Acids and Bases: Comprehensive Notes

Ch. 17 Acids & Bases Continued

The pH Scale

  • pH is defined as the negative logarithm of the hydrogen ion concentration:
    pH = -log[H^+]
  • It can also be expressed in terms of hydronium ion concentration:
    pH = -log[H_3O^+]
  • The general formula for pX is:
    pX = -log X
  • pOH is defined as the negative logarithm of the hydroxide ion concentration:
    pOH = -log[OH^-]

Applying the pX Formula

  • The pX formula can be applied to Kw, Ka, and Kb:
    pX = -log X
    pKw = -log(Kw)
    pKa = -log(Ka)
    pKb = -log(Kb)

Conjugate Acid-Base Pairs

  • Example with formic acid (HCHO2) and water:
    • HCHO2 + H2O ⇌ H3O+ + CHO2–
    • CHO2– + H2O ⇌ HCHO2 + OH–

Ka vs. Kb

  • As Ka increases, Kb decreases.
  • The stronger the acid, the weaker its conjugate base.
  • A "stronger weak acid" is still a weak acid.

Example Problem: Formic Acid Ka and pKa

  • Problem: Determine the Ka and pKa of formic acid, given that a 0.100 M formic acid (HCHO2) solution has a pH of 2.38 at 25°C.
  • Step 1: Use the definition of Ka and create an ICE (Initial, Change, Equilibrium) table.
  • Ka expression includes [H+] in the products.
  • Since we know pH, we can solve for [H+].
    [H^+] = 10^{-pH}
  • Use \'x\' and the ICE table to solve for all concentrations needed for the Ka expression.

Example Problem: Methylamine Kb

  • Problem: Methylamine (CH3NH2) is a weak base. In a 0.100 M solution, 6.30% of the base is ionized. What is its Kb?
  • Use an ICE table to find the change in concentration.
  • Percent ionization = (ionized concentration / initial concentration) * 100
  • Calculate Kb using the equilibrium concentrations from the ICE table.

Key Reminder

  • Ka will have [H+].
  • Kb will have [OH-].

Exam Time Saver

  • If the question specifies a base, use the general form: B + H2O ⇌ BH+ + OH-
  • Practice figuring out the BH+ form, but on the exam, only determine it if needed to save time.

Determining Kb from Ka

  • Problem: Determine Kb of the benzoate ion (C6H5COO-) given that the Ka of benzoic acid is 6.5 x 10^{-5}.

Hydrazine Example

  • Problem: Hydrazine (N2H4) has a Kb = 1.7 x 10^{-6} at 25°C. What is the pH and % ionization of a 0.25 M solution?
  • Approximation validity check:
    • x < (0.05) [HA]initial
    • [HA]initial ≥ (400) Ka

Approximation Validation

  • How to check if the approximation is valid:
    • x < (0.05) [HA]_{initial}
    • [HA]_{initial} ≥ (400) Ka

Example Problem: Propionic Acid pH Calculation

  • Problem: Calculate the pH at 25°C of a 0.10 M solution of propionic acid (HC3H5O2; Ka = 1.34 x 10^{-5}).
  • pH = 2.94

When Simplifications Fail

  • If the approximation is not valid, use:
    1. Quadratic equation
    2. Successive approximations

pH Calculation with Inadequate Simplification

  • Problem: What is the pH of a 0.010 M solution of HC2H2O2Cl (Ka = 1.4 x 10^{-3})?

Diprotic and Polyprotic Acids

  • Diprotic and polyprotic acids undergo a series of ionizations (loss of protons).
  • Example: Carbonic acid (H2CO3)
    • H2CO3 ⇌ H+ + HCO3– Ka1 = 4.2 x 10^{-7}
    • HCO3– ⇌ H+ + CO32– Ka2 = 4.8 x 10^{-11}
  • Example: Sulfuric acid (H2SO4)
    • H2SO4 → H+ + HSO4– Ka1 = Large
    • HSO4– ⇌ H+ + SO42– Ka2 = 1.2 x 10^{-2}

Simplifications for Polyprotic Acids

  • Typically there is a large difference between Ka1 and Ka2 (~1000x).
  • The first H+ is easier to lose from a neutral species, while the second H+ must be lost from an anionic species.
  • Since Ka1 >> Ka2:
    • [H+]total = [H+]1st + [H+]2nd
    • [H+]1st >> [H+]2nd
    • [H+]total ≈ [H+]1st

Concentration Approximations for Polyprotic Acids

  • For H2CO3:
    • H2CO3 ⇌ H+ + HCO3– Ka1 = 4.2 x 10^{-7}
    • HCO3– ⇌ H+ + CO32– Ka2 = 4.8 x 10^{-11}
    • [H+]total ≈ [H+]1st
    • [HCO3–]total ≈ [HCO3–]1st
    • [CO32–]: Ka2 = [H+][CO32–] / [HCO3–]
    • [H+] = [HCO3–] (from 1st ionization), so Ka2 = [CO32–]

Example Problem: Polyprotic Acid

  • Problem: You have a 0.050 M H2CO3 solution. What is the concentration of all species?
  • Species: H2CO3, HCO3–, CO32–, H+, OH–

Acid-Base Properties of Salts

  • When salts dissociate in solution, the resulting anions and cations can act like acids or bases.
  • Cations:
    1. Conjugate acid of weak base → weak acid (e.g., ammonium ion NH4+)
    2. Hydrated metals can act like weak acids.

Key Question

  • MUST ASK: What do I have in solution?

Charge Density

  • The higher the charge density, the stronger the acid.
    • Charge density = charge / unit volume
  • Group IA metals: non-acids
  • Group IIA metals: charge density too low (except Be2+)
  • All other metals: weak acids
  • Acidity increases as metal size decreases and charge increases.

Charge Density Explained

  • Charge of ion / Size of ion
  • Small charge, large size = low charge density
  • High charge, small size = high charge density → Better at acting like an acid in water

Anions

  • Conjugate bases of weak acids → weak bases
  • Example: Sodium hypochlorite (NaOCl) is found in bleaches and disinfectants. Is it acidic, basic, or neutral?

NaOCl Example

  • Problem: What is the pH of a 0.10 M NaOCl solution (Ka of HOCl = 3.0 x 10^{-8})?

The Role of Na+

  • Na+ is neutral and will not affect pH.

Why Na+ is Neutral: Option 1

  • Sodium has a low charge density as an alkali metal and is a neutral metal ion.
  • Acidic properties of metal ions like Al3+ were previously discussed

Why Na+ is Neutral: Option 2

  • Sodium is the counter ion of a strong base: NaOH
  • The only way for sodium to act acidic (by protons) is for: Na+ + H2O → NaOH + H+
  • This never happens because NaOH instantly dissociates and the reaction runs backwards.
  • So there is no way for Na+ to produce protons.

Anion and Cation are Acid/Bases

  • pH depends on the relative strengths of the conjugate acid and base.
    • When Kb > Ka, the solution is basic.
    • When Kb < Ka, the solution is acidic.
    • When Kb = Ka, the solution is neutral.

Acidic, Basic, or Neutral Examples

  • NH4C2H3O2: Kb (C2H3O2–) = 5.6 x 10^{-10}, Ka (NH4+) = 5.6 x 10^{-10}
  • NH4CHO2: Kb (CHO2–) = 5.6 x 10^{-11}

Solutions for Previous Example

  • NH4C2H3O2: neutral, since Ka = Kb
  • NH4CHO2: acidic, since Ka > Kb

Polyprotic Acid Example with Na2CO3

  • What is the pH of a 0.15 M Na2CO3 solution?
    • Handle like a polyprotic acid.
    • Only worry about the first ionization.
      • Na2CO3 → 2 Na+ + CO32–
      • CO32– + H2O ⇌ HCO3– + OH–
      • HCO3– + H2O ⇌ H2CO3 + OH–
    • Kb1 >> Kb2
    • Get [CO32–] and [HCO3–] from the first equilibrium.
    • [H2CO3] = Kb2

Lewis Acids and Bases

  • Lewis base = substance that can donate a pair of electrons → must contain 1 or more lone pairs of e–
  • Lewis acid = substance that can accept a pair of electrons → contains incomplete valence shell or multiple bonds that can shift to make room for lone pair

Lewis vs. Bronsted

  • Lewis is a broader definition.
  • If it was an acid by Bronsted, it is still an acid with Lewis.
  • If it was a base by Bronsted, it is still a base with Lewis.
  • Bronsted deals with protons, while Lewis deals with electrons.

Lewis Acid-Base Reaction

  • A Lewis acid-base reaction involves the donation of a pair of electrons from one species to another (formation of a coordinate covalent bond).
  • The Lewis concept includes all Arrhenius and Bronsted acids/bases.
  • Example: H+ + OH–

Lewis Acid/Base Examples

  • Be able to identify Lewis acid and base:
    • Na+ + 6 H2O ⇌ Na(H2O)6 +
    • Ag+(aq) + 2 NH3(aq) ⇌ Ag(NH3)2 +(aq)
    • Cd2+(aq) + 4 I–(aq) ⇌ CdI4 2–(aq)
    • Ni(s) + 4 CO(g) ⇌ Ni(CO)4(g)

Recognizing Lewis Acids

  • Acids from previous definitions (strong and weak like HCl and HC2H3O2)
  • Metals with a positive charge
  • Usually neutral metals
  • Compounds with a positive charge
  • Draw the structure

More on Lewis Acids

  • Lewis acid = substance that can accept a pair of electrons → contains incomplete valence shell or multiple bonds that can shift to make room for lone pair

Recognizing Lewis Bases

  • Bases from previous definitions (strong and weak like NaOH and NH3)
  • Compounds with a negative charge
  • Draw the structure

More on Lewis Bases

  • Lewis base = substance that can donate a pair of electrons → must contain 1 or more lone pairs of e–

Identifying Active Atoms

  • Identify the most likely ATOM in a compound that can accept or donate electrons.
  • Analyze the structure itself.

Active Atoms in Hydroxide and Carbon Dioxide

  • In hydroxide, the oxygen carries the electrons and acts as a Lewis base.
  • In carbon dioxide, the carbon accepts the electrons.
  • The carbon is the atom that is DOING something.