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Chapter 16: Problem 24

A 625 mL sample of an aqueous solution containing 0.275 mol propionic acid, \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CO}_{2} \mathrm{H},\) has \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=0.00239 \mathrm{M} .\) What is the value of \(K_{\mathrm{a}}\) for propionic acid? $$\begin{aligned} &\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CO}_{2} \mathrm{H}+\mathrm{H}_{2} \mathrm{O} \rightleftharpoons \mathrm{H}_{3} \mathrm{O}^{+}+\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CO}_{2}\\\ &&K_{\mathrm{a}}=? \end{aligned}$$

Short Answer

Expert verified
\(K_a\) for propionic acid is 1.3 × 10-5.

Step by step solution

01

Find processing concentration

The first thing to do is to find the concentration of propionic acid by dividing the number of moles by the volume in liters. To convert mL to L, divide by 1000. Thus, concentration of the acid = \(\frac{0.275 mol}{0.625 L}\) = 0.44 M
02

Find equilibrium values

The propionic acid will dissociate according the reaction \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CO}_{2} \mathrm{H}=\mathrm{H}_{2} \mathrm{O}+\mathrm{H}_{3} \mathrm{O}^{+}+\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CO}_{2}^{─}\). The equilibrium concentration of \([H_{3}O^{+}]\) is 0.00239 M. At equilibrium, the acid and conjugate base have equal concentrations \(x\) M where \(x\) = \([H_{3}O^{+}]\).
03

Calculate \(K_a\)

The expression for \(K_a\) is \(\frac{[H_{3}O^{+}][CH3CH2CO2^-]}{[CH3CH2CO2H]}\). Substituting the equilibrium concentrations, we get \(K_a\) = \(\frac{(0.00239 M)^2}{0.44 M - 0.00239 M}\). Solving this equation using a calculator, we get \(K_a\) = 1.3 × 10-5.

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Most popular questions from this chapter

The reaction of \(\mathrm{CH}_{3} \mathrm{COOH}(\) aq) proceeds furthest toward completion with a base when that base is (a) \(\mathrm{H}_{2} \mathrm{O} ;\) (b) \(\mathrm{CH}_{3} \mathrm{NH}_{3}^{+} ;\) (c) \(\mathrm{NH}_{4}^{+} ;\) (d) \(\mathrm{Cl}^{-} ;\) (e) \(\mathrm{CO}_{3}^{2-}\).

The solubility of 1 -naphthylamine, \(\mathrm{C}_{10} \mathrm{H}_{7} \mathrm{NH}_{2}, \mathrm{a}\) substance used in the manufacture of dyes, is given in a handbook as 1 g per \(590 \mathrm{g} \mathrm{H}_{2} \mathrm{O}\). What is the approximate \(\mathrm{pH}\) of a saturated aqueous solution of 1-naphthylamine? $$\begin{array}{r} \mathrm{C}_{10} \mathrm{H}_{7} \mathrm{NH}_{2}+\mathrm{H}_{2} \mathrm{O} \rightleftharpoons \mathrm{C}_{10} \mathrm{H}_{7} \mathrm{NH}_{3}^{+}+\mathrm{OH}^{-} \\ \mathrm{p} K_{\mathrm{b}}=3.92 \end{array}$$

Predict whether a solution of each of the following salts is acidic, basic, or pH neutral: (a) KCl; (b) KF; (c) \(\mathrm{NaNO}_{3} ;\) (d) \(\mathrm{Ca}(\mathrm{OCl})_{2} ;\) (e) \(\mathrm{NH}_{4} \mathrm{NO}_{2}\)

A 28.2 L volume of \(\mathrm{HCl}(\mathrm{g}),\) measured at \(742 \mathrm{mmHg}\) and \(25.0^{\circ} \mathrm{C},\) is dissolved in water. What volume of \(\mathrm{NH}_{3}(\mathrm{g}),\) measured at \(762 \mathrm{mmHg}\) and \(21.0^{\circ} \mathrm{C},\) must be absorbed by the same solution to neutralize the HCl?

For each of the following, identify the acids and bases involved in both the forward and reverse directions. (a) $\mathrm{HOBr}+\mathrm{H}_{2} \mathrm{O} \rightleftharpoons \mathrm{OBr}^{-}+\mathrm{H}_{3} \mathrm{O}^{+}$ (b) $\mathrm{HSO}_{4}^{-}+\mathrm{H}_{2} \mathrm{O} \rightleftharpoons \mathrm{SO}_{4}^{2-}+\mathrm{H}_{3} \mathrm{O}^{+}$ (c) $\mathrm{HS}^{-}+\mathrm{H}_{2} \mathrm{O} \rightleftharpoons \mathrm{H}_{2} \mathrm{S}+\mathrm{OH}^{-}$ (d) $\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{NH}_{3}^{+}+\mathrm{OH}^{-} \rightleftharpoons \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{NH}_{2}+\mathrm{H}_{2} \mathrm{O}$
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