Problem 109 - Chemistry and Chemical Reactivity

Question

You prepare a 0.10 M solution of oxalic acid, \(\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4} .\) What molecules and ions exist in this solution? List them in order of decreasing concentration.

Step-by-Step Solution

Answer

The order is \(\mathrm{H}_2\mathrm{C}_2\mathrm{O}_4\), \(\mathrm{HC}_2\mathrm{O}_4^-\), \(\mathrm{H}^+\), and \(\mathrm{C}_2\mathrm{O}_4^{2-}\).

Step 1: Identify Key Components of Oxalic Acid

Oxalic acid, \(\mathrm{H}_2\mathrm{C}_2\mathrm{O}_4\), is a weak diprotic acid and can donate two protons (H\^+ ions) in aqueous solutions. Therefore, it exists in equilibrium with its dissociation products.

Step 2: Determine Major Species in Solution

In a 0.10 M solution of oxalic acid, the major species present will be the undissociated oxalic acid molecules, \(\mathrm{H}_2\mathrm{C}_2\mathrm{O}_4\). Since it's a weak acid, most of the molecules remain undissociated.

Step 3: First Ionization Step

Oxalic acid dissociates in a stepwise manner. The first ionization step is \(\mathrm{H}_2\mathrm{C}_2\mathrm{O}_4 \rightleftharpoons \mathrm{H}^+ + \mathrm{HC}_2\mathrm{O}_4^-\). \Due to its weak nature, this dissociation is partial, so \(\mathrm{H}^+\) and \(\mathrm{HC}_2\mathrm{O}_4^-\) ions are less concentrated than the \(\mathrm{H}_2\mathrm{C}_2\mathrm{O}_4\) molecules.

Step 4: Second Ionization Step

The second ionization of oxalic acid is even weaker: \(\mathrm{HC}_2\mathrm{O}_4^- \rightleftharpoons \mathrm{H}^+ + \mathrm{C}_2\mathrm{O}_4^{2-}\). The \(\mathrm{C}_2\mathrm{O}_4^{2-}\) ions are the least concentrated species due to the weak nature of the second dissociation.

Step 5: Order Species by Concentration

Based on the ionization equilibria, the species in order of decreasing concentration are: \(\mathrm{H}_2\mathrm{C}_2\mathrm{O}_4\) (most concentrated), \(\mathrm{HC}_2\mathrm{O}_4^-\), \(\mathrm{H}^+\) (from both steps), \(\mathrm{C}_2\mathrm{O}_4^{2-}\) (least concentrated).

Key Concepts

Weak Diprotic Acid

Oxalic acid, with the chemical formula \(\mathrm{H}_2\mathrm{C}_2\mathrm{O}_4\), is characterized as a weak diprotic acid. This means it has two hydrogen ions (protons) that it can donate in a stepwise manner when dissolved in water. Being a weak acid implies that it does not fully dissociate in solution.

The term 'diprotic' indicates that the acid undergoes two distinct ionization steps, each releasing one proton. In practical terms, even in a 0.10 M solution, not all oxalic acid molecules release their protons, and many stay in their undissociated form.

This behavior is essential in understanding the concentrations of different chemical species when oxalic acid is in aqueous solution. Most of the acid will remain as \(\mathrm{H}_2\mathrm{C}_2\mathrm{O}_4\), while only a small fraction will convert to its ionized forms.

Ionization Equilibrium

The concept of ionization equilibrium is crucial for understanding how weak acids like oxalic acid behave in solution. When oxalic acid is in water, ionization occurs according to equilibrium reactions that establish a balance between undissociated acid molecules and the ions formed.

For oxalic acid, there are two ionization steps:

• The first step involves the formation of hydrogen ions \(\mathrm{H}^+\) and the hydrogensalt ion \(\mathrm{HC}_2\mathrm{O}_4^-\).
• The second step yields more \(\mathrm{H}^+\) ions and oxalate ions \(\mathrm{C}_2\mathrm{O}_4^{2-}\).

These equilibria establish because at equilibrium, the rate of the forward reaction equals the rate of the reverse reaction. The equilibrium constant for the second step is typically smaller than the first, indicating a lower tendency for the second hydrogen to ionize.

Due to these equilibrium positions, in solutions, the initial acid \(\mathrm{H}_2\mathrm{C}_2\mathrm{O}_4\) is the most prevalent species, far exceeding the concentration of ions it produces.

Acid Dissociation

Acid dissociation is the process by which an acid donates protons into a solution, thereby generating ions. For a weak acid like oxalic acid, dissociation does not go to completion.

In the case of diprotic oxalic acid, dissociation takes place in two stages:

• The first dissociation is \(\mathrm{H}_2\mathrm{C}_2\mathrm{O}_4 \rightleftharpoons \mathrm{H}^+ + \mathrm{HC}_2\mathrm{O}_4^-\), where the molecule releases one proton. As a weak acid, only a small fraction undergoes this change.
• In the second dissociation stage, the \(\mathrm{HC}_2\mathrm{O}_4^-\) ion releases its remaining proton \(\rightleftharpoons \mathrm{H}^+ + \mathrm{C}_2\mathrm{O}_4^{2-}\). However, because this is a weaker reaction than the first, even fewer molecules dissociate here.

Understanding dissociation and its partial nature helps in predicting the proportions of each species in solution. The concept underpins rules for writing equilibrium expressions and calculating the pH of the solution.

Chemical Species Concentration

Chemical species concentration within a solution refers to how many molecules or ions of a particular species are present. When discussing weak diprotic acids such as oxalic acid, it becomes important to determine the relative concentrations of the molecular form and its ionic byproducts.

In a 0.10 M oxalic acid solution, the various species present in decreasing order of concentration are:

• The undissociated form \(\mathrm{H}_2\mathrm{C}_2\mathrm{O}_4\) is the most prevalent.
• Then follows the \(\mathrm{HC}_2\mathrm{O}_4^-\) ion, produced from the first ionization step.
• The hydrogen ion \(\mathrm{H}^+\) from both ionization steps comes next.
• Finally, the \(\mathrm{C}_2\mathrm{O}_4^{2-}\) ion, being the product of the second, weaker ionization, is the least concentrated.

This order reveals the nature of weak acids—most molecules tend to remain in their original form, with fewer ions forming unless more acidic or basic conditions are applied. This concept is applied in knowing how to adjust chemical processes and their calculations.