Question

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

Short answer

In the stomach with a \(\mathrm{pH}\) of 2.5, nicotine (\(\mathrm{pK}_{a}=7.84\)), strychnine (\(\mathrm{pK}_{a}=8.0\)), and quinine (\(\mathrm{pK}_{a}=8.04\)) will be present in their protonated forms, while caffeine (\(\mathrm{pK}_{a}=0.60\)) will be present in its neutral base form.

Step-by-step solution

Calculate the \(K_{a}\) values for each compound.

We are given the \(K_{b}\) values and the relationship \(K_{w} = K_{a} K_{b}\), where \(K_{w}\) (the ion product constant for water) is equal to \(1 \times 10^{-14}\). We can calculate the \(K_{a}\) values for each compound as follows: Nicotine: \(K_{b} = 7 \times 10^{-7}\) \[K_{a} = \frac{K_{w}}{K_{b}} = \frac{1 \times 10^{-14}}{7 \times 10^{-7}} = 1.43 \times 10^{-8}\] Caffeine: \(K_{b} = 4 \times 10^{-14}\) \[K_{a} = \frac{K_{w}}{K_{b}} = \frac{1 \times 10^{-14}}{4 \times 10^{-14}} = 2.5 \times 10^{-1}\] Strychnine: \(K_{b} = 1 \times 10^{-6}\) \[K_{a} = \frac{K_{w}}{K_{b}} = \frac{1 \times 10^{-14}}{1 \times 10^{-6}} = 1 \times 10^{-8}\] Quinine: \(K_{b} = 1.1 \times 10^{-6}\) \[K_{a} = \frac{K_{w}}{K_{b}} = \frac{1 \times 10^{-14}}{1.1 \times 10^{-6}} = 9.09 \times 10^{-9}\]

Calculate the \(\mathrm{pK}_{a}\) values for each compound.

Using the calculated \(K_{a}\) values, we can find the \(\mathrm{pK}_{a}\) values for each compound: Nicotine: \[ \mathrm{pK}_{a} = - \log_{10} (1.43 \times 10^{-8}) = 7.84 \] Caffeine: \[ \mathrm{pK}_{a} = - \log_{10} (2.5 \times 10^{-1}) = 0.60 \] Strychnine: \[ \mathrm{pK}_{a} = - \log_{10} (1 \times 10^{-8}) = 8.0 \] Quinine: \[ \mathrm{pK}_{a} = - \log_{10} (9.09 \times 10^{-9}) = 8.04 \]

Compare the \(\mathrm{pH}\) values to determine the form of each compound in the stomach.

The \(\mathrm{pH}\) in the stomach is 2.5, so we can now compare the \(\mathrm{pK}_{a}\) values to determine the form of each compound: - Nicotine: \(\mathrm{pH} < \mathrm{pK}_{a}\) (2.5 < 7.84), so it will be present in its protonated form. - Caffeine: \(\mathrm{pH} > \mathrm{pK}_{a}\) (2.5 > 0.60), so it will be present in its neutral base form. - Strychnine: \(\mathrm{pH} < \mathrm{pK}_{a}\) (2.5 < 8.0), so it will be present in its protonated form. - Quinine: \(\mathrm{pH} < \mathrm{pK}_{a}\) (2.5 < 8.04), so it will be present in its protonated form. Therefore, in the stomach with a \(\mathrm{pH}\) of 2.5, nicotine, strychnine, and quinine will be present in their protonated forms, while caffeine will be present in its neutral base form.

Key concepts

pH

The concept of pH is critical in understanding acid-base equilibria. pH is a measure of the hydrogen ion concentration, \([H^+]\), in a solution, defining whether a solution is acidic or basic. The pH scale ranges from 0 to 14, with 7 being neutral. Values below 7 indicate an acidic solution, while values above 7 represent a basic or alkaline solution.
The stomach's environment typically has a pH of around 2.5, which is quite acidic. This acidic environment affects the solubility and chemical form of different substances, including drugs and nutrients. When considering organic molecules with nitrogen, their solubility and form — whether as protonated or neutral — will depend significantly on the ambient pH.
By comparing the pH of the stomach with the pKa of a compound, it's possible to predict the compound's state in that environment. If the pH is lower than the pKa value, the compound is more likely to gain a proton (protonated form). Conversely, if the pH is higher than the pKa, the compound tends to stay in its neutral form. Understanding this interplay helps determine the bioavailability and behavior of substances like drugs upon ingestion.

pKa

The pKa of a compound is a specific type of equilibrium constant that measures how easily a molecule donates a proton, i.e., its acidity. Mathematically, it's expressed as the negative base-10 logarithm of the acid dissociation constant, \((Ka)\): \(pKa = - \log_{10}(Ka)\).
The lower the pKa, the stronger the acid, meaning the molecule more readily gives up its proton. This property is crucial for understanding how nitrogen-containing organic molecules behave in different pH environments.
For example, nicotine, caffeine, strychnine, and quinine each have unique pKa values, indicating their tendency to exist in protonated or neutral forms at different pH levels. In the acidic environment of the stomach, these compounds will tend to become protonated unless the pH is below their pKa value.
Calculating the pKa from the given \(K_b\) requires using the relationship between \(K_a, K_b,\) and \(K_w\) (the ion product of water), where \(K_w = K_a \times K_b\). By understanding and calculating these values, you can predict whether a compound will predominantly appear as its acid or base form under specific physiological conditions.

Nitrogen-containing organic compounds

Nitrogen-containing organic compounds are abundant and play crucial roles in both physiological functions and therapeutic applications. They often contain amine groups, which can act as bases. This basicity is essential in predicting how these compounds will interact with acids and the resultant solubility changes.
Compounds like nicotine, caffeine, strychnine, and quinine feature nitrogen atoms that participate in acid-base reactions. These reactions can significantly affect their solubility and form in various pH environments. For instance, in an acidic setting like the stomach, these compounds are more soluble in their protonated form. However, their behavior differs based on their specific \(pKa\) values.
The nitrogen atom in these molecules generally acts as a proton acceptor. In the stomach's low pH, the surrounding hydrogen ions interact with the nitrogen, leading to protonation. Understanding this characteristic of nitrogen-containing compounds helps anticipate their behavior and absorption in biological systems, particularly in pharmacology and medicine.

• Nitrogen atoms allow for hydrogen bonding, increasing solubility in water in their protonated state.
• They can participate in electron-pair donation, making them essential in metabolic pathways.
• Their basic properties are leveraged in drug formulation for targeted delivery and release mechanisms.