Ch. 16—Acid-Base Equilibria• Acid & Base Properties: A Brief Review

- Acids taste sour and are corrosive to metals.

- Bases taste bitter and feel slippery.

- Bases neutralize acids to form salt + water.

• There are several ways we define acids and bases…

(1)Arrhenius Definition

acids: Increase the [H+] in a solution

- Example: HCl(aq) H+(aq) + Cl−

(aq)

bases: Increase the [OH−] in a solution

- Example: NaOH(aq) Na+(aq) + OH−

(aq)

(This definition is very narrow in scope.)

Defining Acids & Bases(2) Brønsted-Lowry: (a broader definition)

acid: donates H+ (Remember…H+ is really just a proton!)

base: accepts H+ (With this definition, bases do not need to contain OH−.)

Examples: 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.

NH3 (aq) + H2O(l) NH4+

(aq) + OH−(aq)

- H2O donates a proton to NH3. Therefore, H2O is an acid.- NH3 accepts a proton from H2O. Therefore, NH3 is a

base.

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

• Amphoteric substances can behave as acids and/or bases…(HCO3−)

Conjugate Acids & Conjugate Bases

Examples: HCl(aq) + H2O(l) H3O+(aq) + Cl−

(aq)

acid base conjugate acid conjugate base

NH3 (aq) + H2O(l) NH4+

(aq) + OH−(aq)

base acid conjugate acid conjugate base

• H+ and H3O+ are pretty much the same thing…(H2O + H+ H3O+)• H3O+ is called the hydronium ion.

• 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.

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

Relative Strengths of Acids & Bases• The stronger the acid, the weaker

the conjugate base.

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

• OH− is the strongest base that can exist in equilibrium in aqueous solutions.

• In every acid-base reaction, the position of the equilibrium favors the transfer of a proton from the stronger acid to the stronger base.

• Notice CH4…it cannot donate H+ so it is not an acid.

Self-Ionization of Water• In pure water the following equilibrium is established

H2O(l) + H2O(l) H3O+(aq) + OH−

(aq)

• At 25 C Keq or Kw= [H3O+][OH−] = 1 x 10−14

The above is called the autoionization (or self-ionization) of water.

The pH Scale• In most solutions [H+] is quite small, so we express it in a

logarithmic scale…pH = −(log [H+]) [H+] = 10−pH

pOH = −(log [OH−]) [OH−] = 10−pOH

pH + pOH = 14

• In neutral water at 25 C, pH = pOH = 7.00• In acidic solutions, [H+] > 1.0 10-7, so pH is below 7.00• In basic solutions, [H+] < 1.0 10-7, so pH is above 7.00• The higher the pH, the lower the pOH, the more basic the solution.

The pH Scale

Measuring pH• The most accurate method to measure pH is to use a pH meter.

However, certain dyes change color as pH changes. They are called acid-base indicators.

• Indicators are weak acids that change color when they become basic… HIn H+ + In−

(clear) (red)

• Since it is an equilibrium the color change is gradual and the equilibrium is controlled by pH.

• The color change is noticeable when the ratio of [In−]/[HIn] or [HIn]/[In−] is 1/10.

• Since the Indicator is a weak acid, it has a Ka.

• Some natural products can be used as indicators.

- Examples: tea, red cabbage juice extract

Color Changes and pH of Indicators

Litmus paper: Red= Acid; Blue=Base (changes pH ≈7.0)

Red Cabbage Juice: R.O.Y. = acid; G= neutral; B.I.V. = base

Relative Strengths of Acids• Strong acids completely transfer their protons to water thus

leaving no undissociated molecules and no equilibrium.

• Therefore, the [H+] of the solution is the initial molarity of the acid.

Common Strong Acids: HCl, HBr, HI, HNO3, H2SO4, HClO3, HClO4

Practice Problem: What is the pH of a solution of 0.001 M HNO3?

HNO3 (aq) H+(aq) + NO3

−(aq)

So… [HNO3] = [H+] = 0.001 M, therefore pH = − (log [0.001]) = 3.0

• Weak acids only partially dissociate and exist as a mixture of acid molecules and their constituent ions in equilibrium.

Common Weak Acids: HF, H2CO3, HC2H3O2, H3PO4

HF(aq) H+ (aq) + F−(aq)

Relative Strengths of AcidsCarboxylic Acids

• Carboxylic acids are organic acids. They all contain a carboxyl group, COOH.

• All carboxylic acids are weak acids.• When the carboxylic acid loses a proton, it generates the

carboxylate anion, COO−.

RC

OH

O

−+ H+

Examples:

Relative Strengths of Bases• Strong bases are those hydroxides of Group 1 & the hydroxides of

the heavier metals in Group 2. They can be thought of as completely dissociating into ions in aqueous solutions.

Common Strong Bases: NaOH, KOH, Ca(OH)2 , Ba(OH)2

Note: Any hydroxide has to be soluble in order for it to form a basic solution!

• Ionic metal oxides, hydrides, and nitrides are also basic. The oxide, hydride and nitride ions are stronger bases than hydroxide. They are thus able to abstract a proton from water and generate OH–…Examples: Na2O, NaH, Na3N.

Ionization… O–2(aq) + H2O(l) 2OH–

(aq)

H–(aq) + H2O(l) H2(g) + OH–

(aq)

N–3(aq) + 3H2O(l) NH3 (aq) + 3OH−

(aq)

• The pOH of a strong base in solution is determined by the initial molarity of the base. (Be careful of stoichiometry!)

Relative Strengths of Bases• Practice Problem: What is the pH of a 0.001 M Ca(OH)2 solution?

Ca(OH)2(aq) Ca+2(aq) + 2 OH−

(aq)

So… [OH−] = 2 x [Ca(OH)2] = 0.002 M

Therefore… pOH = − (log [0.002]) = 2.70 so…pH = 11.3

• Weak bases only partially dissociate and are in equilibrium. • Most neutral weak bases contain nitrogen. (Example: NH3)• Amines are related to ammonia and have one or more N-H bonds replaced with N-C bonds…(Example: H3C−NH2 is methylamine.)

Other weak bases: Al(OH)3 , anions of weak acids…(C2H3O2−)

Al(OH)3(aq) Al+3(aq) + 3OH−

(aq)

C2H3O2−

(aq) + H2O(l) HC2H3O2(aq) + OH−(aq)

• Because weak acids and weak bases are in equilibrium with their ions, we need to know the Keq in order to determine the amount of [H+] or [OH−] in the solution. (From there we can calculate pH.)

Weak Acids—Finding pH• Lets look at an example…

HCN(aq) H+(aq) + CN−

(aq)

Keq or Ka = [H+][CN−]/[HCN] = 4.9 x 10−10 (from p.628)

Ka is called the acid-dissociation constant.

Practice Problem: What is the pH of a 0.3 M HCN solution?

Set it up just like any other equilibrium problem…“ICEbox!”

[HCN] [H+] [CN−]

Initial

Change

Equilibrium

0.3 M

− x

0 0

+ x + x

0.3 − x + x + x

Weak Acids—Finding pH

Ka = [H+][CN−]/[HCN] = 4.9 x 10−10 so… Ka = [x][x]/[0.3−x ] = 4.9 x 10−10

• Since the value of “x” is going to be very small compared to 0.3, we can assume that 0.3 – x ≈ 0.3 (If “x” is more than 5% of the initial value, we would have to use the quadratic equation to solve for “x”, and that would be yucky!)

Ka = x2/0.3 = 4.9x 10−10

Solving for “x” leads us to an answer of …x = 1.21 x 10−5 M.

This is the [H+], so… pH = −(log [1.21 x 10−5 ]) = 4.917

(Notice that our assumption was valid… 0.3 – 1.21 x 10−5 = 0.3 with one sig. fig.)

• The same sort of thing could be done using the Kb values of weak bases.

[HCN] [H+] [CN−]

Initial

Change

Equilibrium

0.3 M

− x

0 0

+ x + x

0.3 − x + x + x

Percent Ionization• Percent ionization is another method to assess acid strength.

• The higher percent ionization, the stronger the acid.

• Percent ionization of a weak acid decreases as the molarity of the solution increases.

% Ionization of [HA]= ([H+]eq/[HA]initial) x 100

Practice Problem: What was the % ionization of HCN from the previous problem?

% Ionization of [HCN] = (1.21 x 10−5 M)/(0.3 M) x 100 = 0.00403 %

Other Acid Facts•Ka x Kb = Kw = 1.0 x 10−14 (…at 25° C)

• As Ka increases, acid strength increases. (As Kb increases, base strength increases.)

•If Ka>> 1, then the acid is completely ionized and the acid is classified as a strong acid. (% Ionization ≈100%)

•The value for Ka for weak acids are usually in the range of 10-3 to 10-10.

•Monoprotic acids have 1 ionizable H atom…(HCl).

•Some acids have 2 ionizable H atoms. They are called diprotic…(H2SO4)

• Some acids have 3 ionizable H atoms. They are called triprotic…(H3C6H5O7 = citric acid)

Other Acid Facts•- The Ka value for the 2nd or 3rd H atom is less and less…

•The overall Ka for H2SO3 is… (Ka1 ) x ( Ka2 ) = Ka =1.09 x10-9

•As long as successive Ka values differ by more than 103 or more, you can simply use Ka1 to estimate the pH.

•Since pH gives the equilibrium concentration of [H+], we can use the “ICEbox” method to calculate Ka. (See Practice Problems.)

•Nonmetal oxides in water are acidic:

-Examples: SO2(g) + H2O(l) H2SO3(aq) H+(aq) + HSO3

-(aq)

P2O5(s) + 3H2O(l) 2H3PO4(aq) 2H+(aq) + 2H2PO4

-3(aq)

H2SO3(aq) H+(aq) + HSO3-(aq) Ka1 = 1.7 x 10-2

HSO3-(aq) H+(aq) + SO3

2-(aq) Ka2 = 6.4 x 10-8

Acid-Base Properties of Salt Solutions• Nearly all salts are strong electrolytes. Therefore, salts in solution exist entirely of ions.

• Acid-base properties of salts are a consequence of the reactions of their ions in solution.

• Many salt ions can react with water to form OH– or H+. This process is called hydrolysis…

Example: C2H3O2−

(aq) + H2O(l) HC2H3O2(aq) + OH−(aq)

• Anions from weak acids are basic…(see above example)

• Anions from strong acids are neutral…(Cl−(aq) will not gain H+.)

• Anions with ionizable protons are amphoteric… [HPO4–2] or [HCO3

–]

• All cations, except those of the alkali metals or heavier alkaline earth metals, are weak acids…Cu+

(aq) + H2O(l) CuOH(aq) + H+(aq)

Acid-Base Properties of Salt Solutions• The pH of a solution may be qualitatively predicted using the following guidelines:

- Salts derived from a strong acid and strong base are neutral.

Examples: NaCl [ NaOH + HCl NaCl + H2O ]

Ca(NO3)2 [ Ca(OH)2 + HNO3 Ca(NO3)2 + 2H2O ]

- Salts derived from a strong base and weak acid are basic.

Examples: NaClO Ba(C2H3O2)2

strong base ion/weak acid ion strong base ion/weak acid ion

-Salts derived from a weak base and strong acid are acidic.

Example: NH4Cl Mg(NO3)2

weak base ion/strong acid ion weak base ion/strong acid ion

What is happening in the solutions that make these salts acidic or basic?

Acid-Base Properties of Salt Solutions• Let’s look at Ba(C2H3O2)2 as an example… (strong base ion/weak acid ion)

Ba(C2H3O2)2 dissolves into ions…Ba+2(aq) + 2(C2H3O2)−

(aq)

• These ions will attempt to react with H2O…hydrolysis!

Ba+2(aq) + 2 H2O(l) Ba(OH)2(aq) + 2 H+

(aq)

• Since Ba(OH)2 is a strong base, the “equilibrium” lies almost entirely to the left, so hydrolysis will not happen. No H+ will form.

C2H3O2−

(aq) + H2O(l) HC2H3O2(aq) + OH−(aq)

• Since HC2H3O2(aq) is a weak acid, there will be an equilibrium established, and therefore some [OH−] will be present in the solution making the solution slightly basic!

Acid-Base Properties of Salt Solutions• What about a salt that has a “weak acid ion/weak base ion” combination? (Examples: NH4F , NiCO3 )

• The ion with the largest ionization constant will have the greatest influence on the pH.

Practice Problem: Will a solution of NH4F be acidic or basic?

NH4+

(aq) + H2O(l) NH3(aq) + H3O+(aq) Ka = 5.6 x 10−10

F−(aq) + H2O(l) HF(aq) + OH−

(aq) Kb = 1.5 x 10−11

Since Ka > Kb, the solution will be slightly acidic!

• There are some salts that contain ionizable protons such as NaHCO3 or NaH2PO4. The pH of these salts is affected not only by the hydrolysis of the anion but also by it’s Ka. (See Textbook example 16.17 for further details.)

Factors that Affect Acid Strength• Consider the acid with the formula, H-X. For this substance to be

an acid we need the following:

(1) H-X bond must be polar with H+ and X-…(If X is a metal then the bond polarity is H- , X+ and the substance is a base…Example: HNa, (or as we usually write it, NaH), is basic.

(2) the H-X bond must be weak enough to be broken

(3) the conjugate base, X−, must be stable. (The more stable the anion, the more acidic it will be.)

Strength of Binary Acids• Acid strength increases across a period and down a group.

Conversely, base strength decreases across a period and down a group.

• HF is a weak acid because the bond is highly polar so the bond energy is high. Therefore, H-F doesn’t dissociate as much as HCl.

• The electronegativity difference between C and H is so small that the C-H bond is non-polar so CH4 is neither an acid nor a base.

Strength of Oxyacids• Oxyacids contain O-H bonds.

• All oxyacids have the general structure Y-O-H.

• The strength of the acid depends on Y and the atoms attached to Y.

– If Y is a metal (low electronegativity), then the substances are bases…Example: Na-O-H

– If Y has intermediate electronegativity, (EN), the electrons are between Y and O and the substance is a weak oxyacid.

– If Y has a large EN, the electrons are located closer to Y than O and the O-H bond is polarized to lose H+ more readily and is stronger.

Strength of Oxyacids• As the number of O atoms attached to Y increases, the O–H bond

polarity increases.

• Consequently, the electrons in the O-H bond are pulled away from the H, and this makes it easier to ionize!

• The strength of the acid will therefore increase.

H – O – Cl vs. H – O – Cl – O vs. H – O – Cl – O vs. H – O – Cl – O

O O

O

Increasing Acidity

Strength of Carboxylic Acids• Why can CH3COO–H ionize, but CH3CH2O–H cannot?

1. The additional oxygen atom on the carboxyl group increases the polarity of the O–H bond and stabilizes the conjugate

base.

2. The conjugate base of CH3COO− exhibits resonance further increasing the stability of the conjugate base.

• The carboxylic acid strength also increases as the number of electronegative groups in the acid increases.

Example: Acetic acid is much weaker than trichloroacetic acid.

CH3COOH vs. CCl3COOH

weaker stronger

−

−

Lewis Acids and Bases• There is one last way to define acids and bases…

(3) Lewis Definition:

- acids: electron pair acceptor

- bases: electron pair donor(Notice that it is the exact opposite of Brønsted-Lowry’s

definition…acids are proton donors; bases are proton acceptors.)

• Note: Lewis acids and Lewis bases do not need to contain protons, therefore, the Lewis definition is the most general definition of acids and bases we have.

• Lewis acids generally have an incomplete octet…(Example: BF3 )

• Lewis acids must have a vacant orbital (into which the electron pairs can be donated).

• Here’s an example of a Lewis acid and Lewis base…

H – N: + B – F H – N – B – F

• Compounds with multiple bonds can act as Lewis acids.

- For example, consider the reaction:

H2O(l) + CO2(g) H2CO3(aq)

• Water acts as the electron pair donor and carbon dioxide as the electron pair acceptor in this reaction.

Lewis Acids and Bases

H

H

H

H F

F

F

Fe- pair donor

(base)e- pair acceptor

(acid)

+

Hydrolysis of Metal Ions• Metal ions are (+) charged and attract water molecules (via the

lone pairs on oxygen).

• The higher the charge, the smaller the metal ion and the stronger the M-OH2 interaction. Both factors increase Ka, so…

Summary: (1) Smaller ions are more acidic.

(2) Higher charged ions are more acidic.

Practice Problems: (1) Ca2+ vs. Zn2+ Which is more acidic in water?

As you go across the periodic table, size generally decreases, so Zn+2 is smaller than Ca+2 which makes Zn+2 more acidic.

(2) Ca+2 vs. Al+3 Which is more acidic in water?

Al+3 is more acidic. Not only is its charge larger, but it is also a smaller cation.

Hydrolysis of Metal Ions

Weaker acid

Smaller Ka

Higher pH

Stronger acid

Larger Ka

Lower pH