Question

A solution of formic acid \(\left(\mathrm{HCOOH}, K_{\mathrm{a}}=1.8 \times 10^{-4}\right)\) has a \(\mathrm{pH}\) of \(2.70 .\) Calculate the initial concentration of formic acid in this solution.

Short answer

The initial concentration of formic acid in the solution is approximately \(0.0221 \, M\).

Step-by-step solution

Write the dissociation equation for formic acid and Ka expression.

The chemical equation for the dissociation of formic acid into its ions can be written as: \(HCOOH \rightleftharpoons H^+ + HCOO^-\) And the Ka expression for this reaction is: \(K_a = \frac{[H^+][HCOO^-]}{[HCOOH]}\)

Calculate the concentration of hydrogen ions, H+.

We can use the given pH value to find the concentration of H+ in the solution, since pH is the negative logarithm of the concentration of hydrogen ions: \(pH = -\log[H^+]\) We'll rearrange this equation to solve for the concentration of hydrogen ions: \( [H^+] = 10^{-pH}\) Plugging in the given pH value, we'll have: \( [H^+] = 10^{-2.70} ≈ 1.995 \times 10^{-3} \, M\)

Write the reaction in terms of an initial concentration.

We'll call the initial concentration of formic acid "C." After dissociation, we'll have: [HCOOH] = C - x [H+] = x [HCOO-] = x Since formic acid is a weak acid, we can assume that x is very small compared to C, so C - x ≈ C.

Substitute the concentrations into the Ka expression and solve for C.

With our simplified assumptions, we can substitute the values back into the Ka expression: \(K_a = \frac{[H^+][HCOO^-]}{[HCOOH]}\) Simplifying to: \(1.8 \times 10^{-4} = \frac{(1.995 \times 10^{-3})^2}{C}\) Now, we need to solve for "C": \(C = \frac{(1.995 \times 10^{-3})^2}{1.8 \times 10^{-4}} ≈ 0.0221 \, M\)

Report the initial concentration of formic acid.

The initial concentration of formic acid in the solution is approximately 0.0221 M.

Key concepts

Formic Acid

Formic acid, chemically represented as HCOOH, is the simplest carboxylic acid and occurs naturally in the venom of bee and ant stings. It is a colorless liquid with a pungent odor at room temperature. In this context, we are concerned with its behavior in aqueous solutions, specifically its ability to release hydrogen ions (H+) into the solution.
Formic acid is used in various industrial applications, such as in textile processing and as a preservative. Its importance in chemistry arises from its nature as a weak acid, which means it partially dissociates (splits into ions) in water, unlike strong acids which completely dissociate. This property is crucial in calculating its dissociation constant, which further helps us understand its acid strength and calculate the pH of its solutions.

Dissociation Constant (Ka)

The dissociation constant, represented by the symbol \( K_a \), is a vital parameter for quantifying the strength of an acid in solution. It specifically measures the tendency of an acid to dissociate into its ions when dissolved in water.
For formic acid, the dissociation equation is:

• \(HCOOH \rightleftharpoons H^+ + HCOO^- \)

The expression for \( K_a \) is given by the formula:

• \( K_a = \frac{[H^+][HCOO^-]}{[HCOOH]} \)

A small \( K_a \) value, like \(1.8 \times 10^{-4}\) for formic acid, indicates a weak acid, meaning it does not dissociate completely. Understanding \( K_a \) helps predict the behavior of the acid under various conditions like changes in concentration and temperature. This concept is pivotal in studying chemical equilibria involving weak acids.

pH Calculation

pH is a scale that measures how acidic or basic a solution is, with lower values being more acidic. The pH of a solution can be calculated using the concentration of hydrogen ions (\([H^+]\)). The formula to find pH is:

• \( \mathrm{pH} = -\log[H^+] \)

Given a specific pH value, you can find \([H^+]\) with the equation:

• \( [H^+] = 10^{-\mathrm{pH}} \)

In this problem, when the pH is given as 2.70, it represents the logarithmic concentration of hydrogen ions in the solution. Calculating \([H^+]\) is the first step in determining the initial concentration of formic acid as part of the solution. These calculations are integral to a wide range of chemical applications including determining the acidity of solutions and adjusting them for various scientific and industrial processes.

Weak Acids

Weak acids are characterized by their partial dissociation into ions in solution. Unlike strong acids which fully dissociate, weak acids like formic acid (HCOOH) release only some of their hydrogen ions into the solution.
In weak acids, the equilibrium between the undissociated molecules and the ions is dynamic, which means that at any given time, a balance is maintained between the dissociated ions and the unionized form of the acid.
Some properties of weak acids include:

• Less conductivity due to fewer free ions in solution
• Higher pH values compared to strong acids
• Reversible reactions that can be shifted by concentration changes

For weak acids, understanding their behavior requires consideration of both dissociation constants (\( K_a \)) and their equilibrium nature. These insights are important for accurately predicting the effects of weak acids in chemical reactions and solution preparation.