Answer:
a. 9.34
b. 9.06
c. 6 mL
Explanation:
Part a.
The pH of a buffer solution is given by the Henderson-Hasselbach equation:
pH = pKa + log [A⁻] / [HA]
where pKa is the negative log of Ka for the weak acid H₃BO₃ and can be obtained from reference tables, [A⁻] and [HA] are the concentrations of the weak conjugate base H₂BO₃⁻ and and the weak acid H₃BO₃ respectively.
Proceeding with the calculations, we have
Ka H₃BO₃ = 5.80 x 10⁻¹⁰
pKa = - log (5.80 x 10⁻¹⁰) = 9.24
[H₂BO₃⁻ ] = 0.250 M
[H₃BO₃] = 0.200 M
pH = 9.24 + log (0.250/0.200) = 9.34
part b.
When 1.0 mL of 6.0 M HCl is added to the buffer , we know that it will react with the conjugate base in the buffer doing what buffers do: keeping the pH within a small range according to the capacity of the buffer:
H₂BO₃⁻ + H⁺ ⇒ H₃BO₃
So lets calculate the new concentrations of acid and conjugate base after reaction and apply the Henderson equation again:
Initial # of moles:
H₃BO₃ = 0.300 L x 0.200 mol/L = 0.06 mol
H₂BO₃⁻ = 0.200 L x 0.250 mol/L = 0.05 mol
mol HCl = 0.001 L x 6.0 mol/L = 0.006 mol
After reaction
H₃BO₃ = 0.06 mol + 0.006 mol = 0.066 mol
H₂BO₃⁻ = 0.05 mol - 0.006 mol = 0.044 mol
New pH
pH = 9.24 + log ( 0.044 / 0.66 ) = 9.06
Note: There is no need to calculate the new concentrations since we have a quotient in the expression where the volumes cancel each other.
Part c.
We will be using the Henderson-Hasselbach equationm again but now to calculate ratio [H₂BO₃⁻] / [HBO₃] that will give us a pH of 10.00. Thenwe will make use of the stoichiometry of the reaction to calculate the volume of NaOH required.
pH = pKa + log[H₂BO₃⁻]-[H₃BO₃]
10.00 = 9.24 + log [H₂BO₃⁻]-[H₃BO₃]
⇒[H₂BO₃⁻] / [H₃BO₃] = antilog (0.76) = 5.75
Initiall # moles:
mol H₃BO₃ = 0.06 mol
mol H₂BO₃ = 0.05 mol
after consumption of H₃BO₃ from the reaction with NaOH:
H₃BO₃ + NaOH ⇒ Na⁺ + H₂BO₃⁻ + H₂O
mol H₃BO₃ = 0.06 - x
mol H₂BO₃⁻ = 0.05+ x mol
Therefore we have the algebraic expression:
[H₂BO₃⁻] / [H₃BO₃] = mol H₂BO₃⁻ / mol HBO₃ = 5.75
( again volumes cancel each other)
0.05 + x / 0.06 - x = 5.75 ⇒ x = 0.044
SO 0.037 mol NaOH were required, and since we know Molarity = mol / V we can calculate the volume of 6.0 M NaOH added:
V = 0.044 mol / 6.0 mol/L = 0.0073 L
V = 7.3 mL
