Problem 113 - Chemistry The Molecular Science

Question

A solid sample of benzoic acid, a carboxylic acid, is in equilibrium with an aqueous solution of benzoic acid. A tiny quantity of \(\mathrm{D}_{2} \mathrm{O},\) water containing the isotope \({ }^{2} \mathrm{H}\), deuterium, is added to the solution. The solution is allowed to stand at constant temperature for several hours, after which some of the solid benzoic acid is removed and analyzed. The benzoic acid is found to contain a tiny quantity of deuterium, D, and the formula of the deuterium-containing molecules is \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COOD}\). Explain how this can happen.

Step-by-Step Solution

Answer

Deuterium from \(\text{D}_2\text{O}\) replaces hydrogen in benzoic acid through equilibrium reactions, forming deuterated acid.

Step 1: Understanding the Concept of Equilibrium

When benzoic acid, a carboxylic acid, is in equilibrium with its aqueous solution, the acid can transfer protons (H+) between the solid and liquid phases. This is due to the nature of acid-base equilibrium, where an acid can donate protons to a base, in this case, primarily water.

Step 2: Introduction of Deuterium and its Role

When a small amount of \(\text{D}_2\text{O}\), which contains deuterium, a heavier isotope of hydrogen with one proton and one neutron, is added, it participates in chemical equilibrium similarly to normal water (\(\text{H}_2\text{O}\)). Deuterium can replace hydrogen atoms in molecules forming deuterium analogs.

Step 3: Proton (or Deuterium) Exchange Mechanism

In the aqueous solution, a series of proton exchange reactions can occur due to the dynamic nature of equilibrium. The regular hydrogen in benzoic acid can be replaced by deuterium from the added \(\text{D}_2\text{O}\), resulting in the formation of \(\text{C}_6\text{H}_5\text{COOD}\), a deuterated benzoic acid molecule.

Step 4: Reversibility and Time Allowance at Constant Temperature

By allowing the solution to stand for several hours at constant temperature, the equilibrium reaches a state where exchange reactions have distributed deuterium into the solid form of benzoic acid. This is why, upon removal and analysis, solid benzoic acid is found with a small quantity of deuterium.

Key Concepts

Acid-Base Equilibrium

Acid-base equilibrium is a fundamental concept in chemistry involving the transfer of protons (H⁺) between acids and bases. In our example, benzoic acid is in equilibrium with its aqueous solution. What's happening here is that benzoic acid can give away protons to water molecules. This interaction allows the protons to move between the solid benzoic acid and the dissolved molecules in the water, maintaining a balance.

A key aspect of equilibrium is that both forward and backward reactions occur at the same rate, meaning the concentrations of reactants and products remain constant over time. When deuterated water ( D₂O) is introduced, it behaves like any regular water in this equilibrium but adds an interesting twist due to the presence of deuterium. Adding deuterated water to the mix doesn't disturb the equilibrium significantly, it just introduces deuterium atoms into the environment, which can participate in exchanges like their hydrogen counterparts.

Deuterium

Deuterium is an isotope of hydrogen, and it is heavier because it contains one neutron along with the one proton typical of hydrogen atoms. So, on its own, deuterium forms a molecule like water called deuterium oxide ( D₂O). Although similar to regular water, it's distinguishable by its physical properties like being heavier.

• Deuterium can replace hydrogen in many compounds.
• Its chemical behavior is very close to regular hydrogen.
• It serves as a useful tracer in experimental chemistry because of these properties.

In the context of our benzoic acid scenario, deuterium from D₂O can substitute a regular hydrogen atom in the acid, forming a compound called C₆H₅COOD. This substitution highlights deuterium's role in the proton exchange reactions that occur during equilibrium with hydrogen.

Proton Exchange Reaction

Proton exchange reactions are key in understanding isotope exchanges like those seen with deuterium. These reactions involve swapping protons between molecules. In the case of benzoic acid, it involves trading places between hydrogen and deuterium atoms due to their similar chemical properties.

• The aqueous environment supports dynamic interactions where hydrogen can be swapped with deuterium from D₂O.
• This exchange doesn't require added energy due to the equilibrium established.
• Such reactions can occur repeatedly, given the right conditions.

When you let the solution sit for hours, the benzoic acid can incrementally substitute its hydrogen atoms for deuterium across its molecules. Over time, some of these switches become evident in the solid form of benzoic acid. This incremental exchange results in a measurable amount of deuterium integrated into the compound, observable during analysis.