Problem 58 - Chemistry The Molecular Nature of Matter

Question

Pentanoic acid, \(\mathrm{HC}_{5} \mathrm{H}_{9} \mathrm{O}_{2}\), is found in a plant called valerian, which cats seem to like almost as much as catnip, and is a weak acid. Write an equation showing its reaction with water

Step-by-Step Solution

Answer

The equation for the reaction of pentanoic acid with water is: \(\mathrm{HC}_{5} \mathrm{H}_{9} \mathrm{O}_{2} + \mathrm{H}_{2}\mathrm{O} \rightarrow \mathrm{C}_{5} \mathrm{H}_{9} \mathrm{O}_{2}^- + \mathrm{H}_{3}\mathrm{O}^+\).

Step 1 Title - Identify the Acid and its Ionization

Recognize that pentanoic acid, \(\mathrm{HC}_{5} \mathrm{H}_{9} \mathrm{O}_{2}\), is a weak acid and will undergo ionization in water. In this process, the acid donates a hydrogen ion \(\mathrm{H}^+\) to water.

Step 2 Title - Write the Ionization Equation

Express the ionization of pentanoic acid in water by writing a balanced chemical equation. The acid \(\mathrm{HC}_{5} \mathrm{H}_{9} \mathrm{O}_{2}\) donates a hydrogen ion to form its conjugate base \(\mathrm{C}_{5} \mathrm{H}_{9} \mathrm{O}_{2}^-\) and \(\mathrm{H}^+\) combines with water \(\mathrm{H}_{2}\mathrm{O}\) to form the hydronium ion \(\mathrm{H}_{3}\mathrm{O}^+\).

Key Concepts

Weak Acid Reaction with Water

Understanding the behavior of weak acids, such as pentanoic acid, in water is fundamental in chemistry. Unlike strong acids that disassociate completely, a weak acid only partially ionizes. This means that when added to water, only a small proportion of the acid molecules donate their hydrogen ions, resulting in an equilibrium between the undissociated and dissociated forms.

Equilibrium Expression

For pentanoic acid (HC_{5}H_{9}O_{2}), the chemical equation representing its reaction with water to form hydronium ions (H_3O^+) and its conjugate base (C_{5}H_{9}O_{2}^-) is dynamic. The acid and water react to form the products, but simultaneously, the products can recombine to form the reactants. This ongoing process establishes an equilibrium condition, symbolized by a double arrow in the equation.

Chemical Equation Writing

Writing a balanced chemical equation involves translating the description of a chemical reaction into a symbolic representation. To capture the ionization of pentanoic acid accurately, we write the molecular formula, account for each atom on both sides of the equation, and ensure charge balance.

Ionization Equation Tips

When dealing with weak acids:

• Begin with the molecular formula of the weak acid.
• Indicate the hydrogen ion (H^+) being donated.
• Show the formation of the conjugate base by removing a hydrogen atom from the acid's molecular formula.
• Combine the donated hydrogen ion with water (H_2O) to form the hydronium ion (H_3O^+).
• Confirm that the total number of each type of atom and the net charge is the same on both sides of the equation.

It's crucial to remember that coefficients may be needed to achieve balance in more complex reactions.

Conjugate Base Formation

Conjugate bases play a vital role in the understanding of acid-base chemistry. When a weak acid like pentanoic acid reacts with water, it donates a hydrogen ion, resulting in the formation of its conjugate base.

Stability and Reactivity

The stability of a conjugate base is a key factor in an acid’s strength; more stable conjugate bases usually come from weaker acids. For pentanoic acid, the conjugate base formed is (C_{5}H_{9}O_{2}^-). This base can also be viewed as a potential reactant, capable of accepting a hydrogen ion to revert to the original acid, highlighting its amphoteric nature. Such characteristics influence the acid's behavior in solution and its ability to participate in further chemical reactions, like neutralization or buffering.