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Chapter 15: Problem 60

From the relationship \(K_{\mathrm{a}} K_{\mathrm{b}}=K_{\mathrm{w}},\) what can you deduce about the relative strengths of a weak acid and its conjugate base?

Short Answer

Expert verified
From the relationship \(K_{\mathrm{a}} K_{\mathrm{b}}=K_{\mathrm{w}}\), one can deduce that the weaker the acid, the stronger its conjugate base, and vice versa, because the product of the acid and base dissociation constants remains constant and equals to the ion product of water.

Step by step solution

01

Understanding what \(K_{\mathrm{a}}\), \(K_{\mathrm{b}}\), and \(K_{\mathrm{w}}\) represent

The acid dissociation constant, \(K_{\mathrm{a}}\), measures the strength of an acid in solution. The base dissociation constant, \(K_{\mathrm{b}}\), measures the strength of a base in solution. The ion product of water, \(K_{\mathrm{w}}\), is essentially the product of the concentration of the hydrogen ions and the hydroxide ions in water at a particular temperature. It is a constant value at a given temperature.
02

Interpreting the equation \(K_{\mathrm{a}} K_{\mathrm{b}}=K_{\mathrm{w}}\)

The equation \(K_{\mathrm{a}} K_{\mathrm{b}}=K_{\mathrm{w}}\) shows that the product of the acid dissociation constant of a weak acid and the base dissociation constant of its conjugate base equals the ion product of water. This implies that when a weak acid is in solution, its ability to donate a proton is balanced by its corresponding base's ability to accept a proton.
03

Deducing the relative strengths of the weak acid and its conjugate base

If the acid has a high \(K_{\mathrm{a}}\) value, meaning it strongly donates protons, then its conjugate base must have a low \(K_{\mathrm{b}}\) value, indicating it does not readily accept protons. Conversely, if the acid has a low \(K_{\mathrm{a}}\) value, the conjugate base must have a high \(K_{\mathrm{b}}\) value. Therefore, one can deduce that the weaker the acid, the stronger its conjugate base, and vice versa.

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Most popular questions from this chapter

Classify each of the following species as a Lewis acid or a Lewis base: (a) \(\mathrm{CO}_{2},\) (b) \(\mathrm{H}_{2} \mathrm{O},\) (c) \(\mathrm{I}^{-}\), (f) \(\mathrm{OH}^{-},(\mathrm{g}) \mathrm{H}^{+},\) (d) \(\mathrm{SO}_{2}\), (e) \(\mathrm{NH}_{3}\), (h) \(\mathrm{BCl}_{3}\).

The disagreeable odor of fish is mainly due to organic compounds \(\left(\mathrm{RNH}_{2}\right)\) containing an amino group, \(-\mathrm{NH}_{2},\) where \(\mathrm{R}\) is the rest of the molecule. Amines are bases just like ammonia. Explain why putting some lemon juice on fish can greatly reduce the odor.

How does the strength of an oxoacid depend on the electronegativity and oxidation number of the central atom?

Calculate the hydrogen ion concentration in \(\mathrm{mol} / \mathrm{L}\) for each of the following solutions: (a) a solution whose \(\mathrm{pH}\) is \(5.20,\) (b) a solution whose \(\mathrm{pH}\) is 16.00 , (c) a solution whose hydroxide concentration is \(3.7 \times 10^{-9} M\).

Describe the following reaction in terms of the Lewis theory of acids and bases: $$ \mathrm{AlCl}_{3}(s)+\mathrm{CI}^{-}(a q) \longrightarrow \mathrm{AlCl}_{4}^{-}(a q) $$
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