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Chapter 47: Problem 3

For each of the following, describe the common features: a) all \(K_{\mathrm{a}}\) expressions b) all \(K_{\mathrm{b}}\) expressions c) all \(K_{\mathrm{a}} \times K_{\mathrm{b}}\) products

Short Answer

Expert verified
Common features include: \(K_{\mathrm{a}}\) expressions are equilibrium concentrations in acid-based reactions with the acid concentration in the denominator and the product concentrations in the numerator. \(K_{\mathrm{b}}\) expressions express equilibrium concentrations in base-acid reactions, with the base concentration in the denominator and product concentrations in the numerator. \(K_{\mathrm{a}}\) and \(K_{\mathrm{b}}\) products connect the dissociation constants of acid and a base with the self-ionization constant of water, \(K_{\mathrm{w}}\).

Step by step solution

01

Common Features of All \(K_{\mathrm{a}}\) Expressions

\(K_{\mathrm{a}}\) expressions are meant for acid-base reactions where an acid donates a proton (hydrogen ion) to water (acting as a base), leading to hydronium ions and the anion of the acid. \n\nThe generic formula for a \(K_{\mathrm{a}}\) expression is: \n\n\[K_{\mathrm{a}} = \frac{{[\mathrm{Hydronium\ Ion}][\mathrm{Anion\ of\ Acid}]}{{[\mathrm{Acid}]}}\]\n\nConcentrations are at equilibrium, with the solute concentration in the denominator and the product concentrations in the numerator.
02

Common Features of All \(K_{\mathrm{b}}\) Expressions

\(K_{\mathrm{b}}\) expressions describe reactions in which a base accepts a proton from water, forming hydroxide ions and the cation of the base. \n\nThe generic formula for a \(K_{\mathrm{b}}\) expression is: \n\n\[K_{\mathrm{b}} = \frac{{[\mathrm{Hydroxide\ Ion}][\mathrm{Cation\ of\ Base]}} {{[\mathrm{Base}]}}\] \n\nAgain, the equilibrium concentrations are used, with the base concentration in the denominator and the product concentrations in the numerator.
03

Common Features of All \(K_{\mathrm{a}}K_{\mathrm{b}}\) Products

The product of \(K_{\mathrm{a}}\) (for reacting acid) and \(K_{\mathrm{b}}\) (for reacting base) corresponds to the equilibrium expression for the overall reaction where an acid reacts with a base. It equals the ionic constant of water, \(K_{\mathrm{w}}\), at the same temperature. \n\nThis can be written as: \n\n\[K_{\mathrm{a}}K_{\mathrm{b}} = K_{\mathrm{w}}\]\n\nThus, it connects the dissociation constants of an acid and a base with the self-ionization constant of water.

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Most popular questions from this chapter

The chloride ion is the conjugate base of hydrochloric acid. Explain why \(\mathrm{Cl}^{-}\) does not produce a basic solution when dissolved in water.

Consider two acids, HA and HX, with HA being a stronger acid than HX. a) Which acid has a larger value of \(K_{\mathrm{a}}\) ? b) Which conjugate base, \(\mathrm{A}^{-}\) or \(\mathrm{X}^{-}\), has a larger value of \(K_{\mathrm{b}}\) ? c) Provide a qualitative description of the relationship between the relative strength of an acid and the relative strength of its conjugate base.

Provide an expression relating \(K_{\mathrm{w}}\) to \(K_{\mathrm{a}}\) and \(K_{\mathrm{b}}\) of a conjugate acid-base pair.

Describe how to determine the value of \(K_{\mathrm{b}}\) for a base-given the value of \(K_{\mathrm{a}}\) for its conjugate acid.

Explain why the conjugate bases of the strong acids do not produce basic solutions when dissolved in water.
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