Acid-Base Equilibria

Acid Base Theories

Arrhenius

Bronsted-Lowry

Definition

Acid: hydrogen-containing compounds in an aq solution that ionize to yield hydrogen ions (H+)

Base: compounds that ionize to yield hydroxide ions (OH-) in an aq solution

Acid: a hydrogen-ion (or proton) donor

Base: a hydrogen-ion (or proton) acceptor

General reaction equation

Acid + water → acid-anion + hydrogen-anion

HA -H20→ H+ + A-

Base + water → hydroxide-ion + base-cation

OHB -H20→ OH- + B+

Acid + base ⇋ conjugate base + conjugate acid

HA + B ⇋ A- + BH+

Additional explanations

Not every hydrogen-containing substance is acidic because some bonds are nonpolar (electronegativity is balanced). Therefore it is more difficult for these substances to ionize compared to polar bonds.

When a reverse reaction occurs, the roles of acid and base are swapped according to their definitions since the ions are exchanged again. The products of the forward reaction are therefore distinguished through the word “conjugate”. These conjugated acids and bases are paired with their respective reactants. These pairs are called conjugate acid-base pairs. 

Self-Ionization of Water

→ One water molecule can donate a hydrogen ion to another water molecule and become a dynamic equilibrium because it can act as a Bronsted acid or base


Reaction Equation:

                (l)                       (l)                                                 (aq)                              (aq)


Equilibrium-Constant:

[H3O+] · [OH-] = Kc


Specific ion-product constant for water Kw:

Kc = Kw

Indicators

A pH indicator is a chemical compound that changes color depending on the pH of the solution it is in. Indicators are typically weak acids or bases and undergo a reversible chemical reaction when they gain or lose hydrogen ions (H+). When the indicator is in an acidic environment, it tends to accept H+ ions, shifting the equilibrium towards the protonated form, which has one color. In a base environment, the indicator loses H+ ions, shifting the equilibrium towards the deprotonated form which has a different color. 


Reaction Equation:

Hln (acid form) ⇋ H+ + ln- (base form)


Indicator Chart: 

Tafelwerk S. 137

Titration Curve

Titration Procedure

  1. Clamp the burette into the stand with the opening facing upwards

  2. Fill the burette with the standard solution with a funnel beyond the scale

    1. The tap needs to be closed so that the solution won’t drip out

  3. Drain the excess solution to let out any trapped air and set the standard solution to 0ml

    1. The solution needs to be set at 0ml exactly and the solution will rise slightly to form a meniscus where the volume is shown

  4. Add the standard solution in drops and mix in between

    1. The tap needs to be only carefully turned slightly

    2. Volume of one drop: number of dropsvolume of drops

  5. Clean the burette by draining the standard solution into a beaker and rinse it out with water

    1. Don’t drain it down the sink before asking

  6. Open the tap, turn the burette upside down with a paper towel underneath, and store it away


Unit

Definition

Formula

c

concentration of a substance

nV

n

number of moles of a substance

c V

V

volume of a substance

nc

V(total)

total volume of a solution (acid and base)

Va + Vb

pH

the molar concentration of hydronium-ions in an aqueous solution

-log[H3O+]

14 - pOH

pKa + log([A- (conjugate base)][HA] (acid))

↳ Henderson-Hasselbalch Equation (only for buffer systems that only exist with weak acids)

pOH

the molar concentration of hydroxide-ions in an aqueous solution

-log[OH-]

14 - pH

Ka

acid dissociation constant

[A-] [H3O+][HA]

10-pKa

14 - Kb

Kb

base dissociation constant

[BH+] [OH-][B]

10-pKb

14 - Ka

pKa

acid dissociation constant (Ka) of a solution (defined in Tafelwerk - S. 137)

→ lower pKa = more acid dissociates in the water, a stronger acid

→ higher pKa = less acid dissociates in the water, a weaker acid

pH - log([A-][HA]) (only for weak acids)

-logKa

pKb

base dissociation constant (Kb) of a solution (defined in Tafelwerk - S. 137)

→ lower pKb = more base dissociates in the water, a stronger base

→ higher pKb = less base dissociates in the water, a weaker base

pH - log([BH+][B]) (only for weak bases?)

-logKb

Graph

→ can be used to learn how much of a solution needs to be added to get the desired pH


Stronger vs. Weaker Acids and Bases

Stronger Acids and Bases

Weaker Acids and Bases

  • Dissociate (almost) completely

  • Low pKa/pKb

  • High Ka/Kb

  • High concentration of H+/H3O+ bzw. OH-

  • Low (0-3.5) bzw. high (12-14) pH

  • Dissociate partially

  • High pKa/pKb

  • Low Ka/Kb

  • Low concentration of H+/H3O+ bzw. OH-

  • High (3.5-6) bzw. low (8-11) pH

Titration of a strong acid with a strong base

  • Equivalence point (pH = 7): n(H3O+) (moles of base) = n(OH-) (moles of acid)
    → all hydronium-ions reacted with the hydroxide-ions and form a salt solution (neutralized)

  • Before the equivalence point: pH = -log[H3O+]
    but the concentration changes     pH = -log(Ca Va - Cb VbVa + Vb) = (na - nbVa + Vb)

  • After the equivalence point: all hydronium-ions have reacted = no more H3O+ - can’t calculate pH directly:
    pOH = -log[OH-] = -log(Cb VbV(total))
    pH    = 14 - pOH

Titration of a strong acid with a strong base

  • Equivalence point (pH ~8 → conjugate base is slightly basic): n(H3O+) = n(OH-)
    → all the H3O+ are neutralized

  • Before the equivalence point = buffer region: enzymes take up the H3O+, keeping the pH neutral (~7 pH) Henderson-Hasselbalch-Equation
    pH = pKa + log([A-][HA])

  • Half-equivalence point:
    pH = pKa + log([A-][HA]) → c is the same
    pH = pKa + log(1)
    pH = pKa → 10-pKa = Ka = [A-] [H3O+][HA]
    → solve for [H3O+]
    = pH = -log([H3O+])

  • After the equivalence point:
    pOH = -log[OH-] = -log(Cb VbV(total))
    pH    = 14 - pOH


Buffers

Function

The ability of buffers is to resist changes in pH when an acid or a base is added is a result of their chemical composition. All buffers contain a mixture of a conjugate acid-base pair; either a weak acid (HA) and its conjugate base (A-), or a weak base (B), and its conjugate acid (BH+). Weak acid and weak bases both dissociate slightly in water.


How They Work

A buffer solution resists drastic pH changes better than pure water because it contains an acid and a base that neutralize added hydrogen or hydroxide ions, maintaining stability.


Buffer Capacity

The amount of acid or base that can be added to a buffer solution before a significant change in pH occurs → the buffer becomes ineffective and cannot control the pH


Change in Concentration

By adding a base (OH-), the concentration of the acid goes down to consume the base and the concentration of the conjugate base goes up since it’s a product due to Le Chatelier’s Principles. Similarly, by adding an acid (H3O+), the concentration of the base goes down and the concentration of the conjugate acid goes up. 


Different Types

  • Ethanoic acid - ethanoate ion buffer
    CH3COOH/CH3COO-

  • Dihydrogen phosphate - ion hydrogen phosphate-ion buffer
    H2PO4-/HPO42-

  • Phosphoric acid - dihydrogen phosphate-ion buffer
    H3PO4/H2PO4-

  • Carbonic acid - hydrogen carbonate-ion buffer
    H2CO3/HCO3-

  • Ammonium ion - ammonia buffer
    NH4+/NH3