HAc is the abbreviation for acetic acid (CH3COOH); it is by random chance that the numerical value of the acid dissociation constant for acetic acid is equal to the base hydrolysis constant of ammonia. 1.00L of buffer is prepared in which [HAc] = 0.35M and [NaAc] = 0.75M. What is the pH of this buffer?
Ka,HAc = 1.8×10^-5 Kb,NH3 = 1.8×10^-5
The correct answer and explanation is :
To determine the pH of the buffer solution consisting of acetic acid (HAc) and sodium acetate (NaAc), we use the Henderson-Hasselbalch equation:
[
\text{pH} = \text{pKa} + \log \left( \frac{[\text{A}^-]}{[\text{HA}]} \right)
]
where:
- pKa is the negative logarithm of the acid dissociation constant ( K_a ).
- [A⁻] is the concentration of the conjugate base (sodium acetate, NaAc).
- [HA] is the concentration of the weak acid (acetic acid, HAc).
Step 1: Calculate pKa of Acetic Acid
[
\text{pKa} = -\log(1.8 \times 10^{-5})
]
[
\text{pKa} \approx 4.74
]
Step 2: Apply the Henderson-Hasselbalch Equation
Given:
- [HAc] = 0.35 M
- [NaAc] = 0.75 M
[
\text{pH} = 4.74 + \log \left( \frac{0.75}{0.35} \right)
]
[
\text{pH} = 4.74 + \log (2.14)
]
[
\text{pH} = 4.74 + 0.33
]
[
\text{pH} \approx 5.07
]
Explanation
The buffer solution is made up of a weak acid (acetic acid) and its conjugate base (acetate ion from sodium acetate). The pH of the buffer is determined using the Henderson-Hasselbalch equation, which calculates the pH based on the acid/base ratio.
In this case:
- Acetic acid partially ionizes in water.
- Sodium acetate completely dissociates into acetate ions (CH₃COO⁻) and Na⁺.
- The higher concentration of acetate ions shifts the equilibrium to the left, resisting pH changes when small amounts of acid or base are added.
Since [A⁻] > [HA], the solution is slightly more basic than the pKa of acetic acid, giving a final pH of 5.07.
The pH of the buffer solution is 5.07, as determined using the Henderson-Hasselbalch equation. The pie chart visually represents the composition of the buffer system, showing the relative amounts of acetic acid (HAc) and sodium acetate (NaAc), which together maintain the buffer’s resistance to pH changes.