Question

The disinfectant phenol,${\mathbf{\text{C}}}_{\mathbf{6}}{\mathbf{\text{H}}}_{\mathbf{5}}\mathbf{\text{OH,}}$, has a${\mathbf{\text{pK}}}_{\mathbf{\text{a}}}$of$\mathbf{\text{10.0}}$in water, but$\mathbf{\text{14.4}}$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) The values are different because depends on the acid-base character of the other reactant

b) The${\text{pK}}_{\text{a}}$of methanol is greater than the ${\text{pK}}_{\text{a}}$of water, it is a weaker base than water.

c) The dissociation reaction is${\text{C}}_6{\text{H}}_5\text{OH}+{\text{CH}}_3\text{OH}\rightleftharpoons {\text{C}}_6{\text{H}}_5{\text{O}}^{-}+{\text{CH}}_3{\text{OH}}_2^{+}$

d) An expression for the auto ionization constant of methanol is$\text{K=}\left[{\text{CH}}_{\text{3}}{\text{OH}}_{\text{2}}^{\text{+}}\right]\left[{\text{CH}}_{\text{3}}{\text{O}}^{\text{-}}\right]$

Step-by-step solution

To find why the values are different

(a)

${\text{pK}}_{\text{a}}$shows how much an acid will dissociate. The lowerthe,${\text{pK}}_{\text{a}}$the higher the value of${\text{K}}_{\text{a}}$Higher${\text{K}}_{\text{a}}$ dissociatesmore. phenol have different${\text{pK}}_{\text{a}}$values because the dissociation reaction depends on the strength of the other reactant. Hence It depends on the acid-base character of the other reactant.${\text{pK}}_{\text{a}}$

To find the methanol is stronger or weaker

(b)

Phenol has${\text{pK}}_{\text{a}}$=$10.0$in water and a${\text{pK}}_{\text{a}}$=$14.4$in methanol. Since lower${\text{pK}}_{\text{a}}$indicates higher${\text{K}}_{\text{a}}$value and higher ${\text{K}}_{\text{a}}$dissociates more, the lower${\text{pK}}_{\text{a}}$is the stronger base. This is because a stronger base helps in the dissociation of the acid. A weaker base will be as "stagnant" as the weak acid so less dissociation will happen.

Since the ${\text{pK}}_{\text{a}}$of methanol is greater than the${\text{pK}}_{\text{a}}$ of water, it is a weaker base than water.

Write the dissociation reaction of phenol in methanol

(c)

The dissociation reaction of phenol in methanol is written below.

${\text{C}}_6{\text{H}}_5\text{OH}+{\text{CH}}_3\text{OH}\rightleftharpoons {\text{C}}_6{\text{H}}_5{\text{O}}^{-}+{\text{CH}}_3{\text{OH}}_2^{+}$

The hydrogen from the OH group in phenol will transfer to the OH group of methanol.Hencethedissociation reaction is

${\text{C}}_6{\text{H}}_5\text{OH}+{\text{CH}}_3\text{OH}\rightleftharpoons {\text{C}}_6{\text{H}}_5{\text{O}}^{-}+{\text{CH}}_3{\text{OH}}_2^{+}$

Write an expression for the auto ionization constant of methanol

(d)

First, write auto ionization reaction of methanol.

${\text{CH}}_3\text{OH}+{\text{CH}}_3\text{OH}\rightleftharpoons {\text{CH}}_3{\text{OH}}_2^{+}+{\text{CH}}_3{\text{O}}^{-}$

The hydrogen from the OH group in methanol will transfer to the OH group of the other methanol.

Now, write the K of the reaction.

$\begin{array}{l}\text{K=}\frac{\text{[product]}}{\text{[reactant]}}\\ \text{K=}\left[{\text{CH}}_{\text{3}}{\text{OH}}_{\text{2}}^{\text{+}}\right]\left[{\text{CH}}_{\text{3}}{\text{O}}^{\text{-}}\right]\end{array}$

The methanol is not included since it is liquid.

Hence an expression for the auto ionization constant of methanol is$\text{K=}\left[{\text{CH}}_{\text{3}}{\text{OH}}_{\text{2}}^{\text{+}}\right]\left[{\text{CH}}_{\text{3}}{\text{O}}^{\text{-}}\right]$