Question

A buffered solution is prepared containing acetic acid, \(\mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}\) and sodium acetate, \(\mathrm{NaC}_{2} \mathrm{H}_{3} \mathrm{O}_{2},\) both at \(0.5 \mathrm{M}\). Write a chemical equation showing how this buffered solution would resist a decrease in its \(\mathrm{pH}\) if a few drops of aqueous strong acid \(\mathrm{HCl}\) solution were added to it. Write a chemical equation showing how this buffered solution would resist an increase in its \(\mathrm{pH}\) if a few drops of aqueous strong base \(\mathrm{NaOH}\) solution were added to it.

Short answer

When a strong acid (HCl) is added to the buffered solution, it reacts with acetate ions to neutralize the added protons and resist the decrease in pH: \[HCl_{(aq)} + C_2H_3O_2^-_{(aq)} \rightarrow HC_2H_3O_2_{(aq)} + Cl^-_{(aq)}\] When a strong base (NaOH) is added to the buffered solution, it reacts with acetic acid to neutralize the added hydroxide ions and resist the increase in pH: \[NaOH_{(aq)} + HC_2H_3O_2_{(aq)} \rightarrow NaC_2H_3O_2_{(aq)} + H_2O_{(l)}\]

Step-by-step solution

Understand the concept of a buffer solution

A buffer solution is a mixture of a weak acid and its conjugate base, or a weak base and its conjugate acid. Buffer solutions resist changes in pH when a small amount of a strong acid or a strong base is added. In this case, the buffer solution is prepared using acetic acid (a weak acid) and sodium acetate (its conjugate base).

Write the chemical equation for acetic acid ionization

The ionization of acetic acid in water can be represented by the following equilibrium equation: \[HC_2H_3O_2_{(aq)} + H_2O_{(l)} \rightleftharpoons H_3O^+_{(aq)} + C_2H_3O_2^-_{(aq)}\]

Write the chemical equation when strong acid (HCl) is added

When strong acid HCl is added to the buffered solution, it will react with acetate ions (the conjugate base) present in the buffer. This will help to neutralize the added protons and resist the decrease in pH: \[HCl_{(aq)} + C_2H_3O_2^-_{(aq)} \rightarrow HC_2H_3O_2_{(aq)} + Cl^-_{(aq)}\] Here, the added HCl reacts with the acetate ions, converting them back into acetic acid and simultaneously generating chloride ions. The balanced equation shows how the buffer works to reduce the impact of the added acid on the solution's pH.

Write the chemical equation when strong base (NaOH) is added

When strong base NaOH is added to the buffered solution, it will react with acetic acid (the weak acid) present in the buffer. This will help to neutralize the added hydroxide ions and resist the increase in pH: \[NaOH_{(aq)} + HC_2H_3O_2_{(aq)} \rightarrow NaC_2H_3O_2_{(aq)} + H_2O_{(l)}\] Here, the added NaOH reacts with the acetic acid, converting it into sodium acetate and water. The balanced equation shows how the buffer works to minimize the impact of the added base on the solution's pH.

Key concepts

Acetic Acid

Acetic acid is a weak acid, which means it does not completely dissociate in water. It is represented by the chemical formula \( HC_2H_3O_2 \).
In a buffered solution, it plays a pivotal role, as it helps to moderate pH changes by reacting with bases. When dissolved in water, acetic acid partially ionizes into hydrogen ions \( H_3O^+ \) and acetate ions \( C_2H_3O_2^- \).
As part of a buffer system, acetic acid's ability to convert back and forth between its molecular and ionic forms is crucial.Understanding acetic acid's equilibrium in solution provides insights into its buffering action:

• The ionization equilibrium can be expressed as:
  \( HC_2H_3O_2_{(aq)} + H_2O_{(l)} \rightleftharpoons H_3O^+_{(aq)} + C_2H_3O_2^-_{(aq)} \)
  This reversible reaction allows the buffer to minimize pH changes.
• When a strong base like \( NaOH \) is added, the extra hydroxide ions are neutralized by acetic acid, forming water and sodium acetate:
  \( NaOH_{(aq)} + HC_2H_3O_2_{(aq)} \rightarrow NaC_2H_3O_2_{(aq)} + H_2O_{(l)} \)

Sodium Acetate

Sodium acetate acts as the conjugate base in a buffer solution containing acetic acid. Its chemical formula is \( NaC_2H_3O_2 \).
Sodium acetate readily dissociates in water into sodium ions \( Na^+ \) and acetate ions \( C_2H_3O_2^- \).
These acetate ions are crucial in the buffer's ability to resist pH changes.The role of sodium acetate in the buffer solution includes:

• Acting as a proton acceptor, which means it can neutralize added acids like \( HCl \).
  The reaction involves the acetate ions combining with the additional protons to form acetic acid again:
  \( HCl_{(aq)} + C_2H_3O_2^-_{(aq)} \rightarrow HC_2H_3O_2_{(aq)} + Cl^-_{(aq)} \)
• This process helps maintain the solution's pH by preventing a significant increase in hydrogen ion concentration.

Sodium acetate, through its ions, ensures the buffer can suppress pH fluctuations effectively.

pH Change

Buffer solutions are specifically designed to resist pH changes. The mixture of acetic acid and sodium acetate helps manage these changes when acids or bases are added.
The mechanism involves the equilibrium between the weak acid and its conjugate base, which allows the buffer to "absorb" excess hydrogen or hydroxide ions.
When small quantities of a strong acid like \( HCl \) are added, the buffer consumes the added hydrogen ions:

• The acetate ions react with the hydrogen ions to form acetic acid, as shown:
  \( HCl_{(aq)} + C_2H_3O_2^-_{(aq)} \rightarrow HC_2H_3O_2_{(aq)} + Cl^-_{(aq)} \)
• This limits the increase in hydrogen ion concentration, thereby resisting a drop in pH.

Conversely, when a strong base such as \( NaOH \) is introduced:

• The hydroxide ions react with acetic acid to create water and acetate ions:
  \( NaOH_{(aq)} + HC_2H_3O_2_{(aq)} \rightarrow NaC_2H_3O_2_{(aq)} + H_2O_{(l)} \)
• This prevents a rise in pH by neutralizing the excess base.

Understanding how buffer solutions work helps us appreciate why they are important in various chemical and biological contexts, helping maintain stable environments.