Question

\( A buffer is prepared by adding \)20.0 \mathrm{~g}\( of sodium acetate \)\left(\mathrm{CH}_{3} \mathrm{COONa}\right)\( to \)500 \mathrm{~mL}\( of a \)0.150 \mathrm{M}\( acetic acid \)\left(\mathrm{CH}_{3} \mathrm{COOH}\right)$ solution. (a) Determine the pH of the buffer. (b) Write the complete ionic equation for the reaction that occurs when a few drops of hydrochloric acid are added to the

Short answer

The pH of the buffer is 5.92. When hydrochloric acid is added to the buffer, the resulting complete ionic equation is CH3COO¯ (aq) + H⁺ (aq) → CH3COOH (aq).

Step-by-step solution

Calculate the concentration of the sodium acetate

Given that 20.0 g of sodium acetate has been used, we can find the molar concentration of sodium acetate using its molar mass. Molar mass of sodium acetate (CH3COONa) = 12.01 + 3(1.01) + 16 + 12.01 + 3(1.01) + 22.99 = 82.03 g/mol Mass of sodium acetate = 20.0 g Volume of the solution = 500 mL Moles of sodium acetate = \( \frac{20.0}{82.03} \) = 0.2436 mol So, the concentration of sodium acetate = \( \frac{0.2436}{0.5}\) = 0.4872 M

Use the Henderson-Hasselbalch equation to find the pH of the buffer

First, we need to find the pKa of acetic acid. The Ka of acetic acid is 1.8 x \(10^{-5}\). To find pKa, use the formula: \(pK_{a} = -log_{10}K_{a}\) \(pK_{a} = -log_{10}(1.8 \times 10^{-5}) = 4.74\) Now we can use the Henderson-Hasselbalch equation: \(pH = pK_{a} + log_{10}\frac{[\text{Conjugate Base}]}{[\text{Acid}]}\) \(pH = 4.74 + log_{10}\frac{0.4872}{0.150}\) \(pH = 4.74 + 1.18 = 5.92\) Therefore, the pH of the buffer is 5.92.

Write the complete ionic equation for the reaction when hydrochloric acid is added

When a few drops of hydrochloric acid (HCl) are added to the buffer solution, the following reaction occurs: CH3COO¯ (aq) + H⁺ (aq) → CH3COOH (aq) The complete ionic equation is: CH3COO¯ (aq) + H⁺ (aq) → CH3COOH (aq) In conclusion, the pH of the buffer is 5.92. When hydrochloric acid is added to the buffer, the resulting complete ionic equation is CH3COO¯ (aq) + H⁺ (aq) → CH3COOH (aq).

Key concepts

Sodium Acetate

Sodium acetate, which is represented as \( \mathrm{CH}_3\mathrm{COONa} \), is a common component used in buffer solutions. It's composed of sodium ions and acetate ions. When you dissolve sodium acetate in water, it disassociates into these ions.
Sodium acetate is used in buffers due to its ability to maintain a stable pH when acids or bases are added. Here's how it works: the acetate ion \( (\mathrm{CH}_3\mathrm{COO}^-) \) acts as a conjugate base that can neutralize added acids.
This characteristic makes sodium acetate a valuable compound in both laboratory and industrial applications. It serves to stabilize pH in processes such as dye production, textile manufacturing, and biological experiments.

Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation is a formula that relates the pH of a buffer solution to the concentration of acid and its conjugate base. This equation is essential for understanding how buffers resist changes in pH. The formula is:
\[pH = pK_{a} + \log_{10} \left(\frac{[\text{Conjugate Base}]}{[\text{Acid}]\right)}\]
In our case, it helps us find the pH of a solution containing acetic acid and sodium acetate. The \( pK_{a} \) is derived from the acid dissociation constant \( K_a \), which measures the strength of an acid.
By knowing these values, you can use the equation to predict the pH of the buffer based on the concentration of the acid and the conjugate base it includes. This is particularly useful for preparing accurate buffer solutions for various chemical reactions.

Ionic Equation

An ionic equation represents chemical reactions at the ionic level. These equations help demonstrate the species involved in the reaction in their ionic forms.
When hydrochloric acid is added to the sodium acetate buffer, the acetate ion \( (\mathrm{CH}_3\mathrm{COO}^-) \) reacts with the hydrogen ion \( (\mathrm{H}^+) \) from the acid. This results in the formation of acetic acid \( (\mathrm{CH}_3\mathrm{COOH}) \).
The complete ionic equation for this interaction is:

• \( \mathrm{CH}_3\mathrm{COO}^- (aq) + \mathrm{H}^+ (aq) \rightarrow \mathrm{CH}_3\mathrm{COOH} (aq) \)

This equation illustrates the neutralization process where the buffer effectively reduces the changes in pH by converting strong acidic ions into a weak acid, managing the solution's overall pH stability.

Acetic Acid

Acetic acid, known chemically as \( \mathrm{CH}_3\mathrm{COOH} \), is a weak acid commonly found in vinegar. Its weak nature means that it does not completely dissociate in water, making it perfect for buffers.
In buffer solutions, acetic acid provides the necessary acidic component. It pairs with the conjugate base acetate ion \((\mathrm{CH}_3\mathrm{COO}^-)\) to resist changes in pH.
Weak acids like acetic acid are effective in buffers because they can donate protons and react with added bases, thereby diminishing any significant shift in pH. The ability to slightly ionize helps maintain this stability, crucial in various chemical and biological reactions.
Understanding acetic acid's role in buffers underscores its importance in both everyday emulsions like vinegar and sophisticated laboratory reactions.