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Chapter 16: Problem 59

Calculate the pH of each of the following solutions \(\left(K_{a}\right.\) and \(K_{b}\) values are given in Appendix D): (a) \(0.150 \mathrm{M}\) propionic acid $\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{COOH}\right)$ (b) \(0.250 \mathrm{M}\) hydrogen chromate ion \(\left(\mathrm{HCrO}_{4}^{-}\right),(\mathbf{c}) 0.750 \mathrm{M}\) pyridine \(\left(\mathrm{C}_{5} \mathrm{H}_{5} \mathrm{~N}\right)\)

Short Answer

Expert verified
The pH of the given solutions can be calculated as follows: (a) Propionic acid: Using the given \(K_a\), set up an equilibrium expression and solve for \(\mathrm{H^+}\) ions concentration. Then, use the pH formula to find the pH: \(\mathrm{pH} = -\log_{10} [\mathrm{H^+}]\). (b) Hydrogen chromate ion: Repeat the process for the acidic solution using the appropriate \(K_a\), and find the pH using the \(\mathrm{H^+}\) ions concentration. (c) Pyridine: As a basic solution, use the given \(K_b\) and solve for \(\mathrm{OH^-}\) ions concentration. Find the \(\mathrm{H^+}\) ions concentration using the ion product of water \((K_w)\), and finally calculate the pH using the \(\mathrm{H^+}\) ions concentration. By following these steps, you can determine the pH of each solution.

Step by step solution

01

Identify the nature of each compound

(a) Propionic acid is an organic acid and will dissociate in the solution to form \(\mathrm{H^+}\) ions. Therefore, it is an acidic solution. We will use its \(K_a\) to find the concentration of \(\mathrm{H^+}\) ions. (b) Hydrogen chromate ion is an anion containing a hydrogen ion and will also dissociate in the solution to form \(\mathrm{H^+}\) ions. Therefore, it is also an acidic solution. We will use its \(K_a\) to find the concentration of \(\mathrm{H^+}\) ions. (c) Pyridine is a weak base and will accept \(\mathrm{H^+}\) ions from water. Therefore, it is a basic solution. We will use its \(K_b\) to find the concentration of \(\mathrm{OH^-}\) ions and then calculate the concentration of \(\mathrm{H^+}\) ions.
02

Write the dissociation equilibrium equations

(a) For propionic acid: \[\mathrm{C_2H_5COOH} \rightleftharpoons \mathrm{C_2H_5COO^-} + \mathrm{H^+}\] (b) For hydrogen chromate ion: \[\mathrm{HCrO_4^-} \rightleftharpoons \mathrm{CrO_4^{2-}} + \mathrm{H^+}\] (c) For pyridine: \[\mathrm{C_5H_5N} + \mathrm{H_2O} \rightleftharpoons \mathrm{C_5H_5NH^+} + \mathrm{OH^-}\]
03

Calculate the concentration of H+ or OH- ions

For each solution, we will use the \(K_a\) or \(K_b\) values and create an equilibrium table to find the concentrations of \(\mathrm{H^+}\) or \(\mathrm{OH^-}\) ions. Since the exercise provides the \(K_a\) and \(K_b\) values in Appendix D, we can use them for our calculations. (a) Let \(x\) be the concentration of \(\mathrm{C_2H_5COO^-}\) and \(\mathrm{H^+}\): \[K_{a}=\frac{[\mathrm{C_2H_5COO^-}][\mathrm{H^+}]}{[\mathrm{C_2H_5COOH}]}\] (b) Let \(x\) be the concentration of \(\mathrm{CrO_4^{2-}}\) and \(\mathrm{H^+}\): \[K_{a}=\frac{[\mathrm{CrO_4^{2-}}][\mathrm{H^+}]}{[\mathrm{HCrO_4^-}]}\] (c) Let \(x\) be the concentration of \(\mathrm{C_5H_5NH^+}\) and \(\mathrm{OH^-}\): \[K_{b}=\frac{[\mathrm{C_5H_5NH^+}][\mathrm{OH^-}]}{[\mathrm{C_5H_5N}]}\]
04

Calculate the pH of each solution

For each solution, find the concentration of \(\mathrm{H^+}\) ions and use the pH formula: \[\mathrm{pH} = -\log_{10} [\mathrm{H^+}]\] For the basic solution (c), first find the concentration of \(\mathrm{H^+}\) ions from the \(\mathrm{OH^-}\) ion concentration using the relation: \[[\mathrm{H^+}][\mathrm{OH^-}] = K_w\] where \(K_w (1\times 10^{-14})\) is the ion product of water. Then, calculate the pH using the found concentration of \(\mathrm{H^+}\) ions. Finally, you will have the pH for each of the given solutions.

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Most popular questions from this chapter

Predict which member of each pair produces the more acidic aqueous solution: (a) \(\mathrm{K}^{+}\) or \(\mathrm{Cu}^{2+}\), (b) \(\mathrm{Fe}^{2+}\) or \(\mathrm{Fe}^{3+}\) (c) \(\mathrm{Al}^{3+}\) or \(\mathrm{Ga}^{3+}\)

The acid-dissociation constant for chlorous acid \(\left(\mathrm{HClO}_{2}\right)\) is \(1.1 \times 10^{-2}\). Calculate the concentrations of \(\mathrm{H}_{3} \mathrm{O}^{+}, \mathrm{ClO}_{2}^{-}\), and \(\mathrm{HClO}_{2}\) at equilibrium if the initial concentration of \(\mathrm{HClO}_{2}\) is \(0.0200 \mathrm{M}\)

Many moderately large organic molecules containing basic nitrogen atoms are not very soluble in water as neutral molecules, but they are frequently much more soluble as their acid salts. Assuming that \(\mathrm{pH}\) in the stomach is 2.5 , indicate whether each of the following compounds would be present in the stomach as the neutral base or in the protonated form: nicotine, $K_{b}=7 \times 10^{-7}\(; caffeine, \)K_{b}=4 \times 10^{-14} ;\( strychnine, \)K_{b}=1 \times 10^{-6} ;\( quinine, \)K_{b}=1.1 \times 10^{-6} .$

Identify the Brønsted-Lowry acid and the BrønstedLowry base on the left side of each equation, and also identify the conjugate acid and conjugate base of each on the right side. $$ \begin{array}{l} \text { (a) } \mathrm{HBrO}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons \mathrm{H}_{3} \mathrm{O}^{+}(a q)+\mathrm{BrO}^{-}(a q) \\\ \text { (b) } \mathrm{HSO}_{4}^{-}(a q)+\mathrm{HCO}_{3}^{-}(a q) \rightleftharpoons \mathrm{SO}_{4}^{2-}(a q)+\mathrm{H}_{2} \mathrm{CO}_{3}(a q) \\ \text { (c) } \mathrm{HSO}_{3}^{-}(a q)+\mathrm{H}_{3} \mathrm{O}^{+}(a q) \rightleftharpoons \mathrm{H}_{2} \mathrm{SO}_{3}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \end{array} $$

(a) Using dissociation constants from Appendix D, determine the value for the equilibrium constant for each of the following reactions. (i) $\mathrm{HCO}_{3}^{-}(a q)+\mathrm{OH}^{-}(a q) \rightleftharpoons \mathrm{CO}_{3}^{2-}(a q)+\mathrm{H}_{2} \mathrm{O}(l)$ (ii) $\mathrm{NH}_{4}^{+}(a q)+\mathrm{CO}_{3}^{2-}(a q) \rightleftharpoons \mathrm{NH}_{3}(a q)+\mathrm{HCO}_{3}^{-}(a q)$ (b) We usually use single arrows for reactions when the forward reaction is appreciable ( \(K\) much greater than 1) or when products escape from the system, so that equilibrium is never established. If we follow this convention, which of these equilibria might be written with a single arrow?
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