Answer:
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
