The \(K_{\mathrm{a}}\) for formic acid is \(1.78 \times 10^{-4} M.\) a. What is the pH of a \(0.1 \mathrm{M}\) solution of formic acid? b. \(150 \mathrm{mL}\) of \(0.1 \mathrm{MNaOH}\) is added to \(200 \mathrm{mL}\) of \(0.1 \mathrm{M}\) formic acid, and water is added to give a final volume of 1 L. What is the pH of the final solution?

When discussing weak acids, one important concept to grasp is the acid dissociation constant, symbolized as Ka. This reveals the extent to which an acid can donate protons to water, i.e., dissociate to form hydronium ions ()). The general equation for an acid, HA, dissociating in water is: ) in which ) and ) are the concentrations of the dissociated ions, respectively, and ) is the concentration of the undissociated acid. A small Ka value indicates a weak acid because it signifies less dissociation into ions. For example, formic acid ()) with a Ka of ) is considered a weak acid. Understanding the value of Ka helps predict the behavior of an acid in solution and, importantly, the pH of the solution – which is a measure of acidity.

For the calculation of pH, the dissociation constant provides the necessary relationship to evaluate how much an acid dissociates. The formula ) can be used to determine ), the concentration of hydronium ions ()), which is essential in calculating the pH as pH = -log ). With the given Ka and the acid's initial concentration, the equation enables us to solve for ) after setting up the problem with an ICE table and applying appropriate approximations.

To calculate the pH of a weak acid solution, chemists often use an ICE table, which stands for Initial, Change, Equilibrium. It is a systematic way to organize what happens during a reaction. Initially, you list the concentrations of all reactants and products. For weak acids like formic acid in water, this would look like: ), ), ). From there, you specify the changes that occur as the acid dissociates (), ), )). Finally, the table reflects the new equilibrium concentrations after accounting for the change ().

Using the ICE table alongside the equilibrium constant equation simplifies solving for ), the change in concentration for the reactants and products. It assumes that the concentration of undissociated acid remains almost the same () as its initial value, which is reasonable when dealing with weak acids and small dissociation rates, thus simplifying the algebra required for finding ). This approximation is fundamental for calculating the pH in part a of our exercise.

Understanding weak acid behavior is crucial in pH calculations. Unlike strong acids, which completely ionize in water, weak acids only partially dissociate. This means that when adding a weak acid like formic acid () to water, not all formic acid molecules will become ions; instead, a dynamic equilibrium is established between the undissociated acid and the ions produced. The extent of this dissociation is given by the Ka value of the acid.

Weak acids also have a less pronounced change in pH when neutralized with a base like NaOH than strong acids would. Part b of the textbook problem demonstrates this concept by having ) react with ), where the reaction proceeds to completion, and uses the mole ratio to find the remaining concentration of the acid. The subsequent change in pH is then calculated, considering the weak acid’s equilibrium behavior, which is not as straightforward as the immediate and total neutralization seen with strong acids.

A neutralization reaction occurs when an acid and a base react to form water and a salt. In the context of the exercise, the reaction between ) (a weak acid) and ) (a strong base) demonstrates a neutralization reaction where the result is a formate ion ()) and water ()) This kind of reaction typically goes to completion, meaning all the base reacts with the acid available until one of the reactants is fully consumed.

The textbook example illustrates that the moles of ) are less than the moles of ), indicating that upon reaction completion, there will be some leftover formic acid. It is essential to understand this concept because it affects the pH calculation post-reaction, as any excess acid or base would impact the hydrogen ion concentration in the final solution. In our case, we calculate the remaining concentration of the acid after the neutralization to determine the final pH of the solution.