Problem 75 - Chemistry The Central Science In Si Units

Question

Phenol, \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{OH},\) has a \(K_{a}\) of \(1.3 \times 10^{-10}\) (a) Write out the \(K_{a}\) reaction for phenol. (b) Calculate \(K_{b}\) for phenol's conjugate base. (c) Is phenol a stronger or weaker acid than water?

Step-by-Step Solution

Answer

(a) \([\mathrm{C}_6\mathrm{H}_5\mathrm{OH}] \rightleftharpoons [\mathrm{C}_6\mathrm{H}_5\mathrm{O^-}] + [\mathrm{H^+}]\); (b) \(K_b = 7.69 \times 10^{-5}\); (c) Phenol is a stronger acid than water.

Step 1: Write the Ionization Reaction

Phenol, when dissolved in water, can donate a proton (\(H^+\)) to form its conjugate base, phenoxide ion \(\mathrm{C}_6\mathrm{H}_5\mathrm{O}^-\). The reaction is: \[\mathrm{C}_6\mathrm{H}_5\mathrm{OH(aq)} \rightleftharpoons \mathrm{C}_6\mathrm{H}_5\mathrm{O^-}(aq) + \mathrm{H^+}(aq)\]This expression represents the acid dissociation reaction of phenol in water.

Step 2: Calculate Phenol's Conjugate Base Kb

The relationship between the acid dissociation constant \(K_a\) and the base dissociation constant \(K_b\) for a conjugate acid-base pair is given by the product of \(K_a\) and \(K_b\) being equal to the ion product constant of water \(K_w\), which is \(1.0 \times 10^{-14}\) at 25°C. \[K_a \times K_b = K_w \]Substituting the known values, we get:\[1.3 \times 10^{-10} \times K_b = 1.0 \times 10^{-14} \]Solving for \(K_b\): \[K_b = \frac{1.0 \times 10^{-14}}{1.3 \times 10^{-10}} = 7.69 \times 10^{-5}\]

Step 3: Compare Phenol to Water

Water has a \(K_a\) of approximately \(1.0 \times 10^{-14}\) due to its autoionization. Comparing the \(K_a\) values: - Phenol: \(1.3 \times 10^{-10}\)- Water: \(1.0 \times 10^{-14}\) Since the \(K_a\) of phenol is much greater than that of water, phenol is a stronger acid than water.

Key Concepts

Phenol

Phenol, also known by its chemical formula \( \text{C}_6\text{H}_5\text{OH} \), is an aromatic compound consisting of a benzene ring bonded to a hydroxyl group \((\text{-OH})\). This structure gives phenol both its acidic properties and distinctive characteristics. Its acidity is much weaker compared to strong acids like hydrochloric acid but stronger than alcohols due to the resonance stabilization of its conjugate base.

• Phenol's aromatic ring allows for resonance delocalization, stabilizing the phenoxide ion \( \text{C}_6\text{H}_5\text{O}^- \) after dissociation.
• The hydroxyl group is directly attached to the aromatic ring, enhancing acidity by lowering the electron density on the oxygen atom.

Phenol is a significant compound in organic chemistry, serving as a starting material for many industrial chemicals and playing a role in disinfectants and antiseptics.

Conjugate Base

A conjugate base is formed when an acid donates a proton. For phenol, this happens when it loses a hydrogen ion to form its conjugate base, the phenoxide ion \( \text{C}_6\text{H}_5\text{O}^- \). This change can be shown in an equation as:\[ \text{C}_6\text{H}_5\text{OH(aq)} \rightleftharpoons \text{C}_6\text{H}_5\text{O}^-(aq) + \text{H}^+(aq) \]The conjugate base retains the aromatic structure of phenol but with an additional negative charge thanks to the loss of a hydrogen ion.

• Phenoxide ion is stable due to resonance, which helps in spreading the negative charge across the aromatic ring.
• This stability directly influences the weak acidity of phenol, making the conjugate base less likely to re-associate with a proton.

Understanding the concept of conjugate bases is critical in predicting the direction of acid-base reactions and the relative strengths of acids.

Acid Dissociation Constant

The Acid Dissociation Constant, symbolized as \( K_a \), quantifies the strength of an acid in solution. For phenol, the \( K_a \) is \( 1.3 \times 10^{-10} \), indicating it is a weak acid but stronger than many others, such as water with a lower \( K_a \). The \( K_a \) value is derived from the equilibrium constant of the dissociation reaction:\[ \text{C}_6\text{H}_5\text{OH(aq)} \rightleftharpoons \text{C}_6\text{H}_5\text{O}^-(aq) + \text{H}^+(aq) \]

• High \( K_a \) values mean stronger acids as they dissociate more completely.
• Phenol's \( K_a \) value suggests it partially dissociates in water, yielding some phenoxide ions and protons.

Measuring \( K_a \) allows chemists to compare acid strengths, predict reaction products, and determine the pH of solutions.