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Chapter 14: Problem 24

What is the \(\mathrm{p} K_{\mathrm{a}}\) of an acid? As the $\mathrm{p} K_{\mathrm{a}}$ value increases, does acid strength increase or decrease? Explain.

Short Answer

Expert verified
The pKa of an acid is the negative logarithm of its acid dissociation constant (Ka), given by the equation \(pKa = -\log_{10}(Ka)\). It indicates the relative strength of an acid in a solution by quantifying its tendency to donate protons. As the pKa value increases, the acid strength decreases, making it a weaker acid. Conversely, as the pKa value decreases, the acid strength increases, making it a stronger acid.

Step by step solution

01

Define pKa

The pKa value of an acid represents the negative logarithm of the acid dissociation constant (Ka). It is expressed as: \(pKa = -\log_{10}(Ka)\). The pKa value gives us an idea of the relative strength of an acid in a solution by quantifying how readily the acid donates a proton (H+) in the solution.
02

Understand acid dissociation constant (Ka)

Ka is the acid dissociation constant, which is a measure of the tendency of an acid to dissociate into its conjugate base and a proton in the solution. For a general acid HA, the equilibrium reaction in a solution can be represented as: \[HA \rightleftharpoons A^- + H^+\] The equilibrium constant of this reaction is represented by Ka: \[Ka = \frac{[A^-][H^+]}{[HA]}\] where [HA], [A^-], and [H^+] are the equilibrium concentrations of the acid, its conjugate base, and the proton, respectively.
03

Explain the relationship between pKa and acid strength

As the pKa value increases, the Ka value decreases since \(pKa = -\log_{10}(Ka)\). A lower Ka value indicates a lower degree of dissociation, which in turn implies a weaker acid, as it is less likely to donate a proton in the solution. Therefore, as the pKa value of an acid increases, its strength decreases, i.e., the acid becomes weaker. Conversely, when the pKa value decreases, the acid's strength increases, making it a stronger acid.
04

Summary

In conclusion, the pKa value of an acid represents the negative logarithm of its acid dissociation constant (Ka), which indicates the degree of dissociation and thus the strength of the acid in the solution. As the pKa value increases, the acid strength decreases, making it a weaker acid. Conversely, as the pKa value decreases, the acid strength increases, making it a stronger acid.

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Most popular questions from this chapter

A typical sample of vinegar has a pH of \(3.0 .\) Assuming that vinegar is only an aqueous solution of acetic acid \(\left(K_{\mathrm{a}}=1.8 \times\right.\) \(10^{-5}\) ), calculate the concentration of acetic acid in vinegar.

A \(0.20-M\) sodium chlorobenzoate $\left(\mathrm{NaC}_{7} \mathrm{H}_{4} \mathrm{ClO}_{2}\right)\( solution has \)\mathrm{a} \mathrm{pH}\( of \)8.65 .$ Calculate the \(\mathrm{pH}\) of a \(0.20-M\) chlorobenzoic acid \(\left(\mathrm{HC}_{7} \mathrm{H}_{4} \mathrm{ClO}_{2}\right)\) solution.

Monochloroacetic acid, \(\mathrm{HC}_{2} \mathrm{H}_{2} \mathrm{ClO}_{2},\) is a skin irritant that is used in "chemical peels" intended to remove the top layer of dead skin from the face and ultimately improve the complexion. The value of \(K_{\mathrm{a}}\) for monochloroacetic acid is \(1.35 \times 10^{-3}\) Calculate the pH of a \(0.10-M\) solution of monochloroacetic acid.

The pH of human blood is steady at a value of approximately 7.4 owing to the following equilibrium reactions: $$ \mathrm{CO}_{2}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons \mathrm{H}_{2} \mathrm{CO}_{3}(a q) \rightleftharpoons \mathrm{HCO}_{3}^{-}(a q)+\mathrm{H}^{+}(a q) $$ Acids formed during normal cellular respiration react with the \(\mathrm{HCO}_{3}^{-}\) to form carbonic acid, which is in equilibrium with \(\mathrm{CO}_{2}(a q)\) and \(\mathrm{H}_{2} \mathrm{O}(l) .\) During vigorous exercise, a person's \(\mathrm{H}_{2} \mathrm{CO}_{3}\) blood levels were $26.3 \mathrm{mM},\( whereas his \)\mathrm{CO}_{2}\( levels were 1.63 \)\mathrm{mM}$ . On resting, the \(\mathrm{H}_{2} \mathrm{CO}_{3}\) levels declined to 24.9 \(\mathrm{m} M\) . What was the \(\mathrm{CO}_{2}\) blood level at rest?

At \(25^{\circ} \mathrm{C},\) a saturated solution of benzoic acid \(\left(K_{\mathrm{a}}=6.4 \times 10^{-5}\right)\) has a pH of \(2.80 .\) Calculate the water solubility of benzoic acid in moles per liter.
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