Problem 14 - Biochemistry: A Short Course

Question

The \(\mathrm{p} K_{\mathrm{a}}\) of acetic acid is 4.76 and the \(\mathrm{p} K_{\mathrm{a}}\) of trichloroacetic acid, which is used to remove warts, is 0.7. Calculate the dissociation constant of each acid. Which is the stronger acid? \(6\)

Step-by-Step Solution

Answer

Trichloroacetic acid is the stronger acid with a dissociation constant of approximately 0.2.

Step 1: Understand the Relationship between pKa and Ka

The pKa value is related to the acid dissociation constant, Ka, using the relationship \( \mathrm{p}K_a = -\log_{10}(K_a) \). Thus, to find the dissociation constant \( K_a \), you will need to use the inverse of the logarithmic function, which is the exponentiation.

Step 2: Calculate the Ka for Acetic Acid

Using the pKa for acetic acid, 4.76, calculate its Ka. The formula is \( K_a = 10^{-\mathrm{p}K_a} \). Substitute the given value into the equation: \( K_a = 10^{-4.76} \).

Step 3: Perform the Calculation for Acetic Acid

Convert the pKa to Ka using the previous step: \( K_a = 10^{-4.76} \approx 1.74 \times 10^{-5} \).

Step 4: Calculate the Ka for Trichloroacetic Acid

Similarly, calculate the Ka for trichloroacetic acid using the formula: \( K_a = 10^{-\mathrm{p}K_a} \). Substitute the given pKa of 0.7 into the equation: \( K_a = 10^{-0.7} \).

Step 5: Perform the Calculation for Trichloroacetic Acid

Convert the pKa to Ka: \( K_a = 10^{-0.7} \approx 0.2 \).

Step 6: Compare the Strength of the Acids

The strength of an acid is determined by the magnitude of its \( K_a \). A larger \( K_a \) value indicates a stronger acid. Comparing the two acids: \( 0.2 \) for trichloroacetic acid and \( 1.74 \times 10^{-5} \) for acetic acid, trichloroacetic acid is the stronger acid because it has a significantly larger \( K_a \).

Key Concepts

pKa

The term "pKa" is a crucial concept in understanding acid strength and dissociation. It represents the negative logarithm of the acid dissociation constant (Ka). Imagine pKa as a scorecard for acids. A lower pKa value means a stronger acid, because it indicates the acid ionizes more completely in solution. When you see pKa, you instantly know how readily an acid releases its proton into the solution.
To put it mathematically, the relationship is expressed as: \[ \mathrm{p}K_a = -\log_{10}(K_a) \]This formula shows how you can convert between pKa and Ka. To find the dissociation constant, simply perform the inverse operation: \[ K_a = 10^{-\mathrm{p}K_a} \]This is a quick way to understand the behavior of different acids.

Acetic Acid

Acetic acid is a common weak acid found in vinegar. It has a distinctive sour taste and pungent smell.
In chemistry, its molecular structure is represented as CH₃COOH. It dissociates into ions less completely compared to strong acids, making it a weak acid.
Given its pKa of 4.76, we can calculate its dissociation constant:\[ K_a = 10^{-4.76} \approx 1.74 \times 10^{-5} \]This low Ka value indicates that most acetic acid molecules remain intact in solution, donating fewer protons to water. Understanding acetic acid's dissociation helps in the culinary and cleaning industries, where it's used for preserving food and as a solvent, respectively.

Trichloroacetic Acid

Trichloroacetic acid (TCA) is a much stronger acid compared to acetic acid. It's often used in dermatology for procedures like wart removal due to its strong acidity.
Its molecular formula is CCl₃COOH.
With a pKa of 0.7, it significantly dissociates in water:\[ K_a = 10^{-0.7} \approx 0.2 \]This relatively large Ka implies that trichloroacetic acid almost completely ionizes in water, releasing more protons. Its high acidity is useful in various medical and industrial applications, allowing it to react more aggressively with organic tissue and substances. Understanding its properties can aid in appreciating why it is chosen over milder acids like acetic acid for certain chemical processes.
Both the lower pKa and higher Ka demonstrate TCA's ability to act as a strong acid.