The hydronium ion concentration in a 0.100 M solution of formic acid is 0.0043 \(\mathrm{M}\) . Calculate \(K_{a}\) for formic acid.

When studying acid-base chemistry, understanding the strength of an acid through its acid dissociation constant, or Ka, is crucial. The Ka value helps gauge how well an acid donates its protons to the solution. For weak acids like formic acid, it is not completely ionized in solution. The Ka is calculated using the formula \[\begin{equation}K_a = \frac{[H_3O^+][A^-]}{[HA]}\end{equation}\]where

• \([HA]\) is the concentration of the acid
• \([H_3O^+]\) represents the concentration of hydronium ions
• \([A^-]\) denotes the concentration of the conjugate base

By determining the concentrations of these constituents at equilibrium, you can effectively calculate the Ka value. For example, with a 0.100 M solution of formic acid and a hydronium ion concentration of 0.0043 M, we can deduce that \([A^-]\) will also be 0.0043 M since formic acid donates one proton per molecule. Inserting these values into the formula gives a Ka value, giving us critical information about the acid's behavior in solution.

The concentration of hydronium ions \([H_3O^+]\) in a solution is a direct indication of the solution's acidity. It is particularly important in the context of weak acids, which do not fully dissociate in water. The hydronium ion concentration is determined from the equilibrium mixture of the acid and water.For instance, in the case of formic acid, knowing its initial concentration and the equilibrium concentration of hydronium ions (found by experimentation or calculation) allows us to describe the acid’s dissociation. In our example with formic acid, a 0.0043 M hydronium ion concentration signifies a partially dissociated acid, reflective of a weak acid, which only relinquishes some of its protons to the solution.

Weak acids, by definition, are those that do not fully dissociate in solution. They only donate a fraction of their protons to form hydronium ions. This partial dissociation is the hallmark of a weak acid’s behavior. It results in a dynamic equilibrium where the forwards reaction (acid dissociating to form hydronium and conjugate base) is balanced by the reverse reaction (hydronium and the conjugate base recombining to form the acid).

• Weak acids have a higher pH compared to strong acids at the same concentration
• Their hydronium ion concentration is lower than their initial concentration
• The equilibrium lies significantly towards the reactants (undissociated acid)

Understanding the nature of weak acids is essential when discussing acidity, pH, and chemical equilibrium in the context of acid-base reactions.

Chemical equilibrium occurs when the rates of the forward and reverse reactions in a chemical system become equal, resulting in no net change in the concentrations of the reactants and products over time. It's important to recognize that equilibrium does not mean the reactants and products are in equal concentrations but that their ratios remain constant.In the context of acids, the establishment of chemical equilibrium between the acid (HA), hydronium ions (\(H_3O^+\)), and the conjugate base (\(A^-\)) is given by the expression: \[\begin{equation}HA + H_2O \leftrightarrow H_3O^+ + A^-\end{equation}\]The Ka value is a quantifier of this equilibrium specific to weak acids. It tells us how far the reaction has proceeded to the right or how much the acid has dissociated. By measuring the equilibrium concentrations of the involved species, as done for our formic acid example, we can calculate Ka and gain insight into the equilibrium position and acid strength.