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Chapter 45: 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
All \(K_{\mathrm{a}}\) expressions are typically written in the form \([A-][H+]/[HA]\). All \(K_{\mathrm{b}}\) expressions are usually of the form \([BH+][OH-]/[B]\). The multiplication of \(K_{\mathrm{a}}\) by \(K_{\mathrm{b}}\) for a conjugate acid-base pair at a particular temperature yields a constant equal to the ion product of water, \(K_{w}\), i.e., \(K_{\mathrm{a}} \times K_{\mathrm{b}} = K_{w}\).

Step by step solution

01

Common features of \(K_{\mathrm{a}}\) expressions

In the case of acids, \(K_{\mathrm{a}}\) is the equilibrium constant for the dissociation of an acid into its conjugate base and a proton. All \(K_{\mathrm{a}}\) expressions are usually written in the form \([A-][H+]/[HA]\), where \(HA\) represents the undissociated acid, \(A-\) is the conjugate base and \(H+\) is the proton. Note: The concentration of water is often omitted in these expressions as water is typically in great excess.
02

Common features of \(K_{\mathrm{b}}\) expressions

For bases, \(K_{\mathrm{b}}\) is the equilibrium constant for the reaction of a base with water to form its conjugate acid and a hydroxide ion. All \(K_{\mathrm{b}}\) expressions are usually of the form \([BH+][OH-]/[B]\), where \(B\) is the initial base, \(BH+\) represents the conjugate acid and \(OH-\) is the hydroxide ion. Similarly to \(K_{\mathrm{a}}\) expressions, the concentration of water is usually not considered.
03

Common features of \(K_{\mathrm{a}} \times K_{\mathrm{b}}\) products

The multiplication of \(K_{\mathrm{a}}\) by \(K_{\mathrm{b}}\) for a conjugate acid-base pair at a particular temperature yields a constant equal to the ion product of water (\(K_{w}\)). Thus, every \(K_{\mathrm{a}} \times K_{\mathrm{b}}\) expressions can be represented as \(K_{\mathrm{a}} \times K_{\mathrm{b}} = K_{w}\). This relationship is a fundamental one in acid-base chemistry.

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Most popular questions from this chapter

\(\mathrm{HNO}_{3}\) is considered to be the weakest of the strong acids. Explain why the conjugate bases of all strong acids do not produce basic solutions when dissolved in water.

Indicate which of the following are potential acids, potential bases, or both (potential acid and potential base). a) \(\mathrm{Al}^{3+}\) b) \(\mathrm{CH}_{3} \mathrm{NH}_{3}^{+}\) c) \(\mathrm{HPO}_{4}{ }^{2-}\) d) \(\quad \mathrm{F}^{-}\) e) \(\mathrm{NH}_{4}^{+}\) f) \(\mathrm{H}_{2} \mathrm{O}\)

The nitrate ion is the conjugate base of nitric acid, \(\mathrm{HNO}_{3}\). Explain why \(\mathrm{NO}_{3}^{-}\) does not produce a basic solution when dissolved in water.

To 2 significant figures, predict the \(\mathrm{pH}\) of a \(1.00\) molar solution of \(\mathrm{NaBr}\). Explain your reasoning carefully.

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