Determine the pH of a buffer that is prepared by mixing 100 mL of 0.2 M NaOH and 150 mL of 0.4 M acetic acid assuming the volume is additive. Calculate the pH of the solution when 0.5 mL of 1 M of HCl was added hence calculate the buffer capacity.(Given:pKa of acetic acid = 4.76 at 25C
6,1 molperdm3
To determine the pH of the buffer solution, we can use the Henderson-Hasselbalch equation:
pH = pKa + log ([A-]/[HA])
where pKa is the logarithmic acidity constant of the acid, [A-] is the concentration of the conjugate base, and [HA] is the concentration of the acid.
First, let's calculate the concentrations of acetic acid (CH3COOH) and its conjugate base acetate (CH3COO-) in the buffer solution.
Given:
Volume of NaOH (base): 100 mL
Concentration of NaOH: 0.2 M
Calculate the amount of NaOH in moles:
moles of NaOH = volume (in L) × concentration
= 0.1 L × 0.2 M
= 0.02 moles
Since NaOH is a strong base, it will completely dissociate in water to form Na+ and OH-. So, the concentration of OH- in the solution is also 0.02 moles.
Given:
Volume of acetic acid: 150 mL
Concentration of acetic acid: 0.4 M
Calculate the amount of acetic acid in moles:
moles of acetic acid = volume (in L) × concentration
= 0.15 L × 0.4 M
= 0.06 moles
Now, based on the balanced equation for the dissociation of acetic acid, we can determine that 1 mole of acetic acid will produce 1 mole of acetate (CH3COO-) ions.
Therefore, the concentration of acetate (CH3COO-) in the solution will also be 0.06 moles.
Now, we can calculate the pH using the Henderson-Hasselbalch equation.
pH = pKa + log ([A-]/[HA])
= 4.76 + log (0.06/0.06)
= 4.76 + log(1)
= 4.76
The pH of the buffer solution, before the addition of HCl, is 4.76.
To calculate the buffer capacity, we need to consider the change in pH after adding an acid (HCl). The buffer capacity is a measure of how well the buffer can resist changes in pH.
Given:
Volume of HCl added: 0.5 mL
Concentration of HCl: 1 M
Calculate the amount of HCl in moles:
moles of HCl = volume (in L) × concentration
= 0.0005 L × 1 M
= 5 x 10^-4 moles
Since HCl is a strong acid, it will fully dissociate in water to form H+ and Cl- ions. So, the concentration of H+ in the solution will also be 5 x 10^-4 moles.
Now, we will calculate the new concentration of the acetate and acetic acid in the buffer solution after the addition of HCl.
The addition of HCl will react with the acetate ions (CH3COO-) in the buffer solution to form acetic acid (CH3COOH) and water. The reaction can be represented as follows:
CH3COO- + H+ → CH3COOH
Since the amount of H+ introduced from HCl is lesser compared to the existing concentration of CH3COO-, we can assume that the concentration of acetate will decrease by the same amount as the concentration of H+ introduced.
Therefore, the new concentration of acetate (CH3COO-) in the buffer solution is:
new [A-] = initial [A-] - moles of H+
= 0.06 moles - 5 x 10^-4 moles
= 0.0595 moles
The change in acetate concentration is 5 x 10^-4 moles.
The buffer capacity can be calculated by dividing the change in moles of the acid (acetic acid) by the change in pH.
buffer capacity = (change in moles of acid) / (change in pH)
= (5 x 10^-4 moles) / (4.76 - 4.76)
= (5 x 10^-4)
Therefore, the buffer capacity is 5 x 10^-4 moles.