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Chapter 16: Problem 126

(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?

Short Answer

Expert verified
The equilibrium constants for the given reactions are found using the dissociation constants from Appendix D. For reaction (i), the equilibrium constant \(K_\mathrm{eq}\) can be calculated as \(K_\mathrm{eq} = \dfrac{K_\mathrm{a1}(\mathrm{HCO}_3^-)}{K_\mathrm{b}(\mathrm{OH}^-)}\). For reaction (ii), the equilibrium constant \(K_\mathrm{eq}\) can be calculated as \(K_\mathrm{eq} = \dfrac{K_\mathrm{a}(\mathrm{NH}_4^+)}{K_\mathrm{a2}(\mathrm{HCO}_3^-)}\). Comparing these equilibrium constants to the criteria mentioned in the problem statement (\(K \gg1\)), it can be determined if any of the equilibria can be represented using a single arrow.

Step by step solution

01

Determine the dissociation constants from Appendix D

You will need to find the dissociation constants for the relevant substances from Appendix D. You should have the following values: \(K_\mathrm{a1} (\mathrm{HCO}_3^-)\): This is the dissociation constant for bicarbonate ion. \(K_\mathrm{b} (\mathrm{OH}^-)\): This is the dissociation constant for hydroxide ion. \(K_\mathrm{a} (\mathrm{NH}_4^+)\): This is the dissociation constant for ammonium ion. \(K_\mathrm{a2} (\mathrm{HCO}_3^-)\): This is another dissociation constant for bicarbonate ion.
02

Determine the equilibrium constant for reaction (i)

First, we will find the equilibrium constant for reaction (i): \(\mathrm{HCO}_{3}^{-}(a q)+\mathrm{OH}^{-}(a q) \rightleftharpoons \mathrm{CO}_{3}^{2-}(a q)+\mathrm{H}_{2} \mathrm{O}(l)\) The relevant dissociation constants are \(K_\mathrm{a1} (\mathrm{HCO}_3^-)\) and \(K_\mathrm{b} (\mathrm{OH}^-)\). To find the equilibrium constant for this reaction, we can use the relationship: \(K_\mathrm{eq} = \dfrac{K_\mathrm{a1}(\mathrm{HCO}_3^-)}{K_\mathrm{b}(\mathrm{OH}^-)}\) Using the dissociation constants obtained from Appendix D, perform the calculation and find the value of \(K_\mathrm{eq}\) for reaction (i).
03

Determine the equilibrium constant for reaction (ii)

Next, we will find the equilibrium constant for reaction (ii): \(\mathrm{NH}_{4}^{+}(a q)+\mathrm{CO}_{3}^{2-}(a q) \rightleftharpoons \mathrm{NH}_{3}(a q)+\mathrm{HCO}_{3}^{-}(a q)\) The relevant dissociation constants are \(K_\mathrm{a} (\mathrm{NH}_4^+)\) and \(K_\mathrm{a2} (\mathrm{HCO}_3^-)\). To find the equilibrium constant for this reaction, we can use the relationship: \(K_\mathrm{eq} = \dfrac{K_\mathrm{a}(\mathrm{NH}_4^+)}{K_\mathrm{a2}(\mathrm{HCO}_3^-)}\) Using the dissociation constants obtained from Appendix D, perform the calculation and find the value of \(K_\mathrm{eq}\) for reaction (ii).
04

Assess if any of the equilibria could be represented by a single arrow

We usually use single arrows for reactions when the forward reaction is appreciable (\(K \gg1\)) or when the products escape from the system. Compare the values of the equilibrium constants for reactions (i) and (ii) to these criteria. If any of the equilibrium constants are much greater than 1, then that equilibrium can be written using a single arrow. By following these steps, you should be able to determine the equilibrium constants for the given reactions and assess if they warrant the use of a single arrow for representation.

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Most popular questions from this chapter

At \(50^{\circ} \mathrm{C}\), the ion-product constant for $\mathrm{H}_{2} \mathrm{O}\( has the value \)K_{w}=5.48 \times 10^{-14} \cdot(\mathbf{a})$ What is the \(\mathrm{pH}\) of pure water at \(50^{\circ} \mathrm{C} ?\) (b) Based on the change in \(K_{w}\) with temperature, predict whether \(\Delta H\) is positive, negative, or zero for the autoionization reaction of water: $$ 2 \mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons \mathrm{H}_{3} \mathrm{O}^{+}(a q)+\mathrm{OH}^{-}(a q) $$

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 \(\left(\mathrm{C}_{5} \mathrm{H}_{5} \mathrm{~N}\right)\)

Calculate the molar concentration of \(\mathrm{OH}^{-}\) in a \(0.050 \mathrm{M}\) solution of ethylamine $\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{NH}_{2} ; K_{b}=6.4 \times 10^{-4}\right) .$ Calculate the \(\mathrm{pH}\) of this solution.

The amino acid glycine $\left(\mathrm{H}_{2} \mathrm{~N}-\mathrm{CH}_{2}-\mathrm{COOH}\right)$ can participate in the following equilibria in water: $\mathrm{H}_{2} \mathrm{~N}-\mathrm{CH}_{2}-\mathrm{COOH}+\mathrm{H}_{2} \mathrm{O} \rightleftharpoons$ $$ \mathrm{H}_{2} \mathrm{~N}-\mathrm{CH}_{2}-\mathrm{COO}^{-}+\mathrm{H}_{3} \mathrm{O}^{+} \quad K_{\mathrm{a}}=4.3 \times 10^{-3} $$ $$ \begin{aligned} \mathrm{H}_{2} \mathrm{~N}-\mathrm{CH}_{2}-\mathrm{COOH}+\mathrm{H}_{2} \mathrm{O} & \rightleftharpoons \\ &{ }^{+} \mathrm{H}_{3} \mathrm{~N}-\mathrm{CH}_{2}-\mathrm{COOH}+\mathrm{OH}^{-} \quad K_{\mathrm{b}}=6.0 \times 10^{-5} \end{aligned} $$ (a) Use the values of \(K_{a}\) and \(K_{b}\) to estimate the equilibrium constant for the intramolecular proton transfer to form a zwitterion: $$ \mathrm{H}_{2} \mathrm{~N}-\mathrm{CH}_{2}-\mathrm{COOH} \rightleftharpoons{ }^{+} \mathrm{H}_{3} \mathrm{~N}-\mathrm{CH}_{2}-\mathrm{COO}^{-} $$ (b) What is the pH of a 0.050 Maqueous solution of glycine? (c) What would be the predominant form of glycine in a solution with \(\mathrm{pH} 13\) ? With \(\mathrm{pH}\) ?

Identify the Brønsted-Lowry acid and the Brønsted-Lowry base on the left side of each of the following equations, and also identify the conjugate acid and conjugate base of each on the right side: (a) $\mathrm{NH}_{4}^{+}(a q)+\mathrm{CN}^{-}(a q) \rightleftharpoons \mathrm{HCN}(a q)+\mathrm{NH}_{3}(a q)$ (b) $\left(\mathrm{CH}_{3}\right)_{3} \mathrm{~N}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons$ $$ \left(\mathrm{CH}_{3}\right)_{3} \mathrm{NH}^{+}(a q)+\mathrm{OH}^{-}(a q) $$ (c) \(\mathrm{HCOOH}(a q)+\mathrm{PO}_{4}^{3-}(a q) \rightleftharpoons\) $$ \mathrm{HCOO}^{-}(a q)+\mathrm{HPO}_{4}^{2-}(a q) $$
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