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?

The acid dissociation constant (Ka) measures how completely an acid dissociates in solution. A larger Ka value indicates a stronger acid. For phenol (\(C_{6}H_{5}OH\)), the Ka reaction represents its tendency to donate a proton to the surrounding medium, revealing its acidic nature.

Phenol dissociates as follows: \[C_{6}H_{5}OH \rightleftharpoons C_{6}H_{5}O^{-} + H^{+}\]The above reaction indicates that a molecule of phenol releases a hydrogen ion (\(H^{+}\)), turning into its conjugate base (\(C_{6}H_{5}O^{-}\)). The equilibrium expression for the reaction is:\[K_{a} = \frac{[C_{6}H_{5}O^{-}][H^{+}]}{[C_{6}H_{5}OH]}\]Understanding this concept is crucial to assessing the strength of phenol as an acid compared to other substances. A compound's tendency to lose a proton, quantified by the Ka value, directly influences its reactivity and interactions in chemical processes.

When phenol loses a proton, it forms a conjugate base, phenolate (\(C_{6}H_{5}O^{-}\)). To assess the basicity of this conjugate base, we compute the Kb value, which represents the base dissociation constant. The Kb calculation requires understanding the inverse relationship between the strength of the acid (Ka) and its conjugate base (Kb). This relationship is conceptualized through the equation:\[K_{w} = K_{a} \times K_{b}\]where \(K_{w}\) is the ion product of water, a constant value of \(1.0 \times 10^{-14} \) at 25°C. To find Kb, rearrange the equation:\[K_{b} = \frac{K_{w}}{K_{a}}\]After substituting the given values for Kw and Ka, the Kb value for the conjugate base of phenol can be calculated. This step is essential for students to evaluate the basicity of various substances and comprehend their behavior in different chemical environments.

To compare the acidity of different substances, we look at their Ka values. Phenol, with a Ka value of \(1.3 \times 10^{-10}\) is considered for comparison. Water, a well-known neutral substance, has a much lower Ka value of \(1.8 \times 10^{-16}\).

These values imply that phenol donates protons more readily than water, classifying it as a stronger acid relative to water. The concept of comparing acidity is fundamental in chemistry, as it influences solubility, reaction rates, and buffer capacities in solutions. Grasping this concept helps students predict how different acids will behave in chemical reactions and how they can alter the environment of a chemical system.