Problem 48 - Chemistry: An Atoms-Focused Approach

Question

Early Antiseptic The use of phenol, also known as carbolic acid, was pioneered in the 19 th century by Sir Joseph Lister (after whom Listerine was named) as an antiseptic in surgery. Its formula is \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{OH}\) (the red hydrogen atom is ionizable). Write the mass action expression for the acid ionization equilibrium of phenol.

Step-by-Step Solution

Answer

Answer: The mass action expression for the acid ionization equilibrium of phenol is \(K_a = \frac{[C_{6}H_{5}O^−][H_{3}O^+]}{[C_{6}H_{5}OH]}\).

Step 1: Write the ionization equilibrium equation for phenol

Phenol undergoes ionization in water to form phenolate ion and hydronium ion. The chemical process can be equation is shown below: \(C_{6}H_{5}OH_{(aq)} \rightleftharpoons C_{6}H_{5}O^−_{(aq)} + H_{3}O^+_{(aq)}\)

Step 2: Write the expression for the mass action law

The mass action law states that the equilibrium constant expression is the product of the molar concentration of the products raised to their stoichiometric coefficients divided by the product of the molar concentration of reactants raised to their stoichiometric coefficients. In this case, the equilibrium constant is denoted as \(K_a\), which is the acidity constant. The mass action expression for the ionization of phenol is as follows: \(K_a = \frac{[C_{6}H_{5}O^−][H_{3}O^+]}{[C_{6}H_{5}OH]}\) This is the mass action expression for the acid ionization equilibrium of phenol.

Key Concepts

Phenol

Phenol, also known as carbolic acid, plays a fascinating role in both chemistry and history. It was described by Sir Joseph Lister, a pioneer in antisepsis. Phenol is an organic compound with the formula \( \mathrm{C}_{6}\mathrm{H}_{5}\mathrm{OH} \). Its unique attribute lies in the hydrogen atom connected to the hydroxyl group \( -OH \) being easily ionizable.
This ionizable hydrogen makes phenol slightly acidic, allowing it to donate a hydrogen ion \( (H^+) \) when in solution.
When phenol ionizes, it turns into a phenolate ion \( C_{6}H_{5}O^- \) and a hydronium ion \( H_{3}O^+ \). This process is an important reaction as it has implications for its function as an antiseptic. Understanding its chemical behavior helps us appreciate why phenol was pivotal as an early antiseptic.

Equilibrium Constant

In the context of phenol, the equilibrium constant \( K_a \) provides insight into the level of ionization in solution. This constant quantifies the balance between phenol (C_{6}\mathrm{H}_{5}\mathrm{OH}]), phenolate ions (C_{6}\mathrm{H}_{5}\mathrm{O}^−), and hydronium ions (H_{3}\mathrm{O}^+) at equilibrium.
The equilibrium constant, \( K_a \), is described by the equation:

• \( K_a = \frac{[C_{6}H_{5}O^-][H_{3}O^+]}{[C_{6}H_{5}OH]} \)

This formula arises from the law of mass action as it relates product concentrations to reactant concentrations.
This ratio indicates how much of the phenol ionizes in water. The higher the \( K_a \) value, the stronger the acid as more of it dissociates.
It is essential for chemists and medical professionals to comprehend \( K_a \) as it informs safety guidelines and practical applications of phenol.

Mass Action Law

The mass action law is a fundamental principle in chemical kinetics and equilibrium. It allows chemists to predict how concentrations change with reactions. For a balanced reaction at a given temperature, the mass action law states that the rate of a reaction is proportional to the product of the concentrations of the reactants, each raised to a power equal to its stoichiometric coefficient.
For the ionization of phenol, this takes shape in the expression for the acid ionization equilibrium:

• The law provides the equilibrium expression: \( K_a = \frac{[C_{6}H_{5}O^-][H_{3}O^+]}{[C_{6}H_{5}OH]} \)

This expression hinges on the fact that, at equilibrium, the ratio of products to reactants remains constant.
Understanding this concept is a stepping stone for students and professionals working with chemical reactions.
The mass action law ensures accurate predictions and calculations surrounding chemicals like phenol in various contexts, including its practical use in disinfectants and other medical solutions.