Question

The disinfectant phenol, \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{OH}\), has a \(\mathrm{pK}_{\text {a of } 10.0}\) in water but 14.4 in methanol. (a) Why are the values different? (b) Is methanol a stronger or weaker base than water? (c) Write the dissociation reaction of phenol in methanol. (d) Write an expression for the autoionization constant of methanol.

Short answer

(a) Different solvents stabilize the ionized form differently. (b) Methanol is a weaker base than water. (c) \[C_6H_5OH + CH_3OH \rightleftharpoons C_6H_5O^- + CH_3OH_2^+\] (d) \[K_{\text{m}} = [CH_3O^-][CH_3OH_2^+]\]

Step-by-step solution

Understand why \(\text{pK}_a\) values are different

The \(\text{pK}_a\) value of an acid is dependent on the solvent it is in. Different solvents stabilize or destabilize the ionized form of the acid differently, affecting the dissociation equilibrium. Water and methanol have different dielectric constants and hydrogen-bonding capabilities, leading to the variation in \(\text{pK}_a\) values.

Determine if methanol is a stronger or weaker base than water

The \(\text{pK}_a\) value indicates the strength of the conjugate base derived from the solvent. Lower \(\text{pK}_a\) indicates a stronger conjugate base. Phenol has a higher \(\text{pK}_a\) in methanol (14.4) compared to water (10.0), indicating that phenolate ion is less stable in methanol. Hence, methanol must be a weaker base than water to have such instability.

Write the dissociation reaction of phenol in methanol

\[ C_6H_5OH + CH_3OH \rightleftharpoons C_6H_5O^- + CH_3OH_2^+ \]

Write an expression for the autoionization constant of methanol

The autoionization of methanol can be expressed similarly to water. For methanol, the reaction is: \[ 2CH_3OH \rightleftharpoons CH_3O^- + CH_3OH_2^+ \] The expression for the autoionization constant, \(K_{\text{m}}\), is: \[ K_{\text{m}} = [CH_3O^-][CH_3OH_2^+] \]

Key concepts

acid-base reactions

Acid-base reactions are a fundamental part of chemistry. One key concept is the dissociation of acids in a solution, which creates positively charged ions (protons) and negatively charged ions. In the case of phenol (C\textsubscript{6}H\textsubscript{5}OH), when it dissociates in methanol, it forms phenolate ions (C\textsubscript{6}H\textsubscript{5}O\textsuperscript{-}) and methanol ions (CH\textsubscript{3}OH\textsubscript{2}\textsuperscript{+}). The reaction can be represented as:
\[ C_6H_5OH + CH_3OH \rightleftharpoons C_6H_5O^- + CH_3OH_2^+ \]
This indicates how phenol behaves as an acid in methanol. Understanding this basic reaction helps in grasping broader concepts in chemistry, such as pKa values and solvent effects.

solvent effects on pKa

The pKa value of an acid is greatly influenced by the solvent it is dissolved in. This is because different solvents have various capacities to stabilize ions. For example, water has a pKa of 10.0 for phenol, whereas methanol has a pKa of 14.4 for the same compound. The fact that methanol has a higher pKa value means that the phenol is less dissociated in methanol compared to water. This difference arises due to varying dielectric constants and hydrogen-bonding capabilities between the solvents.
Here’s the crucial part:

• Water, with its higher dielectric constant, can stabilize the phenolate ion better.
• Methanol, with a lower dielectric constant, leads to less stabilization and a higher pKa.

Thus, the nature of the solvent can significantly alter the pKa and therefore the acidity of a compound. This is an essential consideration in chemical reactions and processes.

autoionization constant

The autoionization constant of a solvent is a measure of its ability to ionize itself. For water, this is known as Kw, and it describes the product of the concentrations of the hydrogen ions and hydroxide ions.
For methanol, the autoionization reaction can be written as:
\[ 2CH_3OH \rightleftharpoons CH_3O^- + CH_3OH_2^+ \]
The equilibrium expression for the autoionization constant, K\textsubscript{m}, is:
\[ K_m = [CH_3O^-][CH_3OH_2^+] \]
This indicates how methanol self-ionizes to form methoxide ions and protonated methanol molecules. The ability of solvents to autoionize is crucial in understanding their behavior in various chemical reactions, especially in acid-base chemistry. Knowing the autoionization constant helps chemists predict how solvents will interact with different solutes, which is essential for designing chemical processes and reactions.