Problem 140 - Chemistry

Question

Trichloroacetic acid \(\left(\mathrm{CCl}_{3} \mathrm{CO}_{2} \mathrm{H}\right)\) is a corrosive acid that is used to precipitate proteins. The \(\mathrm{pH}\) of a \(0.050 \mathrm{M}\) solution of trichloroacetic acid is the same as the \(\mathrm{pH}\) of a \(0.040 \mathrm{M} \mathrm{HClO}_{4}\) solution. Calculate \(K_{\mathrm{a}}\) for trichloroacetic acid.

Step-by-Step Solution

Answer

The Ka for trichloroacetic acid is approximately 0.160.

Step 1: Find the pH of HClO4 solution

HClO4 is a strong acid and completely dissociates in water. Therefore, the [H+] concentration in the solution is equal to its molarity, which is 0.040 M. To find the pH, we use the formula pH = -log[H+]. For this HClO4 solution: pH = -log(0.040) Calculate the pH value using a logarithm function.

Step 2: Determine [H+] concentration in TCA solution

Since the pH of the TCA solution is the same as the pH of the HClO4 solution, the [H+] concentration in the TCA solution is also 0.040 M.

Step 3: Write the expression for acid dissociation

TCA undergoes dissociation in water as follows: CCl3CO2H + H2O <-> CCl3CO2⁻ + H3O⁺ As [H+] = 0.040 M, the concentration of CCl3CO2⁻ must also be 0.040 M. Let the initial concentration of TCA be represented by [CCl3CO2H]₀. After dissociation, the concentration of TCA will be [CCl3CO2H]₀ - 0.040 M. The expression for Ka will be: Ka = \(\frac{[CCl3CO2^{-}][H3O{+}]}{[CCl3CO2H]}\) Since [H3O+] = [H+], we can substitute the values known in the expression: Ka = \(\frac{(0.040)(0.040)}{([CCl3CO2H]_0 - 0.040)}\)

Step 4: Find the initial concentration of TCA

We are given that the initial concentration of TCA in the solution is 0.050 M. Therefore, [CCl3CO2H]₀ = 0.050 M

Step 5: Calculate Ka for TCA

Substitute the initial concentration of TCA into the Ka expression: Ka = \(\frac{(0.040)(0.040)}{(0.050 - 0.040)}\) Evaluate the expression: Ka ≈ 0.160 The Ka for trichloroacetic acid is approximately 0.160.

Key Concepts

Trichloroacetic Acid

Trichloroacetic acid, also known as CCl₃CO₂H, is a chemical that finds its use in various applications, notably in protein precipitation. This compound is characterized by its ability to dissociate in water, which makes it a considered acid in chemical terms. Let's break down what this means:

• It has a relatively high ability to donate hydrogen ions (H⁺), making it an acid.
• The strong electron-withdrawing groups (three chlorine atoms) in its structure help stabilize the negative charge formed when it loses an H⁺ ion.
• This characteristic increases its acidity compared to similar acids with fewer electron-withdrawing capabilities.

Understanding the nature of trichloroacetic acid is crucial as it directly impacts its behavior in solutions and calculations related to its dissociation and strength.

pH Calculation

The \( ext{pH}\) of a solution is a crucial metric in chemistry that indicates the acidity or basicity of that solution. Calculating \( ext{pH}\) involves determining the \([H^+]\) concentration in the solution. Here's how it works:

• The formula used is \( ext{pH} = - ext{log} [H^+]\), where \([H^+]\) is the concentration of hydrogen ions.
• For strong acids, like \( ext{HClO}_4\), the \([H^+]\) concentration is equal to the molarity of the acid, as it dissociates completely in solution.
• For instance, a \(0.040 \text{M}\) \( ext{HClO}_4\) solution has a \([H^+]\) of \(0.040 \text{M}\), leading to a \( ext{pH}\) of approximately 1.4 after calculating it with the logarithmic formula.

By ensuring the \( ext{pH}\) is accurately determined, we can accurately compare and study different acids, such as trichloroacetic acid, especially when their solutions are mixed or compared.

Strong Acids

Strong acids are characterized by their complete dissociation in water, which means they effectively donate their hydrogen ions (H⁺) to the surrounding solvent. Let's take a closer look at the traits of strong acids using \( ext{HClO}_4\) as an example:

• These acids, like \( ext{HClO}_4\), have a dissociation equilibrium that lies far to the right, indicating complete dissociation.
• In solution, the concentration of \([H^+]\) equals the initial concentration of the acid due to this full dissociation.
• This characteristic simplifies calculations, as seen in \( ext{pH}\) determination or when comparing to weak acids like trichloroacetic acid.

Understanding how strong acids behave is essential for tackling complex chemistry problems, particularly as a baseline to study weaker acids with partial dissociation behavior.

Equilibrium Expressions

Equilibrium expressions are critical when dealing with acids that only partially dissociate, like trichloroacetic acid. These expressions help us quantify the extent of dissociation in such weak acids.

• The equilibrium for trichloroacetic acid dissociation in water is written as: \( ext{CCl}_3 ext{CO}_2 ext{H} + ext{H}_2 ext{O} \rightleftharpoons ext{CCl}_3 ext{CO}_2^- + ext{H}_3 ext{O}^+\).
• The corresponding expression for the acid dissociation constant, \( K_a\), is \[ K_a = \frac{[ ext{CCl}_3 ext{CO}_2^-][ ext{H}_3 ext{O}^+]}{[ ext{CCl}_3 ext{CO}_2 ext{H}]} \]
• This helps calculate \( K_a\), indicating the strength of the acid.

These mathematical representations ensure that even partially dissociated compounds can be studied effectively to determine their contribution to the solution's acidity and behavior.