–Base Properties of Salts

Anions that are conjugate bases of strong acids (for examples, Cl or NO3.

These species are such weak bases that they have no effect on solution pH.

acid base properties of salts2
Acid–Base Properties of Salts

Anions such as CO3 that are the conjugate bases of weak acids will raise the pH of a solution.

Hydroxide ions are produced via “Hydrolysis”.

acid base properties of salts3
Acid–Base Properties of Salts

Anions such as CO3 that are the conjugate bases of weak acids will raise the pH of a solution.

Hydroxide ions are produced via “Hydrolysis”.

A partially deprotonated anion (such as HCO3) is amphiprotic. Its behavior will depend on the other species in the reaction.

acid base properties of salts4
Acid–Base Properties of Salts

Alkali metal and alkaline earth cations have no measurable effect on solution pH.

Since these cations are conjugate acids of strong bases, hydrolysis does not occur.

acid base properties of salts5
Acid–Base Properties of Salts

Basic cations are conjugate bases of acidic cations such as [Al(H2O)6]3+.

Acidic cations fall into two categories: (a) metal cations with 2+ and 3+ charges and (b) ammonium ions (and their organic derivatives).

All metal cations are hydrated in water, forming ions such as [M(H2O)6]n+.

predicting the direction of acid base reactions
Predicting the Direction of Acid–Base Reactions
  • According to the Brønsted–Lowry theory, all acid–base reactions can be written as equilibria involving the acid and base and their conjugates.
  • All proton transfer reactions proceed from the stronger acid and base to the weaker acid and base.
predicting the direction of acid base reactions1
Predicting the Direction of Acid–Base Reactions
  • When a weak acid is in solution, the products are a stronger conjugate acid and base. Therefore equilibrium lies to the left.
  • All proton transfer reactions proceed from the stronger acid and base to the weaker acid and base.
slide47
Will the following acid/base reaction occur spontaneously?

Predicting the Direction of Acid–Base Reactions

slide48
Will the following acid/base reaction occur spontaneously?

Predicting the Direction of Acid–Base Reactions

Kb = 5.6  1010

Kb = 1.3  1012

Ka = 1.8  105

Ka = 7.5  105

slide49
Will the following acid/base reaction occur spontaneously?

Equilibrium lies to the right since all proton transfer reactions proceed from the stronger acid and base to the weaker acid and base.

Predicting the Direction of Acid–Base Reactions

Kb = 5.6  1010

Kb = 1.3  1012

Ka = 1.8  105

Ka = 7.5  105

Stronger Acid + Stronger Base

Weaker Base + Weaker Acid

types acids base reactions
Strong acid (HCl) + Strong base (NaOH)

Net ionic equation

Mixing equal molar quantities of a strong acid and strong base produces a neutral solution.

Types Acids–Base Reactions
types acids base reactions1
Weak acid (HCN) + Strong base (NaOH)

Mixing equal amounts (moles) of a strong base and a weak acid produces a salt whose anion is the conjugate base of the weak acid. The solution is basic, with the pH depending on Kb for the anion.

Types Acids–Base Reactions
types acids base reactions2
Strong acid (HCl) + Weak base (NH3)

Mixing equal amounts (moles) of a weak base and a strong acid produces a conjugate acid of the weak base. The solution is basic, with the pH depending on Ka for the acid.

Types Acids–Base Reactions
types acids base reactions3
Weak acid (CH3CO2H) + Weak base (NH3)

Mixing equal amounts (moles) of a weak acid and a weak base produces a salt whose cation is the conjugate acid of the weak base and whose anion is the conjugate base of the weak acid. The solution pH depends on the relative Ka and Kb values.

Types Acids–Base Reactions
types acids base reactions4
Types Acids–Base Reactions

Weak acid + Weak base

  • Product cation = conjugate acid of weak base.
  • Product anion = conjugate base of weak acid.
  • pH of solution depends on relative strengths of cation and anion.
slide56

Calculations with Equilibrium Constants

Determining K from Initial Concentrations and pH

slide57

Calculations with Equilibrium Constants

Determining K from Initial Concentrations and pH

slide58

Calculations with Equilibrium Constants

Determining K from Initial Concentrations and pH

slide59

Calculations with Equilibrium Constants

Determining K from Initial Concentrations and pH

[H3O+] = [NO2] = 6.76  103

slide60

Calculations with Equilibrium Constants

Determining K from Initial Concentrations and pH

calculations with equilibrium constants
Calculations with Equilibrium Constants

Determining K from Initial Concentrations and pH

calculations with equilibrium constants1
Calculations with Equilibrium Constants

Determining K from Initial Concentrations and pH

x = 3.2  104

pH = 3.50

calculations with equilibrium constants2
Calculations with Equilibrium Constants

Determining K from Initial Concentrations and pH

In general, the approximation that

[HA]equilibrium = [HA]initial x [HA]initial

is valid whenever [HA]initial is greater than or equal to 100 Ka.

If this is not the case, the quadratic equation must by used.

calculations with equilibrium constants3
Calculations with Equilibrium Constants

Determining pH after an acid/base reaction:

Calculate the hydronium ion concentration and pH of the solution that results when 22.0 mL of 0.15 M acetic acid, CH3CO2H, is mixed with 22.0 mL of 0.15 M NaOH.

calculations with equilibrium constants4
Calculations with Equilibrium Constants

Determining pH after an acid/base reaction:

Calculate the hydronium ion concentration and pH of the solution that results when 22.0 mL of 0.15 M acetic acid, CH3CO2H, is mixed with 22.0 mL of 0.15 M NaOH.

Solution: From the volume and concentration of each solution, the moles of acid and base can be calculated. Knowing the moles after the reaction and the equilibrium constants, the concentration of H3O+ and pH can be calculated.

slide66

Calculate the hydronium ion concentration and pH of the solution that results when 22.0 mL of 0.15 M acetic acid, CH3CO2H, is mixed with 22.0 mL of 0.15 M NaOH.

All of the acetic acid is converted to acetate ion.

slide67

Calculate the hydronium ion concentration and pH of the solution that results when 22.0 mL of 0.15 M acetic acid, CH3CO2H, is mixed with 22.0 mL of 0.15 M NaOH.

All of the acetic acid is converted to acetate ion.

slide68

Calculate the hydronium ion concentration and pH of the solution that results when 22.0 mL of 0.15 M acetic acid, CH3CO2H, is mixed with 22.0 mL of 0.15 M NaOH.

slide69

Calculate the hydronium ion concentration and pH of the solution that results when 22.0 mL of 0.15 M acetic acid, CH3CO2H, is mixed with 22.0 mL of 0.15 M NaOH.

slide70

Calculate the hydronium ion concentration and pH of the solution that results when 22.0 mL of 0.15 M acetic acid, CH3CO2H, is mixed with 22.0 mL of 0.15 M NaOH.

slide71

Calculate the hydronium ion concentration and pH of the solution that results when 22.0 mL of 0.15 M acetic acid, CH3CO2H, is mixed with 22.0 mL of 0.15 M NaOH.

Since Kb100 > [CH3CO2-]initial, the quadratic equation is not needed.

slide72

Calculate the hydronium ion concentration and pH of the solution that results when 22.0 mL of 0.15 M acetic acid, CH3CO2H, is mixed with 22.0 mL of 0.15 M NaOH.

polyprotic acuids bases
PolyproticAcuids & Bases
  • Because polyprotic acids are capable of donating more than one proton they present us with additional challenges when predicting the pH of their solutions.
  • For many inorganic polyprotic acids, the ionization constant for each successive loss of a proton is about 104 to 106 smaller than the previous step.
  • This implies that the pH of many inorganic polyprotic acids depends primarily on the hydronium ion generated in the first ionization step.
  • The hydronium ion produced in the second step can be neglected.
polyprotic acids bases
Polyprotic Acids & Bases

Sulfurous acid, H2SO3, is a weak acid capable of providing two H+ ions.

(a) What is the pH of a 0.45 M solution of H2SO3?

(b) What is the equilibrium concentration of the sulfite ion, SO32- in the 0.45 M solution of H2SO3?

polyprotic acids bases1
Polyprotic Acids & Bases

Sulfurous acid, H2SO3, is a weak acid capable of providing two H+ ions.

(a) What is the pH of a 0.45 M solution of H2SO3?

(b) What is the equilibrium concentration of the sulfite ion, SO32- in the 0.45 M solution of H2SO3?

polyprotic acids bases2
Polyprotic Acids & Bases

Sulfurous acid, H2SO3, is a weak acid capable of providing two H+ ions.

(a) What is the pH of a 0.45 M solution of H2SO3?

(b) What is the equilibrium concentration of the sulfite ion, SO32- in the 0.45 M solution of H2SO3?

Since 100  Ka is not << 0.45M, the quadratic equation must be used

polyprotic acids bases3
Polyprotic Acids & Bases

Sulfurous acid, H2SO3, is a weak acid capable of providing two H+ ions.

(a) What is the pH of a 0.45 M solution of H2SO3?

(b) What is the equilibrium concentration of the sulfite ion, SO32- in the 0.45 M solution of H2SO3?

(a)

x = [H3O+] = 0.0677 M

pH = 1.17

polyprotic acids bases4
Polyprotic Acids & Bases

Sulfurous acid, H2SO3, is a weak acid capable of providing two H+ ions.

(a) What is the pH of a 0.45 M solution of H2SO3?

(b) What is the equilibrium concentration of the sulfite ion, SO32- in the 0.45 M solution of H2SO3?

(a) in part a we found that x = [H3O+] = 0.0677 M

(b)

molecular structure bonding acid base behavior
Molecular Structure, Bonding, & Acid–Base Behavior

Halide Acid Strengths

  • Experiments show that the acid strength increases in the order: HF << HCl < HBr < HI.
  • Stronger acids result when the HX bond is readily broken (as signaled by a smaller, positive value of H for bond dissociation) and a more negative value for the electron attachment enthalpy of X.
molecular structure bonding acid base behavior1
Molecular Structure, Bonding, & Acid–Base Behavior

Comparing Oxoacids: HNO2 and HNO3

  • In all the series of related oxoacid compounds, the acid strength increases as the number of oxygen atoms bonded to the central element increases.
  • Thus, nitric acid (HNO3) is a stronger acid than nitrous acid (HNO2).
molecular structure bonding acid base behavior2
Molecular Structure, Bonding, & Acid–Base Behavior

Why Are Carboxylic Acids Brønsted Acids?

  • There is a large class of organic acids, all like acetic acid (CH3CO2H) have the carboxylic acid group, CO2H
  • They are collectively called carboxylic acids.
molecular structure bonding acid base behavior3
Molecular Structure, Bonding, & Acid–Base Behavior

Why Are Carboxylic Acids Brønsted Acids?

  • The carboxylate anion is stabilized by resonance.
molecular structure bonding acid base behavior4
Molecular Structure, Bonding, & Acid–Base Behavior

Why Are Carboxylic Acids Brønsted Acids?

  • The acidity of carboxylic acids is enhanced if electronegative substituents replace the hydrogen atoms in the alkyl (–CH3 or –C2H5) groups.
  • Compare, for example, the pKa values of a series of acetic acids in which hydrogen is replaced sequentially by the more electronegative element chlorine.
slide84
Trichloroacetic acid is a much stronger acid owing to the high electronegativity of Cl.
  • Cl withdraws electrons from the rest of the molecule.
  • This makes the O—H bond highly polar. The H of O—H is very positive.

Acetic acid

Trichloroacetic acid

Ka = 1.8 x 10-5

Ka = 0.3

the lewis concept of acids bases
The Lewis Concept of Acids & Bases
  • The concept of acid–base behavior advanced by Brønsted and Lowry in the 1920’s works well for reactions involving proton transfer.
  • However, a more general acid– base concept, was developed by Gilbert N. Lewis in the 1930’s.
  • A Lewis acid is a substance that can accept a pair of electrons from another atom to form a new bond.
  • A Lewis base is a substance that can donate a pair of electrons to another atom to form a new bond.
the lewis concept of acids bases1
The Lewis Concept of Acids & Bases
  • The product is often called an acid–base adduct. In Section 8.3, this type of chemical bond was called a coordinate covalent bond.
  • Lewis acid-base reactions are very common. In general, they involve Lewis acids that are cations or neutral molecules with an available, empty valence orbital and bases that are anions or neutral molecules with a lone electron pair.
the lewis concept of acids bases2
The Lewis Concept of Acids & Bases

Lewis acid

a substance that accepts an electron pair

Lewis base

a substance that donates an electron pair

reaction of a lewis acid lewis base
Reaction of a Lewis Acid & Lewis Base
  • New bond formed using electron pair from the Lewis base.
  • Coordinate covalent bond
  • Notice geometry change on reaction.
the lewis concept of acids bases3
The Lewis Concept of Acids & Bases

O

H

H

O

H

+

H

H

H

A

C

I

D

B

A

S

E

The formation of a hydronium ion is an example of a Lewis acid / base reaction

The H+ is an electron pair acceptor.

Water with it’s lone pairs is a Lewis acid donor.

lewis acids bases
Lewis Acids & Bases

Metal cations often act as Lewis acids because of open d-orbitals.

lewis acids bases1
Lewis Acids & Bases

The combination of metal ions (Lewis acids) with Lewis bases such as H2O and NH3 leads to Coordinate Complex ions.

lewis acids bases2
Lewis Acids & Bases

Aqueous solutions of Fe3+, Al3+, Cu2+, Pb2+, etc. are acidic through hydrolysis.

This interaction weakens this bond

Another H2O pulls this H away as H+

[Al(H2O)6]3+(aq) + H2O(l)  [Al(H2O)5(OH)]2+(aq) + H3O+(aq)

molecular lewis acids
Molecular Lewis Acids
  • Because oxygen is more electronegative than C, the CO bonding electrons in CO2 are polarized away from carbon and toward oxygen.
  • This causes the carbon atom to be slightly positive, and it is this atom that the negatively charged Lewis base OH can attack to give, ultimately, the bicarbonate ion.
molecular lewis acids1
Molecular Lewis Acids
  • Ammonia is the parent compound of an enormous number of compounds that behave as Lewis and Brønsted bases. These molecules all have an electronegative N atom with a partial negative charge surrounded by three bonds and a lone pair of electrons.
  • This partially negative N atom can extract a proton from water.
lewis acids bases3
Lewis Acids & Bases

Many complex ions containing water undergo HYDROLYSIS to give acidic solutions.

+

2+

+

lewis acid base interactions in biology
Lewis Acid–Base Interactions in Biology
  • The heme group in hemoglobin can interact with O2 and CO.
  • The Fe ion in hemoglobin is a Lewis acid
  • O2 and CO can act as Lewis bases

Heme group

slides from chang book
Slides from Chang Book

pH

[H+]

pH – A Measure of Acidity

pH = -log [H+]

Solution Is

At 250C

neutral

[H+] = [OH-]

[H+] = 1 x 10-7

pH = 7

[H+] > 1 x 10-7

pH < 7

acidic

[H+] > [OH-]

basic

[H+] < [OH-]

[H+] < 1 x 10-7

pH > 7

99

slide100

Ionized acid concentration at equilibrium

x 100%

x 100%

Percent ionization =

Initial concentration of acid

[H+]

[HA]0

percent ionization =

% Ionization =

For a monoprotic acid HA

[HA]0 = initial concentration

100

slide101

HNO3(aq) + H2O (l) H3O+(aq) + NO3-(aq)

Ba(OH)2(s) Ba2+(aq) + 2OH-(aq)

What is the pH of a 2 x 10-3 M HNO3 solution?

HNO3 is a strong acid – 100% dissociation.

0.0 M

0.0 M

Start

0.002 M

0.0 M

0.002 M

0.002 M

End

pH = -log [H+] = -log [H3O+] = -log(0.002) = 2.7

What is the pH of a 1.8 x 10-2 M Ba(OH)2 solution?

Ba(OH)2 is a strong base – 100% dissociation.

0.0 M

0.0 M

Start

0.018 M

0.0 M

0.018 M

0.036 M

End

pH = 14.00 – pOH = 14.00 + log(0.036) = 12.6

101

slide102

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

= 7.1 x 10-4

= 7.1 x 10-4

= 7.1 x 10-4

[H+][F-]

x2

x2

Ka

Ka =

Ka =

0.50 - x

0.50

[HF]

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

What is the pH of a 0.5M HFsolution (at 250C)?

Initial (M)

0.50

0.00

0.00

Change (M)

-x

+x

+x

Equilibrium (M)

0.50 - x

x

x

Ka << 1

0.50 – x 0.50

x2 = 3.55 x 10-4

x = 0.019 M

pH = -log [H+] = 1.72

[H+] = [F-] = 0.019 M

[HF] = 0.50 – x = 0.48 M

102

slide103

= 7.1 x 10-4

0.006 M

0.019 M

x2

x 100% = 12%

x 100% = 3.8%

0.50 M

0.05 M

Ka

0.05

When can I use the approximation?

Ka << 1

Ka*100 << [HA]0

0.50 – x 0.50

When x is less than 5% of the value from which it is subtracted.

Less than 5%

Approximation ok.

x = 0.019

What is the pH of a 0.05M HFsolution (at 250C)?

x = 0.006 M

More than 5%

Approximation not ok.

Must solve for x exactly using quadratic equation or method of successive approximations.

103

slide104

= 5.7 x 10-4

= 5.7 x 10-4

0.0083 M

x2

x2

x 100% = 6.8%

0.122 M

Ka

Ka =

0.122 - x

0.122

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

What is the pH of a 0.122Mmonoprotic acid whose

Ka is 5.7 x 10-4?

Initial (M)

0.122

0.00

0.00

Change (M)

-x

+x

+x

Equilibrium (M)

0.122 - x

x

x

Ka << 1

0.122 – x 0.122

x2 = 6.95 x 10-5

x = 0.0083 M

More than 5%

Approximation not ok.

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-b ± b2 – 4ac

= 5.7 x 10-4

x =

2a

x2

Ka =

0.122 - x

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

Initial (M)

0.122

0.00

0.00

Change (M)

-x

+x

+x

Equilibrium (M)

0.122 - x

x

x

x2 + 0.00057x – 6.95 x 10-5 = 0

ax2 + bx + c =0

x = 0.0081

x = - 0.0081

pH = -log[H+] = 2.09

[H+] = x = 0.0081 M

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H2O

NaCl (s)Na+ (aq) + Cl- (aq)

H2O

NaCH3COOH (s)Na+ (aq) + CH3COO- (aq)

CH3COO-(aq) + H2O (l) CH3COOH (aq) + OH-(aq)

Acid-Base Properties of Salts

Neutral Solutions:

Salts containing an alkali metal or alkaline earth metal ion (except Be2+) and the conjugate base of a strong acid (e.g. Cl-, Br-, and NO3-).

Basic Solutions:

Salts derived from a strong base and a weak acid.

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H2O

NH4Cl (s)NH4+ (aq) + Cl- (aq)

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

3+

2+

Al(H2O)6(aq) Al(OH)(H2O)5(aq) + H+(aq)

Acid-Base Properties of Salts

Acid Solutions:

Salts derived from a strong acid and a weak base.

Salts with small, highly charged metal cations (e.g. Al3+, Cr3+, and Be2+) and the conjugate base of a strong acid.

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Acid-Base Properties of Salts

Solutions in which both the cation and the anion hydrolyze:

  • Kb for the anion > Ka for the cation, solution will be basic
  • Kb for the anion < Ka for the cation, solution will be acidic
  • Kb for the anion Ka for the cation, solution will be neutral

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Solution

We begin by writing the equation for the hydrolysis equilibrium and the

equation for Ka in terms of Kw and Kb.

As usual, we can calculate [H3O+] from the pH of the solution.

log[H3O+] = –pH = –4.80

[H3O+] = 10–4.80 = 1.6 x 10–5 M

Strategy

Ammonium nitrate is the salt of a strong acid (HNO3) and a weak base (NH3). In NH4NO3(aq), NH4+ hydrolyzes and NO3– does not. The ICE format must be based on the hydrolysis equilibrium for NH4+(aq). In that format [H3O+], derived from the pH, will be a known quantity, and the initial concentration of NH4+ will be the unknown.

What is the molarity of an NH4NO3(aq) solution that has a pH = 4.80?

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Example 15.15 continued

Solution continued

If we assume that all the hydronium ion comes from the hydrolysis reaction, we can set up an ICE format in which x represents the unknown initial

concentration of NH4+.

We now substitute equilibrium concentrations into the ionization constant

expression for the hydrolysis reaction.

We can assume that the ammonium ion is mostly nonhydrolyzed and that the change in [NH4+] is much smaller than the initial [NH4+], so that 1.6 x 10–5 << x and we can replace (x – 1.6 x 10–5) by x. Then we can solve for x.

The solution is 0.46 M NH4NO3.

110