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Acid-Base Equilibria
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Acid-Base Equilibria Acids and Bases in Water
Autoionization of Water and the pH Scale Brønsted-Lowry Acid-Base: Proton Transfer Solving Problems Involving Weak-Acid Equilibria Weak Bases and Their Relation to Weak Acids Molecular Properties and Acid Strength Acid-Base Properties of Salt Solutions The Leveling Effect Lewis Acid-Base Definition: Electron pair donation
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Some Common Acids and Bases and their Household Uses.
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Arrhenius Acid-Base Definition
This is the earliest acid-base definition, which classifies these substances in terms of their behavior in water. An acid is a substance with H in its formula that dissociates to yield H3O+. A base is a substance with OH in its formula that dissociates to yield OH-. When an acid reacts with a base, they undergo neutralization: H+(aq) + OH-(aq) → H2O(l) DH°rxn = kJ
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Strong and Weak Acids A strong acid dissociates completely into ions in water: HA(g or l) + H2O(l) → H3O+(aq) + A-(aq) A dilute solution of a strong acid contains no HA molecules. A weak acid dissociates slightly to form ions in water: HA(aq) + H2O(l) H3O+(aq) + A-(aq) In a dilute solution of a weak acid, most HA molecules are undissociated. [H3O+][A-] [HA] Kc = has a very small value.
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Reaction of zinc with a strong acid (left) and a weak acid (right).
Zinc reacts rapidly with the strong acid, since [H3O+] is much higher. 1 M HCl(aq) 1 M CH3COOH(aq)
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The Acid Dissociation Constant, Ka
HA(aq) + H2O(l) H3O+(aq) + A-(aq) Kc= Ka = [H3O+][A-] [HA] The value of Ka is an indication of acid strength. Stronger acid larger Ka higher [H3O+] Weaker acid smaller Ka lower % dissociation of HA
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Ka Values for some Monoprotic Acids at 25°C
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Classifying the Relative Strengths of Acids
Strong acids include hydrohalic acids (HCl, HBr, and HI) and oxoacids (number of O atoms exceeds the number of ionizable protons by two or more (eg., HNO3, H2SO4, HClO4.) Weak acids include hydrohalic acid HF, acids in which H is not bonded to O or to a halogen (eg., HCN), oxoacids in which the number of O atoms equals or exceeds the number of ionizable protons by one (eg., HClO, HNO2), and carboxylic acids, which have the general formula RCOOH (eg., CH3COOH and C6H5COOH.)
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Classifying the Relative Strengths of Bases
Strong bases include water-soluble compounds containing O2- or OH- ions. The cations are usually those of the most active metals: M2O or MOH, where M = Group 1A(1) metal (Li, Na, K, Rb, Cs) MO or M(OH)2 where M = group 2A(2) metal (Ca, Sr, Ba). Weak bases include ammonia (NH3), amines, which have the general formula The common structural feature is an N atom with a lone electron pair.
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Autoionization of Water
Water dissociates very slightly into ions in an equilibrium process known as autoionization or self-ionization. 2H2O (l) H3O+ (aq) + OH- (aq)
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The Ion-Product Constant for Water (Kw)
2H2O (l) H3O+ (aq) + OH- (aq) [H3O+][OH-] [H2O]2 Kc = Kc[H2O]2 = Kw = [H3O+][OH-] = 1.0x10-14 (at 25°C) = 1.0x10-7 (at 25°C) In pure water, [H3O+] = [OH-] = Both ions are present in all aqueous systems.
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A change in [H3O+] causes an inverse change in [OH-], and vice versa.
Higher [H3O+] lower [OH-] Higher [OH-] lower [H3O+] We can define the terms “acidic” and “basic” in terms of the relative concentrations of H3O+ and OH- ions: In an acidic solution, [H3O+] > [OH-] In a neutral solution, [H3O+] = [OH-] In basic solution, [H3O+] < [OH-]
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Practice: Stomach acid: [HCl] = M, find [OH-] Liquid plumber™: [NaOH] = 2.5 M, find [H3O+]
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The relationship between [H3O+] and [OH-] and the relative acidity of solutions.
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The pH Scale pH = -log[H3O+]
The pH of a solution indicates its relative acidity: In an acidic solution, pH < 7.00 In a neutral solution, pH = 7.00 In basic solution, pH > 7.00 The higher the pH, the lower the [H3O+] and the less acidic the solution.
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The pH values of some familiar aqueous solutions.
pH = -log [H3O+]
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A low pKa corresponds to a high Ka.
The Relationship between Ka and pKa Acid Name (Formula) Ka at 25°C pKa Hydrogen sulfate ion (HSO4-) 1.0x10-2 1.99 Nitrous acid (HNO2) 7.1x10-4 3.15 Acetic acid (CH3COOH) 1.8x10-5 4.75 Hypobromous acid (HBrO) 2.3x10-9 8.64 Phenol (C6H5OH) 1.0x10-10 10.00 pKa = -logKa A low pKa corresponds to a high Ka.
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pH, pOH, and pKw Kw = [H3O+][OH-] = 1.0x10-14 at 25°C pH = -log[H3O+]
pOH = -log[OH-] pKw = pH + pOH = at 25°C pH + pOH = pKw for any aqueous solution at any temperature. Since Kw is a constant, the values of pH, pOH, [H3O+], and [OH-] are interrelated: If [H3O+] increases, [OH-] decreases (and vice versa). If pH increases, pOH decreases (and vice versa).
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Practice: In an art restoration project, a conservator prepares copper-plate etching solutions by diluting concentrated HNO3 to M HNO3. Calculate [H3O+], pH, [OH-], and pOH of the solution at 25°C. Calculating [H3O+], pH, [OH-], and pOH [H3O+] = M pOH = 11.80 pH = 2.20 [OH-] = =1.6x10-12 M
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Methods for measuring the pH of an aqueous solution.
pH paper pH meter
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Brønsted-Lowry Acid-Base Definition
Acid: a proton donor, any species that donates an H+ ion. An acid must contain H in its formula. Base: a proton acceptor, any species that accepts an H+ ion. A base must contain a lone pair of electrons to bond to H+. An acid-base reaction is a proton-transfer process.
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Dissolving of an acid or base in water as a Brønsted-Lowry acid-base reaction.
Lone pair binds H+ (acid, H+ donor) (base, H+ acceptor) Lone pair binds H+ (base, H+ acceptor) (acid, H+ donor)
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Conjugate Acid-Base Pairs
Forward reaction, _____ is acid, _____ is base: H2S + NH HS- + NH4+ Forward reaction: NH3 accepts a H+ to form NH4+. H2S donates a H+ to form HS-. Reverse reaction, NH4+ donates a H+ to form NH3 HS- accepts a H+ to form H2S. Reverse reaction, _____ is acid, _____ is base: HS- + NH4+ H2S + NH3
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Conjugate Acid-Base Pairs
H2S and HS- : HS- is the conjugate base of H2S. NH3 and NH4+ : NH4+ is the conjugate acid of NH3. An acid _____ protons to form conjugate _____ A base _____ proton to form conjugate ______. Brønsted-Lowry Acid-base Reaction: An acid and a base react to form their conjugate base and conjugate acid, respectively. acid1 + base base2 + acid2
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Conjugate Pairs in some Acid-Base Reactions
+ Conjugate Pair Conjugate Pair Reaction 4 H2PO4- OH- + Reaction 5 H2SO4 N2H5+ Reaction 6 HPO42- SO32- Reaction 1 HF H2O F- H3O+ Reaction 3 NH4+ CO32- Reaction 2 HCOOH CN- HCOO- HCN NH3 HCO3- HSO4- N2H62+ PO43- HSO3-
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Practice: Write the formula of BOTH conjugate acid and conjugate base for the following species: (a) H2PO4- (b) NH3 Identifying Conjugate Acid-Base Pairs
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Net Direction of Reaction
The net direction of an acid-base reaction depends on the relative strength of the acids and bases involved. A reaction will favor the formation of the weaker acid and base. H2S NH HS NH4+ stronger acid weaker acid stronger base weaker base This reaction favors the formation of the products.
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Strengths of conjugate acid-base pairs.
The stronger the acid is, the weaker its conjugate base. When an acid reacts with a base that is farther down the list, the reaction proceeds to the right (Kc > 1).
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Solving Problems Involving Weak-Acid Equilibria
Problem-solving approach Write a balanced equation. Write an expression for Ka. Define x as the change in concentration that occurs during the reaction. Construct a reaction table in terms of x. Make assumptions that simplify the calculation. Substitute values into the Ka expression and solve for x. Check that the assumptions are justified.
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Solving Problems Involving Weak-Acid Equilibria
The notation system Molar concentrations are indicated by [ ]. A bracketed formula with no subscript indicates an equilibrium concentration. The assumptions [H3O+] from the autoionization of H2O is negligible. A weak acid has a small Ka and its dissociation is negligible. [HA] ≈ [HA]init.
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Example: Propanoic acid (CH3CH2COOH, simplified as HPr). What is the [H3O+] of 0.10 M HPr (Ka = 1.3x10−5)? Determining Concentration from Ka and Initial [HA] Set up the ICE table [H3O+] = 1.1x10-3 M
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Practice: A study of the acid shows that the pH of 0.12 M Phenylacetic acid (C6H5CH2COOH, simplified here as HPAc) is What is the Ka of phenylacetic acid? Finding Ka of a Weak Acid from the Solution pH 4.8x10-5
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Concentration and Extent of Dissociation
Percent HA dissociated = [HA]dissoc [HA]init x 100 As the initial acid concentration decreases, the percent dissociation of the acid increases. HA(aq) + H2O(l) H3O+(aq) + A-(aq) A decrease in [HA]init means a decrease in [HA]dissoc = [H3O+] = [A-], causing a shift towards the products. The fraction of ions present increases, even though the actual [HA]dissoc decreases.
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Finding Dissociation% of a Weak Acid from the Solution pH
A study of the acid shows that the pH of 0.12 M Phenylacetic acid (C6H5CH2COOH, simplified here as HPAc) is What is the Dissociation% of this phenylacetic acid? 2.0%
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Polyprotic Acids A polyprotic acid is an acid with more than one ionizable proton. In solution, each dissociation step has a different value for Ka: Ka1 = [H3O+][H2PO4-] [H3PO4] = 7.2x10-3 H3PO4(aq) + H2O(l) H2PO4-(aq) + H3O+(aq) Ka2 = [H3O+][HPO42-] [H2PO4-] = 6.3x10-8 H2PO4-(aq) + H2O(l) HPO42-(aq) + H3O+(aq) Ka3 = [H3O+][PO43-] [HPO42-] = 4.2x10-13 HPO42-(aq) + H2O(l) PO43-(aq) + H3O+(aq) Ka1 > Ka2 > Ka3 We usually neglect [H3O+] produced after the first dissociation.
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Successive Ka values for Some Polyprotic Acids at 25°C
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Weak Bases A Brønsted-Lowry base is a species that accepts an H+. For a weak base that dissolves in water: B(aq) + H2O(l) BH+(aq) + OH-(aq) The base-dissociation or base-ionization constant is given by: [BH+][OH-] [B] Kb = pKb = -logKb Note that no base actually dissociates in solution, but ions are produced when the base reacts with H2O.
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Abstraction of a proton from water by the base methylamine.
Lone pair of N pair binds H+
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Kb Values for Some Molecular (Amine) Bases at 25°C
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Determining pH from Kb and Initial [B]
Dimethylamine, (CH3)2NH, a key intermediate in detergent manufacture, has a Kb of 5.9x What is the pH of 1.5 M (CH3)2NH? pH = -log (3.3x10-13) = 12.48
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Anions of Weak Acids as Weak Bases
The anions of weak acids often function as weak bases. A-(aq) + H2O(l) HA(aq) + OH-(aq) Kb = [HA][OH-] [A-] A solution of HA is acidic, while a solution of A- is basic. HF(aq) + H2O(l) H3O+(aq) + F-(aq) HF is a weak acid, so this equilibrium lies to the left. [HF] >> [F-], and [H3O+]from HF >> [OH-] ; the solution is therefore acidic. from H2O
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F-(aq) + H2O(l) HF(aq) + OH-(aq)
If NaF is dissolved in H2O, it dissolves completely, and F- can act as a weak base: F-(aq) + H2O(l) HF(aq) + OH-(aq) HF is a weak acid, so this equilibrium also lies to the left. [F- ] >> [HF], and [OH- ] >> [H3O+ ] ; the solution is therefore basic. from H2O from F-
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Ka and Kb for a Conjugate Acid-Base Pair
HA + H2O H3O+ + A- A- + H2O HA + OH- 2H2O H3O+ + OH- Kc for the overall equation = K1 x K2, so [H3O+][A-] [HA] [HA][OH-] [A-] x = [H3O+][OH-] Ka x Kb = Kw This relationship is true for any conjugate acid-base pair.
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How to determine the pH of a Solution of Salt from Strong base and Weak acid
A- + H2O HA + OH-
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Determining the pH of a Solution of A-
PROBLEM: What is the pH of 0.25 M Sodium acetate (CH3COONa, or NaAc for this problem)? Ka of acetic acid (HAc) is 1.8x10-5. pH = -log (8.3x10-10) = 9.08 [OH-] = 1.2x10-5 M
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How to determine the pH of a Solution of Salt from weak base and Strong acid
HB+ + H2O B + H3O+
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Determining the pH of a Solution of HB+
PROBLEM: Ammonium chloride (NH4Cl) is the salt of ammonia. What is the pH of 0.10 M NH4Cl? Kb of ammonia is 1.8x10-5. Hint: Identify the ions in the solution; HB+ ionization w/ H2O pH = -log (2.3x10-6) = 5.63 [H+] = 2.3x10-6 M
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How to find pH for a weak acid or base solution
Summary: How to find pH for a weak acid or base solution For weak acid solution, either HA (Ka) or conjugate acid of a weak base (HB+, whose Ka = Kw /Kb) For weak base solution, either the weak base B (Kb) or conjugate base of a weak acid (A-, whose Kb = Kw /Ka)
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Acid Strength of Nonmetal Hydrides
For nonmetal hydrides (E-H), acid strength depends on: the electronegativity of the central nonmetal (E), and the strength of the E-H bond. Across a period, acid strength increases. Electronegativity increases across a period, so the acidity of E-H increases. Example: NH3 < H2O < HF Down a group, acid strength increases. The length of the E-H bond increases down a group and its bond strength therefore decreases. Example: H2O < H2S < H2Se < H2Te
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The effect of atomic and molecular properties on
nonmetal hydride acidity. Electronegativity increases, so acidity increases Bond strength decreases, so acidity increases 6A(16) H2O H2S H2Se H2Te 7A(17) HF HCl HBr HI
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Acid Strength of Oxoacids
All oxoacids have the acidic H bonded to an O atom. Acid strength of oxoacids depends on: the electronegativity of the central nonmetal (E), and the number of O atoms around E. For oxoacids with the same number of O atoms, acid strength increases as the electronegativity of E increases. Example: H4SiO4 < H3PO4 < H2SO4 < HClO4 For oxoacids with different numbers of O atoms, acid strength increases with the number of O atoms. Example: HClO < HClO2 < HClO3 < HClO4
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A B The relative strengths of oxoacids.
Electronegativity increases, so acidity increases. B Number of O atoms increases, so acidity increases.
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Hydrated Metal Ions Some hydrated metal ions are able to transfer an H+ to H2O. These metal ions will form acidic solutions. Consider a metal ion in solution, Mn+: Mn+(aq) + H2O(l) → M(H2O)xn+(aq) If Mn+ is small and highly charged (Al3+, Be2+, Fe3+), it will withdraw enough e- density from the O-H bonds of the bound H2O molecules to release H+: M(H2O)xn+(aq) + H2O(l) M(H2O)x-1OH(n-1)(aq) + H3O+(aq)
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The acidic behavior of the hydrated Al3+ ion.
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Salts that Yield Neutral Solutions
A salt that consists of the anion of a strong acid and the cation of a strong base yields a neutral solution. NaNO3 Na+ is the cation of NaOH, a strong base. NO3- is the anion of HNO3, a strong acid. This solution will be neutral, because neither Na+ nor NO3- will react with H2O to any great extent.
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Salts that Yield Acidic Solutions
A salt that consists of the anion of a strong acid and the cation of a weak base yields an acidic solution. NH4Cl NH4 + is the cation of NH3, a weak base. Cl- is the anion of HCl, a strong acid. This solution will be acidic, because NH4+ will react with H2O to produce H3O+: NH4+(aq) + H2O(l) NH3(aq) + H3O+(aq)
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Salts that Yield Basic Solutions
A salt that consists of the anion of a weak acid and the cation of a strong base yields a basic solution. CH3COONa CH3COO- is the anion of CH3COOH, a weak acid. Na+ is the cation of NaOH, a strong base. This solution will be basic, because CH3COO- will react with H2O to produce OH-: CH3COO-(aq) + H2O(l) CH3COOH(aq) + OH-(aq)
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Summary: How to determine the pH of a Solution of Salt
Ionization rxn pH Calculation St base + Wk Acid A- + H2O → HA + OH- > 7 Wk base + str acid HB+ + H2O → B + H3O+ < 7
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Predicting Relative Acidity of Salt Solutions from Reactions of the Ions with Water
PROBLEM: Predict whether aqueous solutions of the following are acidic, basic, or neutral, and write an equation for the reaction of any ion with water: (a) Potassium perchlorate, KClO4 (b) Sodium benzoate, C6H5COONa (c) Chromium(III) nitrate, Cr(NO3)3 (a) Neutral (KOH as strong base, HClO4 as strong acid). (b) Basic (Benzoic acid is a weak acid) (c) Acidic. Cr(H2O)63+(aq) + H2O(l) Cr(H2O)5OH2+(aq) + H3O+(aq) . This solution will be acidic.
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Salts of Weakly Acidic Cations and Weakly Basic Anions
If a salt that consists of the anion of a weak acid and the cation of a weak base, the pH of the solution will depend on the relative acid strength (Kb) or base strength (Kb) of the ions. NH4CN NH4+ is the cation of a weak base, NH3. CN- is the anion of a weak acid, HCN. NH4+(aq) + H2O(l) NH3(aq) + H3O+(aq) CN-(aq) + H2O(l) HCN(aq) + OH-(aq)
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The reaction that proceeds farther to the right determines the pH of the solution, so we need to compare the Ka of NH4+ with the Kb of CN-. Ka of NH4+ = Kw Kb of NH3 1.0x10-14 1.76x10-5 = = 5.7x10-10 Kb of CN- = Kw Ka of HCN 1.0x10-14 6.2x10-10 = = 1.6x10-5 Since Kb of CN- > Ka of NH4+, CN- is a stronger base than NH4+ is an acid. A solution of NH4CN will be basic.
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The Acid-Base Behavior of Salts in Water
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Predicting the Relative Acidity of Salt Solutions from Ka and Kb of the Ions
Determine whether the following aqueous solutions is acidic, basic, or neutral: (a) NH4ClO4; (b) NaClO4; (c) NH4F; (d) NH4CH3COO Hint: what is the acid and base that lead to the stated compound, consider the general equation for acid-base reaction; What are the Kb and Ka of the base and acid involved? Ka (HClO4)6 = ~108 Ka (HF)6 = ~108 Kb (NaOH) : strong base Kb (NH3) = 1.8 x 10-5
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The Leveling Effect All strong acids and bases are equally strong in water. All strong acids dissociate completely to form H3O+, while all strong bases dissociate completely to form OH-. In water, the strongest acid possible is H3O+ and the strongest base possible is OH-. H2O exerts a leveling effect on any strong acid or base.
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The Lewis Acid-Base Definition
A Lewis base is any species that donates an electron pair to form a bond. A Lewis acid is any species that accepts an electron pair to form a bond. The Lewis definition views an acid-base reaction as the donation and acceptance of an electron pair to form a covalent bond.
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Lewis Acids and Bases A Lewis base must have a lone pair of electrons to donate. Any substance that is a Brønsted-Lowry base is also a Lewis base. A Lewis acid must have a vacant orbital (or be able to rearrange its bonds to form one) to accept a lone pair and form a new bond. Many substances that are not Brønsted-Lowry acids are Lewis acids. The Lewis definition expands the classes of acids.
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Electron-Deficient Molecules as Lewis Acids
B and Al often form electron-deficient molecules, and these atoms have an unoccupied p orbital that can accept a pair of electrons: BF3 accepts an electron pair from ammonia to form a covalent bond.
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Lewis Acids with Polar Multiple Bonds
Molecules that contain a polar multiple bond often function as Lewis acids: The O atom of an H2O molecule donates a lone pair to the S of SO2, forming a new S‒O σ bond and breaking one of the S‒O p bonds.
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Metal Cations as Lewis Acids
A metal cation acts as a Lewis acid when it dissolves in water to form a hydrated ion: The O atom of an H2O molecule donates a lone pair to an available orbital on the metal cation.
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The Mg2+ ion as a Lewis acid in chlorophyll.
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Practice: Identifying Lewis Acids and Bases PROBLEM: Identify the Lewis acids and Lewis bases in the following reactions: (a) H+ + OH H2O (b) Cl- + BCl BCl4- (c) K+ + 6H2O K(H2O6)+ Hint: During the bonding, any change on the lone pair electrons among the reactants? (a) The H+ ion accepts the electron pair from OH-. H+ is the Lewis acid and OH- is the Lewis base. (b) BCl3 accepts an electron pair from Cl-. Cl- is the Lewis base and BCl3 is the Lewis acid. (c) An O atom from each H2O molecule donates an electron pair to K+. H2O is therefore the Lewis base, and K+ is the Lewis acid.
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How many significant figures to keep when calculating pH from [H+]?
Test the uncertainty using an example: [H+] = (5.34 ± 0.01) x 10-5 M (3 sig. figs) -log(5.33 x 10-5) = 4.273 -log(5.35 x 10-5) = (3 decimal places) Sig Fig rule for pH [H+]: #SF of decimal part in [H+] = #DP in pH
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HPr + H2O → A- + H3O+ Initial [HPr] Change -x x Equilibrium [HPr] - x
Determining Concentration from Ka and Initial [HA] PROBLEM: Propanoic acid (CH3CH2COOH, which we simplify as HPr). What is the [H3O+] of 0.10 M HPr (Ka = 1.3x10−5)? Set up the ICE table HPr + H2O → A- + H3O+ Initial [HPr] Change -x x Equilibrium [HPr] - x Check: [HPr]diss = 1.1x10-3 M 0.10 M x 100 = 1.1% (< 5%; assumption is justified.) [H3O+] = 1.1x10-3 M
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[HA]dissoc = [A-] = [H3O+] = 10-pH
Finding Dissociation% of a Weak Acid from the Solution pH Problem: A study of the acid shows that the pH of 0.12 M Phenylacetic acid (C6H5CH2COOH, simplified here as HPAc) is What is the Dissociation% of this phenylacetic acid? HPr + H2O → A- + H3O+ Initial [HPr] Change -x x Equilibrium [HPr] - x [HA]dissoc = [A-] = [H3O+] = 10-pH 2.0%
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B + H2O → HB+ + OH- Initial [B] Change -x x Equilibrium [B] - x
Determining pH from Kb and Initial [B] PROBLEM: Dimethylamine, (CH3)2NH, a key intermediate in detergent manufacture, has a Kb of 5.9x What is the pH of 1.5 M (CH3)2NH? B + H2O → HB+ + OH- Initial [B] Change -x x Equilibrium [B] - x x = [OH-] = 3.0x10-2 M pH = -log (3.3x10-13) = 12.48 3.0x10-2 M 1.5 M x 100 = 2.0% (< 5%; assumption is justified). Check:
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How to determine the pH of a Solution of Salt from Strong base and Weak acid
A- + H2O HA + OH- A- + H2O HA + OH- Initial [A-] Change -x x Equilibrium [A-] - x
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How to determine the pH of a Solution of Salt from weak base and Strong acid
HB+ + H2O B + H3O+ HB+ + H2O B + H3O+ Initial [HB+] Change -x x Equilibrium [HB+] - x
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