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Chapter 16: Problem 113

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 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, \(K_{b}=1.1 \times 10^{-6} .\)

Short Answer

Expert verified
In the stomach with a pH of 2.5, nicotine, strychnine, and quinine will exist in their protonated form, while caffeine will be present as a neutral base.

Step by step solution

01

Convert pH to hydronium ion concentration

To convert the pH (2.5) to the hydronium ion concentration, use the formula: \(pH = -\log[H_3O^+]\). Rearranging this formula, we can solve for the concentration of hydronium ions: \([H_3O^+] = 10^{-pH} = 10^{-2.5} \).
02

Calculate Kw from the provided Kb values

We know that the ionization constant of water \(K_w\) can be calculated as: \(K_w = K_b \cdot K_a\). Since the \(K_w\) is constant at 25°C with a value of \(1 \times 10^{-14}\), we can easily find the associated \(K_a\) values by the equation: \(K_a = \frac{K_w}{K_b}\). Calculate the \(K_a\) values using the given \(K_b\) values: Nicotine: \(K_a = \frac{1 \times 10^{-14}}{7 \times 10^{-7}}\) Caffeine: \(K_a = \frac{1 \times 10^{-14}}{4 \times 10^{-14}}\) Strychnine: \(K_a = \frac{1 \times 10^{-14}}{1 \times 10^{-6}}\) Quinine: \(K_a = \frac{1 \times 10^{-14}}{1.1 \times 10^{-6}}\)
03

Compare Ka values to hydronium ion concentration

Now, we can compare the \(K_a\) values to the hydronium ion concentration we calculated in Step 1. If the \(K_a\) value is much smaller than the hydronium ion concentration, the compound will exist in its protonated form. Nicotine: \(K_a < [H_3O^+]\) (Protonated form) Caffeine: \(K_a \approx [H_3O^+]\) (Neutral base) Strychnine: \(K_a < [H_3O^+]\) (Protonated form) Quinine: \(K_a < [H_3O^+]\) (Protonated form) Based on the comparison of \(K_a\) values and hydronium ion concentration, nicotine, strychnine and quinine will be present in their protonated form in the stomach, while caffeine will exist as a neutral base at pH 2.5.

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Most popular questions from this chapter

At the freezing point of water \(\left(0^{\circ} \mathrm{C}\right), K_{w}=1.2 \times 10^{-15}\) Calculate \(\left[\mathrm{H}^{+}\right]\) and \(\left[\mathrm{OH}^{-}\right]\) for a neutral solution at this temperature.

Calculate the percent ionization of propionic acid \((\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{COOH})\) in solutions of each of the following concentrations (\(K_{a}\) is given in AppendixD): (a) \(0.250 M,(\mathbf{b}) 0.0800 M,\) \((\mathbf{c}) 0.0200 M .\)

(a) Write an equation for the reaction in which \(\mathrm{H}_{2} \mathrm{C}_{6} \mathrm{H}_{7} \mathrm{O}_{5}^{-}(a q)\) acts as a base in \(\mathrm{H}_{2} \mathrm{O}(l) .\) (b) Write an equation for the reaction in which \(\mathrm{H}_{2} \mathrm{C}_{6} \mathrm{H}_{7} \mathrm{O}_{5}^{-}(a q)\) acts as an acid in \(\mathrm{H}_{2} \mathrm{O}(l) .\) (c) What is the conjugate acid of \(\mathrm{H}_{2} \mathrm{C}_{6} \mathrm{H}_{7} \mathrm{O}_{5}^{-}(a q) ?\) What is its conjugate base?

Calculate \(\left[\mathrm{OH}^{-}\right]\) for each of the following solutions, and indicate whether the solution is acidic, basic, or neutral: \((\mathbf{a})\left[\mathrm{H}^{+}\right]=0.0505 M (\mathbf{b})\left[\mathrm{H}^{+}\right]=2.5 \times 10^{-10} M ;(\mathbf{c})\) a solution in which \(\left[\mathrm{H}^{+}\right]\) is 1000 times greater than \(\left[\mathrm{OH}^{-}\right] .\)

Consider the base hydroxylamine, \(\mathrm{NH}_{2} \mathrm{OH}\) . (a) What is the conjugate acid of hydroxylamine? (b) When it acts as a base, which atom in hydroxylamine accepts a proton? (c) There are two atoms in hydroxylamine that have nonbonding electron pairs that could act as proton acceptors. Use Lewis structures and formal charges (Section 8.5) to rationalize why one of these two atoms is a much better proton acceptor than the other.
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