Question

Use the Henderson-Hasselbalch equation to calculate the \(\mathrm{pH}\) of a buffer solution that is \(0.25 \mathrm{M}\) in formic acid \(\left(\mathrm{HCO}_{2} \mathrm{H}\right)\) and \(0.50 \mathrm{M}\) in sodium formate \(\left(\mathrm{HCO}_{2} \mathrm{Na}\right)\).

Short answer

The pH of the buffer solution is approximately 4.05.

Step-by-step solution

Identify Relevant Information

The buffer solution is composed of formic acid, which is a weak acid, and sodium formate, which is its conjugate base. The concentrations of formic acid and sodium formate are given as 0.25 M and 0.50 M, respectively. Also, the pKa of formic acid is approximately 3.75.

Write the Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation is given by: \[ \text{pH} = \text{pKa} + \log \left( \frac{[A^-]}{[HA]} \right) \]where - \([A^-]\) is the concentration of the conjugate base (sodium formate), which is 0.50 M,- \([HA]\) is the concentration of the weak acid (formic acid), which is 0.25 M, and- pKa = 3.75 for formic acid.

Substitute Values Into the Equation

Substitute the given values into the Henderson-Hasselbalch equation:\[ \text{pH} = 3.75 + \log \left( \frac{0.50}{0.25} \right) \]

Calculate the Logarithmic Term

Calculate the value of the logarithmic term:\[ \log \left( \frac{0.50}{0.25} \right) = \log (2) \approx 0.301 \]

Final Calculation

Substitute the logarithmic term back into the Henderson-Hasselbalch equation to find the pH:\[ \text{pH} = 3.75 + 0.301 = 4.051 \]

Key concepts

Buffer Solution

A buffer solution is a special kind of solution that resists changes in pH when small amounts of an acid or a base are added. This makes them incredibly useful in chemical reactions and biological systems where maintaining a stable pH is crucial. Buffer solutions usually consist of a weak acid and its conjugate base (or a weak base and its conjugate acid).
In our exercise, the buffer solution is composed of formic acid, a weak acid, and sodium formate, its conjugate base. Together, they work to maintain the pH of the solution. Here’s how they operate:

• The weak acid (formic acid) can donate protons (H⁺) when the solution becomes too basic, thus leveling out the increase in pH.
• The conjugate base (sodium formate) can accept protons when the solution becomes too acidic, mitigating the decrease in pH.

This dynamic interaction helps buffer solutions keep equilibria largely unchanged upon the addition of small amounts of external acid or base.

Formic Acid

Formic acid is one of the simplest carboxylic acids, with the chemical formula ext{HCO}_2H . It is naturally occurring, found in the venom of ant bites and some plants. In chemistry, formic acid is known for being a weak acid.
As a weak acid, formic acid partially dissociates in water, which means it doesn’t release all its protons (H⁺) in a solution, leading to an equilibrium between the undissociated molecules and the ions in solution. This equilibrium is essential for the buffering action within a buffer solution, as it allows for both the release and absorption of protons as needed to stabilize the pH.
Understanding the behavior of formic acid in a buffer solution helps us comprehend how pH changes can be controlled. By pairing with its conjugate base, sodium formate, formic acid contributes to the buffering system's stability and effectiveness.

pKa

The term ext{pKa} denotes the negative logarithm of the acid dissociation constant ( ext{Ka} ) of an acid. It is a crucial aspect of understanding acid strength and the behavior of acids in solution. For formic acid, the ext{pKa} is approximately 3.75.
Recognizing this value is vital because it allows us to predict how formic acid will behave in a solution, particularly in a buffer system. The Henderson-Hasselbalch equation, ext{pH} = ext{pKa} + ext{log}rac{[A^-]}{[HA]} , utilizes the ext{pKa} to calculate pH by combining it with the concentration ratio of conjugate base to weak acid. This relationship allows us to calculate the pH of a buffer solution effectively.

• Lower ext{pKa} values indicate stronger acids, as they dissociate more easily in water.
• Higher ext{pKa} values suggest weaker acids.

Understanding ext{pKa} allows chemists and students to determine how an acid might interact with other substances in a solution and adjust accordingly for reactions and buffering purposes.

Sodium Formate

Sodium formate, with the chemical formula ext{HCO}_2 ext{Na} , is the sodium salt of formic acid. In the context of a buffer solution, sodium formate acts as the conjugate base of formic acid. It plays a crucial role in the buffering system by accepting protons from the solution.
When formic acid donates a proton, it becomes formate ( ext{HCO}_2^- ), and the sodium ion ( ext{Na}^+ ) from sodium formate doesn't involve itself directly in the acid-base balance but helps maintain the ionic strength of the solution.
This relationship between formic acid and sodium formate is what enables the buffer solution to resist drastic changes in pH:

• If the solution becomes too acidic, the sodium formate can accept protons, converting into formic acid and reducing the amount of free protons.
• If the solution is too basic, formic acid can donate protons, effectively bringing the pH back to balance.

This harmonious balance is central to the action of buffer solutions, demonstrating the interplay between weak acids and their conjugate bases.