Calculate the pH of a 1 L buffer solution that contains 0.050 moles of acetic acid and 0.040 moles of sodium acetate to which 0.020 moles of NaOH has been added.
To calculate the pH of a buffer solution, we need to consider the Henderson-Hasselbalch equation:
pH = pKa + log ([A-] / [HA])
In this equation, pKa represents the negative logarithm (base 10) of the acid dissociation constant (Ka) of the weak acid. [A-] and [HA] represent the concentrations of the conjugate base and weak acid, respectively.
Step 1: Determine the pKa value of acetic acid:
The pKa value of acetic acid is 4.76.
Step 2: Calculate the concentrations of the conjugate base ([A-]) and weak acid ([HA]):
In this case, the weak acid is acetic acid (CH3COOH) and the conjugate base is sodium acetate (CH3COONa). The total volume of the solution is 1 liter.
Concentration of acetic acid ([HA]) = moles of acetic acid / volume of solution
= 0.050 moles / 1 L
= 0.050 M
Concentration of sodium acetate ([A-]) = moles of sodium acetate / volume of solution
= 0.040 moles / 1 L
= 0.040 M
Step 3: Take into account the addition of NaOH:
Since 0.020 moles of NaOH has been added, it reacts with acetic acid to form water and sodium acetate.
NaOH + CH3COOH → CH3COONa + H2O
This reaction consumes 0.020 moles of acetic acid, which means the final concentration of acetic acid will be reduced.
Final concentration of acetic acid ([HA]final) = [HA]initial - moles of added NaOH / volume of solution
= 0.050 M - 0.020 moles / 1 L
= 0.030 M
The concentration of sodium acetate ([A-]) remains unchanged since it is a product of the reaction.
Step 4: Plug the values into the Henderson-Hasselbalch equation:
pH = pKa + log ([A-] / [HA]final)
= 4.76 + log (0.040 M / 0.030 M)
= 4.76 + log (1.33)
= 4.76 + 0.123
= 4.883
Therefore, the pH of the buffer solution after the addition of NaOH is approximately 4.883.