Question

You make 1.00 \(\mathrm{L}\) of a buffered solution \((\mathrm{pH}=4.00)\) by mixing acetic acid and sodium acetate. You have 1.00\(M\) solutions of each component of the buffered solution. What volume of each solution do you mix to make such a buffered solution?

Short answer

To make 1.00 L of a buffered solution with a pH of 4.00, mix approximately 0.854 L (854 mL) of a 1.00 M acetic acid solution and 0.146 L (146 mL) of a 1.00 M sodium acetate solution.

Step-by-step solution

Write down the Henderson-Hasselbalch equation

The equation is given by: \(pH = pKa + log10(\frac{[A-]}{[HA]})\) Here, pH is the desired pH of the buffered solution, pKa is the acidity constant of the weak acid, [HA] is the molar concentration of the weak acid, and [A-] is the molar concentration of the conjugate base.

Find the pKa of acetic acid

The pKa value of acetic acid is 4.76. We will use this value in the Henderson-Hasselbalch equation to find the ratio of [A-]/[HA].

Plug in the given pH value and pKa value into the equation

Given, pH = 4.00 and pKa = 4.76. Substituting these values into the equation, we get: \(4.00 = 4.76 + log10(\frac{[A-]}{[HA]})\)

Solve for the ratio of [A-]/[HA]

Subtract 4.76 from both sides: \(-0.76 = log10(\frac{[A-]}{[HA]})\) Now, take the antilogarithm of both sides: \(\frac{[A-]}{[HA]} = 10^{-0.76}\) Evaluate the expression on the right: \(\frac{[A-]}{[HA]} = 0.17\)

Calculate the volume of each solution

We know that the total volume of the buffered solution is 1.00 L. Let's assume that we mix V1 liters of acetic acid (1.00 M) and V2 liters of sodium acetate (1.00 M) to get this volume. Then: \(V1 + V2 = 1.00 \, L\) Using the [A-]/[HA] ratio, we can write the following equation: \(\frac{1.00*V2}{1.00*V1} = 0.17\) Now, we have two equations and two variables (V1 and V2).

Solve for V1 and V2

From the second equation, we get \(V2 = 0.17*V1\) Substituting this expression in the first equation \(V1 + 0.17*V1 = 1.00 \, L\) \(1.17*V1 = 1.00 \, L\) Divide both sides by 1.17 to get the value of V1: \(V1 = \frac{1.00}{1.17} \, L \approx 0.854 \, L\) Now, substitute the value of V1 back into the second equation to get the value of V2: \(V2 = 0.17*0.854 \, L \approx 0.146 \, L\)

Provide the answer

To make 1.00 L of a buffered solution with a pH of 4.00, we should mix approximately 0.854 L (854 mL) of a 1.00 M acetic acid solution and 0.146 L (146 mL) of a 1.00 M sodium acetate solution.

Key concepts

Henderson-Hasselbalch equation

The Henderson-Hasselbalch equation is a widely used formula in chemistry. It's essential for calculating the pH of a buffered solution. The equation is:
\[ pH = pKa + \log_{10}\left(\frac{[A^-]}{[HA]}\right) \]
In this equation:

• pH represents the acidity level we aim to achieve in the buffered solution.
• pKa is the dissociation constant specific to the acidic component in the buffer.
• [A^-] indicates the concentration of the conjugate base.
• [HA] stands for the concentration of the weak acid.

A buffered solution resists changes in pH, maintaining stability even when small amounts of acids or bases are added. By adjusting the ratio of the components in the buffer using the Henderson-Hasselbalch equation, we determine how the equilibrium shifts to maintain the desired pH. This balance between [A-] and [HA] is what makes buffer solutions incredibly useful in various chemical and biological applications.

Acid-Base Chemistry

Acid-base chemistry plays a crucial role in the creation of buffer solutions. It involves understanding how acids and bases interact in a solution. An acid donates protons (H⁺) to a base, which accepts them. This interaction is key to forming a buffer.

• Weak Acid: A weak acid, like acetic acid, only partially dissociates in a solution. It doesn't completely release its hydrogen ions.
• Conjugate Base: For acetic acid, the conjugate base is acetate (CH₃COO⁻). This ion results from the partial dissociation of the weak acid.

When creating a buffered solution, you mix a weak acid with its conjugate base. This unique combination can effectively stabilize the pH of the solution. If an acid is added, the conjugate base will neutralize some of the excess H⁺, while if a base is added, the weak acid can offer additional H⁺ ions to replace those lost, preventing significant pH fluctuations. Understanding these interactions is vital when adjusting buffer components to target a specific pH level.

pH Calculation

Calculating pH is a foundational skill in chemistry, especially when working with buffers. The pH scale, ranging from 0 to 14, measures acidity or basicity — with 7 being neutral.

Find the pKa: This value is intrinsic to your acid and crucial for your calculations. For acetic acid, it's 4.76.

Determine the Concentrations: You need the molar concentrations of both the weak acid and its conjugate base.

Apply the Equation: Substitute known values into the Henderson-Hasselbalch equation to find the desired ratio of [A-] to [HA].

When dealing with buffered solutions aimed at a specific pH, this ratio is key. For instance, in a solution where the target pH is 4.00 and pKa is 4.76, using the equation we find a ratio of \( \frac{[A^-]}{[HA]} = 0.17 \). This informs us of the specific volumes of acetic acid and sodium acetate needed – a practical example of pH calculation in real-world applications.