Question

The \(\mathrm{pH}\) of a \(0.15 \mathrm{M}\) propionic acid/ \(0.1 \mathrm{M}\) sodium propionate buffer is \(4.71\). What is the \(\mathrm{p} K_{\mathrm{a}}\) of propionic acid?

Short answer

The \(\mathrm{p} K_{\mathrm{a}}\) of propionic acid is approximately 4.89.

Step-by-step solution

Understand the Buffer System

The question involves a buffer system consisting of propionic acid and its salt, sodium propionate. We need to use the Henderson-Hasselbalch equation to find the \(\mathrm{p} K_{\mathrm{a}}\) of propionic acid.

Write the Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation for a buffer solution is: \[ \mathrm{pH} = \mathrm{p} K_{\mathrm{a}} + \log \left( \frac{[\mathrm{A}^-]}{[\mathrm{HA}]} \right) \] where \([\mathrm{HA}]=0.15 \mathrm{M}\) is the concentration of propionic acid and \([\mathrm{A}^-]=0.1 \mathrm{M}\) is the concentration of sodium propionate.

Plug the Known Values Into the Equation

Substitute the given values into the equation: \[ 4.71 = \mathrm{p} K_{\mathrm{a}} + \log \left( \frac{0.1}{0.15} \right) \].

Calculate the Logarithmic Part

Calculate \( \log \left( \frac{0.1}{0.15} \right) \). First, simplify \( \frac{0.1}{0.15} = \frac{2}{3} \). Thus, \( \log \left( \frac{2}{3} \right) \approx -0.176\).

Solve for \( \mathrm{p} K_{\mathrm{a}} \)

Re-arrange the equation to solve for \( \mathrm{p} K_{\mathrm{a}} \): \[ 4.71 = \mathrm{p} K_{\mathrm{a}} - 0.176 \]. Therefore, \( \mathrm{p} K_{\mathrm{a}} = 4.71 + 0.176 = 4.886 \).

Conclusion

The \( \mathrm{p} K_{\mathrm{a}} \) of propionic acid is approximately \(4.89\).

Key concepts

Buffer Systems

Buffer systems are a crucial concept in acid-base chemistry. They help maintain a stable pH in various solutions, resisting changes when small amounts of acid or base are added. A buffer system typically consists of a weak acid and its conjugate base, or a weak base and its conjugate acid.
For example, in our exercise, the buffer system consists of propionic acid (the weak acid) and its salt, sodium propionate (the conjugate base). These components work together to minimize pH changes.
Buffers are essential in many biological and chemical processes. In the human body, for example, they help to maintain blood pH within a narrow range. This is vital for proper physiological function. In the lab, buffers can keep reactions at a desired pH level, which is necessary for reactions that are pH-sensitive.
Understanding how buffer systems work requires familiarizing yourself with the key components and their interactions within the buffer. It's important to grasp the principles behind how buffers counteract pH changes. This involves the equilibrium between the weak acid and its conjugate base.

pKa Calculation

The pKa value is an important concept in understanding the strength of an acid in a buffer system. It denotes the acid dissociation constant and is a measure of the acidity of a given substance. Simply put, pKa tells us how readily an acid will donate its protons.
To find the pKa of propionic acid in the given problem, we used the Henderson-Hasselbalch equation, which relates pH to pKa and the ratio of the concentrations of the conjugate base and the weak acid: \[\mathrm{pH} = \mathrm{p}K_{\mathrm{a}} + \log \left( \frac{[\mathrm{A}^-]}{[\mathrm{HA}]} \right)\]
This equation helps calculate the missing pKa value by rearranging and plugging in the known values. For our specific case, we substituted the pH (4.71) and the concentration ratio of the propionate ions to propionic acid, leading to the calculation of pKa as approximately 4.89.
The concept of pKa is vital because it helps determine the pH at which half of the acid's molecules are dissociated. Knowing the pKa allows scientists to predict the behavior of acids in different environments and is crucial for developing effective buffer systems.

Acid-Base Chemistry

Acid-base chemistry is the study of the properties and reactions of acids and bases. It's a fundamental area in chemistry that helps us understand many natural processes and is used in various applications from pharmaceuticals to environmental science.
Acids are substances that donate protons (H⁺ ions) in a reaction, while bases are substances that accept protons. This ability to donate and accept protons is at the heart of acid-base reactions, which often occur in aqueous solutions.
One key aspect of acid-base chemistry is the concept of pH, a scale used to measure how acidic or basic a solution is. The pH scale ranges from 0 to 14, with 7 being neutral. Values below 7 indicate an acidic solution, and values above 7 indicate a basic one.
In the context of our buffer exercise, understanding acid-base interactions helps us use the Henderson-Hasselbalch equation. This equation illustrates the relationship between pH, pKa, and concentration, which is rooted in these interactions.
Mastery of acid-base chemistry is essential for anyone studying chemistry or related sciences. It provides the foundation needed to explore more complex topics like reaction mechanisms and the design of chemical processes.