Problem 150 - General Chemistry

Question

A buffer solution is prepared by mixing equal volumes of \(0.10 \mathrm{M} \mathrm{NaNO}_{2}\) and \(0.10 \mathrm{M} \mathrm{HNO}_{2}\) solutions.

Step-by-Step Solution

Answer

The pH of the buffer solution is 3.25.

Step 1: Understand the Concept of Buffers

A buffer solution is composed of a weak acid and its conjugate base in similar amounts. In this exercise, the weak acid is HNO₂, and its conjugate base is NO₂⁻, which comes from NaNO₂.

Step 2: Determine the pKa of HNO₂

The pKa value of HNO₂ (nitrous acid) is required to calculate the pH of the buffer solution. The pKa of HNO₂ is approximately 3.25.

Step 3: Apply the Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation is used to calculate the pH of a buffer:\[pH = pKa + \log\left(\frac{[\text{conjugate base}]}{[\text{acid}]}\right)\]For this solution, both [HNO₂] and [NO₂⁻] are 0.10 M, so the ratio \( \frac{[\text{NO}_2^-]}{[\text{HNO}_2]} \) is 1.

Step 4: Calculate the pH

Substitute the known values into the equation:\[pH = 3.25 + \log(1)\]Since \( \log(1) = 0 \), the pH is simply the pKa, which is 3.25.

Key Concepts

Henderson-Hasselbalch Equation

The Henderson-Hasselbalch Equation is a cornerstone for calculating the pH of buffer solutions. This formula is incredibly useful when working with weak acids and their conjugate bases, as it simplifies the process of pH calculation. The equation itself is:\[pH = pKa + \log\left(\frac{[\text{conjugate base}]}{[\text{acid}]\right)\]

• pH: The measure of acidity or basicity of a solution.
• pKa: The negative logarithm of the acid dissociation constant, revealing the strength of the acid.
• Conjugate base and acid concentration: These are typically in molarity (M), showing the amounts of the components in solution.

In a buffer solution, these parameters are critical because they determine the ability of the buffer to maintain a stable pH when acids or bases are added. By substituting the known values into this equation, one can easily find the pH of the buffer, which illustrates why this formula is a go-to tool for chemists.

pKa value

The pKa value is a key concept when working with acids and buffers. It represents the acid dissociation constant, which helps us understand the strength of an acid. A smaller pKa value shows a stronger acid because it means the acid dissociates more completely in solution.
The pKa is determined from the acid's ionization in water, and the process can be expressed as:\[HA \rightleftharpoons H^+ + A^-\]Where:

• HA: Represents the weak acid.
• H⁺: The acid's protons.
• A⁻: The conjugate base.

For our buffer, the pKa of HNO₂ is approximately 3.25. This specific value allows chemists to calculate the pH of solutions containing HNO₂ and its conjugate base, NO₂⁻, with confidence.

Weak Acid and Conjugate Base

In buffer solutions, weak acids and their conjugate bases play a pivotal role. *Weak acids* are those that do not completely dissociate in water, creating an equilibrium between the acid form and the generated ions. The conjugate base is what remains after the acid has donated a proton.

Consider HNO₂ as an example:

• HNO₂ (Weak Acid): Has a slight tendency to release a H⁺ ion, leading to the formation of its conjugate base.
• NO₂⁻ (Conjugate Base): Formed when HNO₂ loses a hydrogen ion.

The equilibrium created between a weak acid and its conjugate base allows the buffer solution to resist changes in pH, providing stability against acids and bases added to the system.

pH Calculation

Calculating pH in buffer solutions often centers around implementing the Henderson-Hasselbalch equation. This simplifies what might seem to be a complex problem with equilibria into straightforward mathematics. For the described buffer with equal concentrations of HNO₂ and NO₂⁻:

• Concentration of HNO₂ [acid]: 0.10 M
• Concentration of NO₂⁻ [conjugate base]: 0.10 M

Substitute these concentrations into the equation:\[pH = 3.25 + \log\left(\frac{0.10}{0.10}\right)\]Since the logarithm of 1 is zero, the calculation simplifies to the pKa of the acid, which is 3.25. Thus, the pH of this buffer is 3.25, demonstrating how the balance of weak acids and their conjugate bases help manage pH effectively.