Acids and Bases | General Chemistry 3

Arrhenius acids and bases:

• Acid: An Arrhenius acid increases the concentration of H⁺ ions (protons) in an aqueous solution.
• Base: An Arrhenius base increases the concentration of OH^- ions in an aqueous solution.
   

• HCl is an Arrhenius acid which dissociates in water to form H⁺ and Cl^- ions:
  HCl $\to$ H⁺ + Cl⁻
• NaOH is an Arrhenius base which dissociates in water to form Na⁺ and OH^- ions:
  NaOH $\to$ Na⁺ + OH⁻

Brønsted-Lowry acids and bases:

• Acid: A Brønsted-Lowry acid is a proton donor.

• Base: A Brønsted-Lowry base is a proton acceptor.

• Conjugate acid-base pairs: In a Brønsted-Lowry reaction, acids and bases are linked through conjugate acid-base pairs. The acid donates a proton to become a conjugate base, while the base accepts a proton to become a conjugate acid.
   

• HCl is a Brønsted acid: it donates a proton to water, leading to the formation of hydronium (H₃O⁺) ions:
  HCl + H₂O $\to$ Cl⁻ + H₃O⁺
• NH₃ is a Brønsted base: it accepts a proton from water:
  NH₃ + H₂O $\to$ NH₄⁺ + OH⁻
• HCl/Cl^-, H₃O⁺/H₂O, NH₄⁺/NH₃, and H₂O/OH⁻ are conjugate acid-base pairs.

Lewis acids and bases:

• Acid: A Lewis acid is a substance that accepts an electron pair.

• Base: A Lewis base is a substance that donates an electron pair.
   

BF_3​ + NH₃​ $\to$ H₃​NBF_3​

• Boron trifluoride (BF₃) acts as a Lewis acid by accepting an electron pair from ammonia.
• Ammonia (NH₃) donates an electron pair to BF₃, making it a Lewis base.

Self-ionization of water:

Water has the unique ability to act as both an acid and a base. In pure water, water molecules can donate a proton to another water molecule, leading to the formation of hydronium (H₃O⁺) and hydroxide (OH⁻) ions. The dissociation of water, known as the self-ionization of water, is described by the equilibrium reaction:
 

2 H₂O (l) $\rightleftharpoons$ H₃O⁺ (aq) + HO^- (aq)

In the dissociation of water, the forward and reverse reactions happen rapidly. However, the equilibrium lies far to the left, meaning that only a small fraction of water molecules are dissociated at any given moment.

Ion-product constant (K_w):

The equilibrium constant for the dissociation reaction of water is called the ion-product constant of water, denoted as K_w​. The value of K_w at 25°C is:
 

Acidic, basic, and neutral solutions:

• Acidic solutions: [H₃O⁺] > [HO^-]
• Basic solutions: [H₃O⁺] < [HO^-]
• Neutral solutions: [H₃O⁺] = [HO^-] = 1.0 x 10^-7 M

Definition of pH:

The pH of a solution is defined as the negative base-10 logarithm of the molar concentration of hydronium ions:
 

Conversely, the concentration of hydronium ions can be calculated from the pH:
 

• The pH scale is logarithmic, meaning that each unit change in pH corresponds to a tenfold change in the concentration of hydronium ions. For instance, a solution with a pH of 4 has ten times the concentration of hydronium ions compared to a solution with a pH of 5.
• pH can be measured using pH indicators, which change color at specific pH values, or more accurately with a pH meter, which measures the electrical potential of the solution to determine pH.

Neutral, acidic, and basic solutions:

• Neutral solution: [H₃O⁺] = [HO^-] = 1.0 x 10^-7 M ⇒ pH =  7
• Acidic solution: [H₃O⁺] < 1.0 x 10^-7 M ⇒ pH < 7
• Basic solution: [H₃O⁺] > 1.0 x 10^-7 M ⇒ pH > 7

Definition of pOH:

The pOH of a solution is defined similarly to pH, as the negative base-10 logarithm of the hydroxide ion concentration:
 

Relationship between pH and pOH:

The relationship between pH and pOH is governed by the ion-product constant for water at 25°C:
 

Strong acids and strong bases:

• Strong acids: These acids completely dissociate in water, meaning they fully donate protons to form hydronium ions (H₃O⁺).
• Strong bases: Similarly, strong bases completely dissociate in water, fully accepting protons and forming hydroxide ions (OH⁻).
   

• HBr is a strong acid: HBr (aq) + H₂O (l) → Br^- (aq) + H₃O⁺ (aq)
• NaOH is a strong base: NaOH (aq) + H₂O (l) → Na⁺ (aq) + HO^- (aq)

There are only a few strong acids and bases in water, including HCl, HBr, H₂SO₄, NaOH, and KOH. The majority of acids and bases in water are weak.

Weak acids and weak bases:

• Weak acids: These acids only partially dissociate in water, establishing an equilibrium between the undissociated acid, hydronium ions, and the conjugate base.
• Weak bases: Similarly, weak bases partially dissociate in water, resulting in an equilibrium between the undissociated base, hydroxide ions, and the conjugate acid.
   

Ammonia (NH₃) is a weak base that partially dissociates in water:
NH₃ (aq) + H₂O (l) $\rightleftharpoons$ NH₄⁺ (aq) + HO^- (aq)

Factors affecting acid strength:

• Bond strength: The strength of the H–A bond is critical in determining acid strength. Acid strength increases down the group for halogens because bond dissociation energy decreases, making it easier to release the proton.
• Electronegativity and polarity: Acid strength also depends on the polarity of the H–A bond. More electronegative atoms pull electron density away from the proton, facilitating its dissociation. In a given period, acid strength increases with the electronegativity of A.
   

HF is a stronger acid than H₂O due to fluorine's higher electronegativity.

• Oxidation number: For oxoacids with the general formula H_nYO_m​, acid strength increases with the electronegativity of Y and the number of oxygen atoms attached. More oxygen atoms stabilize the negative charge on the conjugate base.
   

HClO₄​ is stronger than HClO₃​ due to the additional oxygen atom, which stabilizes the conjugate base more effectively.

Acid ionization constant:

The acid ionization constant (K_a)​ measures the strength of a weak acid. It represents the equilibrium constant for the ionization of the acid in water. The ionization reaction for a weak monoprotic acid HA in water is:

 HA (aq) + H₂O (l) $\rightleftharpoons$ H₃O⁺ (aq) + A^- (aq)

The corresponding expression for the acid ionization constant is:
 

A larger K_a​ value indicates a stronger weak acid, meaning the acid ionizes to a greater extent in water. Conversely, a smaller K_a​ value indicates a weaker acid that ionizes less.
 

• Hydrofluoric Acid (HF): K_a = 7.1 x 10⁻⁴
• Acetic Acid (CH₃COOH): K_a = 1.8 x 10⁻⁵
• Hydrocyanic Acid (HCN): K_a = 4.9 x 10⁻¹⁰

These values show that HF is a stronger weak acid than acetic acid, while hydrocyanic acid is much weaker than both.

Percent ionization:

Percent ionization refers to the percentage of acid molecules that ionize in solution. It is calculated using the following formula:
 

How to calculate pH from K_a:

1. Identify the species present in the solution and classify them as acids or bases.
2. Write the balanced equations for all possible proton-transfer reactions.
3. Identify the reaction that has the largest equilibrium constant. This is the principal reaction.
4. Set up an ICE (Initial, Change, Equilibrium) table to track the initial concentrations, changes during the reaction, and equilibrium concentrations of all species. Define x as the concentration of the acid that dissociates.
5. Use the equilibrium concentrations in the expression for K_a. Solve for x.
6. Calculate pH (= - log [H₃O⁺]).
7. If there are additional reactions or equilibria (such as for polyprotic acids or complex equilibria), calculate the concentrations of the species involved in these secondary equilibria.

Calculate the pH of a 0.50 M solution of HF given that K_a = 7.1 x 10^-4.

• HF (aq) + H₂​O (l) ⇌ H_3​O⁺ (aq) + F⁻ (aq)
• K_a = $\frac{\left[{\mathrm{H}}_3{\mathrm{O}}^{+}\right]\left[{\mathrm{F}}^{-}\right]}{\left[\mathrm{HF}\right]}$ = 7.1 x 10^-4

	HF (aq)	H3​O+ (aq)	F− (aq)
Initial Concentration (M)	0.50	0	0
Change (M)	-x	x	x
Equilibrium Concentration (M)	0.50 - x	x	x

 

• K_a = $\frac{\mathrm{x} · \mathrm{x}}{0.50 - \mathrm{x}}$ = 7.1 x 10^-4
• x² + (7.1 x 10^-4) x - 3.55 x 10^-4 = 0 ⇒ x = 0.0185 (choose the positive solution of the quadratic equation)
• [H_3​O⁺] = x = 0.0185 M ⇒ pH = 1.73

Approximations in pH calculation:

• Principal reaction vs. subsidiary reactions:  

In most cases, the principal reaction (the one with the larger equilibrium constant) is the dominant source of hydronium ions (H₃O⁺). Subsidiary reactions, such as the dissociation of water or secondary dissociations in polyprotic acids, are often considered negligible when calculating the pH.
 

Calculate the pH of a 0.10 M HCN solution:

• Two proton-transfer reactions are possible:
  HCN (aq) + H₂O (l) $\rightleftharpoons$ H₃O⁺ (aq) + CN^- (aq)     [K_a = 4.9 x 10^-10]
  H₂O (l) + H₂O (l) $\rightleftharpoons$ H₃O⁺ (aq) + HO^- (aq)          [K_w = 1.0 x 10^-14]
• Since K_a for HCN is more than 10,000 times greater than K_w, the principal reaction is the dissociation of HCN, while the dissociation of water is a subsidiary reaction.
• For the calculation of pH, we assume that nearly all the H₃O⁺ come from the principal reaction:
  [H₃O⁺] (total) ≈ [H₃O⁺] (from principale reaction)
  The contribution of [H₃O⁺] from subsidiary reactions like water dissociation is negligible.

•  Neglecting the change in concentration of starting material:

When setting up the ICE table, the concentration of the weak acid at equilibrium is represented as [HA] = [HA]₀ − x, where x is the amount that dissociates. However, since weak acids dissociate only to a small extent, x is typically very small compared to the initial concentration [HA]₀​. Therefore, we make the approximation:

[HA]₀ − x ≈ [HA]₀

This simplification makes calculations easier by reducing the complexity of solving the equilibrium expression.

It's important to check the validity of this approximation at the end of the problem, especially when x is not negligible compared to the initial concentration of the acid. If x is significant, the approximation may not be valid, and the exact value must be used to refine the calculation.

Base ionization constant:

The base ionization constant (K_b​) is a measure of the strength of a weak base. It is the equilibrium constant for the ionization of the base in water:

B (aq) + H₂O (l) ⇌  BH⁺ (aq) + HO^- (aq)

The corresponding expression for K_b is:
 

A larger K_b​ value indicates a stronger weak base, meaning the base ionizes more in water. Conversely, a smaller K_b​ value indicates a weaker base that ionizes less.
 

• Ammonia (NH₃): K_b = 1.8 x 10⁻⁵
• Methylamine (CH₃NH₂): K_b = 4.4 x 10⁻⁴
• Pyridine (C₅H₅N): K_b = 1.7 x 10⁻⁹

These values show that methylamine is a stronger base than ammonia, while pyridine is significantly weaker than both.

The strength of a conjugate acid or base:

• Conjugate acid: When a base accepts a proton, it forms its conjugate acid. The strength of the conjugate acid is inversely related to the strength of the original base. A strong base will have a weak conjugate acid, while a weak base will have a relatively stronger conjugate acid.
• Conjugate base: When an acid donates a proton, it forms its conjugate base. The strength of the conjugate base is inversely related to the strength of the original acid. A strong acid will have a very weak conjugate base, whereas a weak acid will have a relatively stronger conjugate base.
   

Conjugate acid-base pairs and their relative strength:

• HNO₃ (strong) / NO₃^- (weak)
• HCN (weak) / CN^- (strong)
• H₂O (weak) / HO^- (strong)

Relation between K_a and K_b:

For a conjugate acid-base pair, the product of K_a​ and K_b​ is equal to the ion-product constant for water (K_w​) at a given temperature (typically 25°C):
 

Since K_w is a constant, as K_a increases (stronger acid), K_b​ must decrease (weaker conjugate base), and vice versa.

Relation between pK_a and pK_b:

The relationship between pK_a​ and pK_b​ for a conjugate acid-base pair at 25°C can be expressed as:
 

• A lower pK_a indicates a stronger acid and a weaker conjugate base (higher pK_b​).
• Conversely, a higher pK_a​ indicates a weaker acid and a stronger conjugate base (lower pK_b​).

Diprotic acids:

A diprotic acid is an acid that can donate two protons (H⁺). The dissociation of a diprotic acid occurs in two distinct steps, each characterized by its own dissociation constant:

• First dissociation:     H₂A $\to$ H⁺ + HA^-     [K_a1]
• Second dissociation:     HA^- → H⁺ + A^2-     [K_a2]
   

• Sulfuric acid (H₂SO₄): H₂SO₄/HSO₄^- and HSO₄^-/SO₄^2-
• Carbonic acid (H₂CO₃): H₂CO₃/HCO₃^- and HCO₃^-/CO₃^2-

Polyprotic acids:

A polyprotic acid is an acid that can donate more than two protons. Like diprotic acids, polyprotic acids dissociate stepwise, with each proton being donated in a separate step, each characterized by its own dissociation constant.
 

Phosphoric acid (H₃PO₄) and citric acid (C₆H₈O₇) are triprotic acids that release 3 protons stepwise.

Dissociation constants for polyprotic acids:

The dissociation constants of polyprotic acids typically follow this order: K_a1 > K_a2 > K_a3. This is because removing a proton from a negatively charged ion (e.g., from HA⁻) is more difficult than removing it from a neutral molecule (e.g., from H₂A).

pH calculation for polyprotic acids:

• First dissociation: The first dissociation step (associated with K_a1) usually has the greatest effect on the pH of the solution.
• Subsequent dissociations: The second and third dissociation steps typically contribute much less to the overall concentration of hydronium ions, and therefore, have a smaller effect on the pH of the solution.