Problem 78 - General Chemistry

Question

A buffer is prepared by mixing \(525 \mathrm{~mL}\) of \(0.50 \mathrm{M}\) formic acid, \(\mathrm{HCHO}_{2}\), and \(475 \mathrm{~mL}\) of \(0.50 \mathrm{M}\) sodium formate, \(\mathrm{NaCHO}_{2}\). Calculate the pH. What would be the pH of \(85 \mathrm{~mL}\) of the buffer to which \(8.6 \mathrm{~mL}\) of \(0.15 \mathrm{M}\) hydrochloric acid had been added?

Step-by-Step Solution

Answer

Initial pH is 3.75; after adding HCl, the pH is 3.70.

Step 1: Understand the Problem

You are given a buffer solution made by mixing formic acid (weak acid) and its conjugate base, sodium formate. You need to calculate the initial pH of the buffer and the pH after adding hydrochloric acid to a portion of the buffer.

Step 2: Calculate Initial pH of the Buffer

Use the Henderson-Hasselbalch equation, which is \[pH = pK_a + \log\left(\frac{[A^-]}{[HA]}\right)\]For formic acid, the \(pK_a\) is approximately 3.75. Since the concentrations of formic acid and sodium formate are equal (\(0.50 M\)), the \(\log\left(\frac{[A^-]}{[HA]}\right) = \log(1) = 0\).Thus, \(pH = 3.75 + 0 = 3.75\).

Step 3: Calculate Moles in the Initial Buffer

Calculate the total moles of formic acid and sodium formate.Moles of formic acid = Volume (L) \(\times\) Molarity \(= 0.525 \times 0.50 = 0.2625\) moles.Moles of sodium formate = Volume (L) \(\times\) Molarity \(= 0.475 \times 0.50 = 0.2375\) moles.

Step 4: Calculate pH Change Due to HCl Addition

Determine moles of HCl added:\[\text{Moles of } \mathrm{HCl} = 8.6 \times 10^{-3} \text{ L} \times 0.15 \text{ M} = 0.00129 \text{ moles}\]The reaction of HCl with formate ion produces formic acid:\(\mathrm{HCOO}^- + \mathrm{HCl} \rightarrow \mathrm{HCOOH} + \mathrm{Cl}^-\).Subtract moles of HCl from sodium formate's moles, and add to formic acid's moles:- New moles of formate: \(0.2375 - 0.00129 = 0.23621\) moles.- New moles of formic acid: \(0.2625 + 0.00129 = 0.26379\) moles.

Step 5: Calculate New pH After Addition of HCl

Use the Henderson-Hasselbalch equation again,\[pH = pK_a + \log\left(\frac{0.23621}{0.26379}\right)\approx 3.75 + \log\left(0.8955\right)\approx 3.75 - 0.0481 = 3.7019\]

Key Concepts

Formic Acid

Formic acid, chemically known as \( ext{HCHO}_2\), is a simple carboxylic acid that is naturally found in the stings and bites of many insects. It is a weak acid, which means it does not completely dissociate in water. This incomplete dissociation is an important concept when dealing with buffer solutions. In our exercise, formic acid is paired with its conjugate base, sodium formate \( ext{NaCHO}_2\), to create a buffer solution. Buffers are used to maintain a stable pH in a solution despite the addition of an acid or a base. Understanding how formic acid behaves as a part of a buffer is crucial for calculating the changes in pH when external substances are added.

Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation is a fundamental tool for understanding the pH of buffer solutions. This equation is given by \(pH = pK_a + \log\left(\frac{[A^-]}{[HA]}\right)\), where \(pK_a\) is the acid dissociation constant, \(\text{[A^-]}\) is the concentration of the conjugate base, and \(\text{[HA]}\) is the concentration of the weak acid. In buffer solutions, this equation allows us to calculate the pH, knowing the concentrations of the acid and its conjugate base. In the context of the exercise, by understanding the ratio of formic acid and formate ion in the solution, we apply this equation to determine the initial pH of the buffer before and after the hydrochloric acid is added.

pH Calculation

Calculating pH is an essential skill in both chemistry studies and real-world applications. The pH scale measures how acidic or basic a solution is, on a scale from 0 to 14. Lower values represent acidic solutions, while higher values represent alkaline solutions. For the formic acid buffer system, the initial pH was determined using the Henderson-Hasselbalch equation, considering that the concentrations of formic acid and sodium formate were equal, resulting in a zero term for the \(\log\) component of the equation. Additionally, after adding hydrochloric acid, the balance between formic acid and formate ions shifted, slightly lowering the pH of the solution. This exemplifies how chemical reactions affect buffer solutions, maintaining as stable a pH as possible.

Weak Acids and Bases

Weak acids, like formic acid, and their conjugate bases play a vital role in buffer solutions. Unlike strong acids and bases that completely dissociate in water, weak acids only partially ionize. This characteristic provides buffers their ability to resist changes in pH. The interaction between formic acid and sodium formate in a buffer highlights this concept; each component neutralizes small amounts of added acids or bases, stabilizing the pH. Understanding the behavior of weak acids and bases, their dissociation, and how they form buffers is key to solving the exercise's pH calculations and comprehending why buffers effectively maintain pH levels in various chemical and biological systems.