Assume you dissolve 0.235 g of the weak benzoic acid, C6H5CO2H in enough water to make 100.0 mL of the solution and then titrate the solution with 0.108 M NaOH. Benzoic acid is a monoprotic acid. 1. What is the pH of the original benzoic acid solution before the titration is started?
2. What is the pH when 7.00 mL of the base is added? (Hint: This is in the buffer region.)
3. What is the pH at the equivalence point?

1. pH = 2.98

2. pH = 4.02

3. pH = 8.12

Explanation:

1. Initial molarity of benzoic acid (Molar mass: 122.12g/mol; Ka = 6.14x10⁻⁵) is:

0.235 ₓ (1mol / 122.12g) = 1.92x10⁻³ moles / 0.100L = 0.01924M

The equilibrium of benzoic acid with water is:

C6H5CO2H(aq) + H2O(l) → C6H5O-(aq) + H3O+(aq)

And Ka is defined as the ratio between equilibrium concentrations of products over reactants, thus:

Ka = 6.14x10⁻⁵ = [C6H5O⁻] [H3O⁺] / [C6H5CO2H]

The benzoic acid will react with water until reach equilibrium. And equilibrium concentrations will be:

[C6H5CO2H] = 0.01924 - X

[C6H5O⁻] = X

[H3O⁺] = X

Replacing in Ka:

6.14x10⁻⁵ = [X] [X] / [0.01924 - X]

1.1815x10⁻⁶ - 6.14x10⁻⁵X = X²

1.1815x10⁻⁶ - 6.14x10⁻⁵X - X² = 0

Solving for X:

X = -0.0010→ False solution. There is no negative concentrations

X = 0.0010567M → Right solution.

pH = - log [H3O⁺] and as [H3O⁺] = X:

pH = - log [0.0010567M]

2.

pH of a buffer is determined using H-H equation (For benzoic acid:

pH = pka + log [C6H5O⁻] / [C6H5OH]

pKa = -log Ka = 4.21 and [] could be understood as moles of each chemical

The benzoic acid reacts with NaOH as follows:

C6H5OH + NaOH → C6H5O⁻ + Na⁺ + H₂O

That means NaOH added = Moles C6H5O⁻ And C6H5OH = Initial moles (1.92x10⁻³ moles - Moles NaOH added)

7.00mL of NaOH 0.108M are:

7x10⁻³L ₓ (0.108 mol / L) = 7.56x10⁻⁴ moles NaOH = Moles C₆H₅O⁻

And moles C6H5OH = 1.92x10⁻³ moles - 7.56x10⁻⁴ moles = 1.164x10⁻³ moles C₆H₅OH

Replacing in H-H equation:

pH = 4.21 + log [7.56x10⁻⁴ moles] / [ 1.164x10⁻³ moles]

3. At equivalence point, all C6H5OH reacts producing C6H5O⁻. The moles are 1.164x10⁻³ moles

Volume of NaOH to reach equivalence point:

1.164x10⁻³ moles ₓ (1L / 0.108mol) = 0.011L. As initial volume was 0.100L, In equivalence point volume is 0.111L and concentration of C₆H₅O⁻ is:

1.164x10⁻³ moles / 0.111L = 0.01049M

Equilibrium of  C₆H₅O⁻ with water is:

C₆H₅O⁻(aq) + H₂O(l) ⇄  C₆H₅OH(aq) + OH⁻(aq)

Kb = [C₆H₅OH] [OH⁻]/ [C₆H₅O⁻]

Kb = kw / Ka = 1x10⁻¹⁴ / 6.14x10⁻⁵ = 1.63x10⁻¹⁰

Equilibrium concentrations of the species are:

C₆H₅O⁻ = 0.01049M - X

C₆H₅OH = X

OH⁻ = X

Replacing in Kb expression:

1.63x10⁻¹⁰ = X² / 0.01049- X

1.71x10⁻¹² - 1.63x10⁻¹⁰X - X² = 0

Solving for X:

X = -1.3x10⁻⁶ → False solution

X = 1.3076x10⁻⁶ → Right solution

[OH⁻] =  1.3076x10⁻⁶

as pOH = -log [OH⁻]

pOH = 5.88

And pH = 14 - pOH