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Chapter 16: Problem 31

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? $$\begin{array}{r} \mathrm{C}_{10} \mathrm{H}_{7} \mathrm{NH}_{2}+\mathrm{H}_{2} \mathrm{O} \rightleftharpoons \mathrm{C}_{10} \mathrm{H}_{7} \mathrm{NH}_{3}^{+}+\mathrm{OH}^{-} \\ \mathrm{p} K_{\mathrm{b}}=3.92 \end{array}$$

Short Answer

Expert verified
The approximate pH of the saturated solution of 1-naphthylamine is 12.0

Step by step solution

01

Understand the problem

The solubility of 1-naphthylamine is given as 1g in 590g of water. The ionization of the compound in water shows that it forms \(OH^-\) ions. The pKb of the compound is also given, which can be used to find the Kb.
02

Find the concentration of the base

First, convert the solubility from g/590g H2O to g/L of H2O by knowing that the density of water is 1g/mL. Then, convert the mass of the compound to moles by dividing by its molar mass. Therefore, \[Concentration = \frac{1g \times 10^3 mL/L}{590g} \times \frac{1 mol}{143g/mol} = 0.012 M\]
03

Find the Kb and [OH-]

Next, find the Kb using the equation \[Kb = 10^{-pKb} = 10^{-3.92} = 1.2 \times 10^{-4}\] Now, because the compound is a weak base and does not ionize completely, we apply the Kb expression: \[Kb = \frac{[OH-][C_{10}H_{7}NH_{3}^{+}]}{[C_{10}H_{7}NH_{2}]}\] As the base is in a 1:1 ratio with the hydroxide and the cation, and is initially present in excess, we get \[Kb = [OH-]^{2}\] From this, we solve for [OH-]: \[[OH-] = \sqrt{Kb} = \sqrt{1.2 \times 10^{-4}} = 1.1 \times 10^{-2} M\]
04

Calculate the pH

The pOH is calculated as the negative logarithm of the OH- concentration: \[pOH = -log[OH-] = -log(1.1 \times 10^{-2}) = 2.0\] To find the pH, use the formula \(pH = 14 - pOH\), which gives \(pH = 14 - 2.0 = 12.0\)

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Most popular questions from this chapter

One handbook lists a value of 9.5 for \(\mathrm{p} \mathrm{K}_{\mathrm{b}}\) of quinoline, \(\mathrm{C}_{9} \mathrm{H}_{7} \mathrm{N},\) a weak base used as a preservative for anatomical specimens and to make dyes. Another handbook lists the solubility of quinoline in water at \(25^{\circ} \mathrm{C}\) as \(0.6 \mathrm{g} / 100 \mathrm{mL} .\) Use this information to calculate the \(\mathrm{pH}\) of a saturated solution of quinoline in water.

Briefly describe each of the following ideas or phenomena: (a) conjugate base; (b) percent ionization of an acid or base; (c) self-ionization; (d) amphiprotic behavior.

Explain why \(\left[\mathrm{PO}_{4}^{3-}\right]\) in \(1.00 \mathrm{M} \mathrm{H}_{3} \mathrm{PO}_{4}\) is not simply \(\frac{1}{3}\left[\mathrm{H}_{3} \mathrm{O}^{+}\right],\) but much, much less than \(\frac{1}{3}\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]\)

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? $$\begin{aligned} &\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CO}_{2} \mathrm{H}+\mathrm{H}_{2} \mathrm{O} \rightleftharpoons \mathrm{H}_{3} \mathrm{O}^{+}+\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CO}_{2}\\\ &&K_{\mathrm{a}}=? \end{aligned}$$

What mass of benzoic acid, \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COOH}\), would you dissolve in \(350.0 \mathrm{mL}\) of water to produce a solution with a \(\mathrm{pH}=2.85 ?\) $$\begin{aligned} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COOH}+\mathrm{H}_{2} \mathrm{O} \rightleftharpoons \mathrm{H}_{3} \mathrm{O}^{+}+\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COO}^{-} & \\ K_{\mathrm{a}}=6.3 \times 10^{-5} \end{aligned}$$
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