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Chapter 16: Problem 10

What is the pH of each of the following solutions? (a) \(0.0045 \mathrm{M} \mathrm{HCl} ;\) (b) \(6.14 \times 10^{-4} \mathrm{M} \mathrm{HNO}_{3} ;\) (c) 0.00683 \(\mathrm{M} \mathrm{NaOH} ;\) (d) \(4.8 \times 10^{-3} \mathrm{M} \mathrm{Ba}(\mathrm{OH})_{2}\)

Short Answer

Expert verified
The respective pH values according to each step are: (a) approximately 2.35, (b) approximately 3.21, (c) approximately 11.17, (d) approximately 11.62.

Step by step solution

01

Calculating for \( \mathrm{HCl} \)

Hydrochloric acid (\( \mathrm{HCl} \)) is a strong acid. It ionizes completely in water, so the concentration of \(\mathrm{H^+}\) ions is 0.0045 M. Use the formula \( \mathrm{pH} = - \log [ \mathrm{H}^+ ] \) to find the pH of the acid. Insert the given concentration, so the pH will be - log(0.0045).
02

Calculating for \( \mathrm{HNO}_{3} \)

Nitric acid (\( \mathrm{HNO}_{3} \)) is also a strong acid that ionizes completely. The concentration of \( \mathrm{H}^+ \) ions is \(6.14 \times 10^{-4} M\). Use the formula \( \mathrm{pH} = - \log [ \mathrm{H}^+ ] \) to find the pH of the acid. The pH of this acid is - log(\(6.14 \times 10^{-4}\)).
03

Calculating for \( \mathrm{NaOH} \)

Sodium hydroxide (\( \mathrm{NaOH} \)) is a strong base, so we need to calculate the pOH first. The pOH is calculated the same way as pH but instead of \( \mathrm{H}^+ \) we use \( \mathrm{OH}^- \) ions. Thus, pOH = - log(0.00683). To find the pH use \( \mathrm{pH} = 14 - \mathrm{pOH} \).
04

Calculating for \( \mathrm{Ba}(\mathrm{OH})_{2} \)

Barium hydroxide (\( \mathrm{Ba}(\mathrm{OH})_{2} \)) is a strong base and has two \( \mathrm{OH}^- \) ions. The total \( \mathrm{OH}^- \) concentration will be twice the concentration of the base, so 2 * \(4.8 \times 10^{-3} M = 9.6 \times 10^{-3} M\). So the initial pOH = - log(\(9.6 \times 10^{-3}\)). Then to find the pH we use \(\mathrm{pH} = 14 - \mathrm{pOH}\)

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Most popular questions from this chapter

\(50.00 \mathrm{mL}\) of \(0.0155 \mathrm{M} \mathrm{HI}(\mathrm{aq})\) is mixed with \(75.00 \mathrm{mL}\) of 0.0106 M KOH(aq). What is the pH of the final solution?

What is the (a) degree of ionization and (b) percent ionization of propionic acid in a solution that is \(0.45 \mathrm{M}\) \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CO}_{2} \mathrm{H} ?\) $$\begin{aligned} &\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CO}_{2} \mathrm{H}+\mathrm{H}_{2} \mathrm{O} \rightleftharpoons \mathrm{H}_{3} \mathrm{O}^{+}+\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CO}_{2}^{-}\\\ &&\mathrm{p} K_{\mathrm{a}}=4.89 \end{aligned}$$

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.

The following four equilibria lie to the right: \(\mathrm{N}_{2} \mathrm{H}_{5}^{+}+\) \(\mathrm{CH}_{3} \mathrm{NH}_{2} \longrightarrow \mathrm{N}_{2} \mathrm{H}_{4}+\mathrm{CH}_{3} \mathrm{NH}_{3}^{+} ; \mathrm{H}_{2} \mathrm{SO}_{3}+\mathrm{F}^{-} \longrightarrow\) \(\mathrm{HSO}_{3}^{-}+\mathrm{HF} ; \mathrm{CH}_{3} \mathrm{NH}_{3}^{+}+\mathrm{OH}^{-} \longrightarrow \mathrm{CH}_{3} \mathrm{NH}_{2}+\) \(\mathrm{H}_{2} \mathrm{O} ;\) and \(\mathrm{HF}+\mathrm{N}_{2} \mathrm{H}_{4} \longrightarrow \mathrm{F}^{-}+\mathrm{N}_{2} \mathrm{H}_{5}^{+}\) (a) Rank all the acids involved in order of decreasing acid strength. (b) Rank all the bases involved in order of decreasing base strength. (c) State whether each of the following two equilibria lies primarily to the right or to the left: (i) \(\mathrm{HF}+\mathrm{OH}^{-} \longrightarrow \mathrm{F}^{-}+\mathrm{H}_{2} \mathrm{O} ;\) (ii) \(\mathrm{CH}_{3} \mathrm{NH}_{3}^{+}+\) \(\mathrm{HSO}_{3}^{-} \longrightarrow \mathrm{CH}_{3} \mathrm{NH}_{2}+\mathrm{H}_{2} \mathrm{SO}_{3}\).

Predict which is the stronger acid: (a) \(\mathrm{HClO}_{2}\) or \(\mathrm{HClO}_{3} ;(\mathrm{b}) \mathrm{H}_{2} \mathrm{CO}_{3}\) or \(\mathrm{HNO}_{2} ;(\mathrm{c}) \mathrm{H}_{2} \mathrm{SiO}_{3}\) or \(\mathrm{H}_{3} \mathrm{PO}_{4}\) Explain.
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