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 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 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

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: \([H_3O^+] = 10^{-pH} = 10^{-2.5} \).

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: \(K_a = \frac{1 \times 10^{-14}}{1.1 \times 10^{-6}}\)

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.

Key concepts

Organic Chemistry

Organic chemistry is the study of carbon-based compounds, which are essential to life. Many organic molecules consist of basic nitrogen atoms, making them fascinating subjects for exploration. These molecules often have diverse physical and chemical properties due to the presence of the nitrogen atom.
Basic nitrogen atoms can be found in several organic compounds such as alkaloids, proteins, amino acids, and nucleic acids. Alkaloids like nicotine, caffeine, strychnine, and quinine, have nitrogen atoms that can accept protons, making them fundamental to understanding acid-base equilibrium.
In organic chemistry, when we discuss the solubility of compounds in water, the protonation state plays a crucial role. Protonation can increase the solubility of organic molecules in their salt form rather than their neutral base form. This concept is integral to the pharmaceutical industry, where drugs need to be soluble to be absorbed into the bloodstream efficiently.

pH Calculation

The term 'pH' refers to the potential of hydrogen, and it quantifies the acidity or basicity of a solution. pH is calculated using the formula \[pH = -\log[H_3O^+]\] where \([H_3O^+]\) is the hydronium ion concentration in the solution.
A low pH indicates a high concentration of hydronium ions, suggesting an acidic environment. Part of solving the original exercise involved converting a pH value of 2.5 into the corresponding hydronium ion concentration using the formula:
\[[H_3O^+] = 10^{-2.5}\] which simplifies to approximately \([H_3O^+] = 3.16\times 10^{-3}~mol/L\). Understanding how to calculate pH is vital because it allows scientists to predict the behavior of compounds in various environments, such as the acidic stomach environment in the original problem.

Ionization Constant

The ionization constant, often discussed in terms of \(K_b\) and \(K_a\), is a measure of a compound's strength as a base or an acid, respectively. These constants represent the equilibrium between the protonated and deprotonated forms of a compound.
In the exercise, the base ionization constant, \(K_b\), was provided for several compounds. To find the acid ionization constant, \(K_a\), we use the relationship with the ionization constant of water \(K_w = 1 \times 10^{-14}\) at 25°C:\[K_a = \frac{K_w}{K_b}\] By calculating \(K_a\), we can predict whether a compound will hold onto its proton or lose it, thus existing in a protonated form or as a neutral base. This plays a pivotal role in determining the solubility and activity of compounds in different pH environments.

Protonation

Protonation refers to the addition of a proton (H+ ion) to a molecule, forming a conjugate acid. This process is crucial for understanding the acid-base behavior of organic compounds.
When the pH is lower than the pKa of a compound, the protonation of the compound is favored. In the stomach’s acidic environment (with a pH of 2.5), many basic nitrogen-containing organic molecules will likely be protonated. This means they have gained protons, making them more soluble in the stomach's aqueous environment.
In the context of the exercise, comparing each compound's ’s \(K_a\) to the stomach's hydronium ion concentration helps determine their predominant form. Compounds like nicotine and quinine are more likely to be found in their protonated form at pH 2.5.

Hydronium Ion Concentration

Hydronium ions, denoted as \[H_3O^+]\], play a vital role in determining the acidity of a solution. The concentration of these ions is directly related to the solution's pH level. In a highly acidic environment like the stomach, the hydronium ion concentration is high.
Understanding how to calculate and interpret hydronium ion concentrations helps to predict the behavior of various substances in a solution. In the exercise, computing the hydronium ion concentration at a given pH (2.5) helps understand which form organic molecules, like nicotine and caffeine, will predominantly take in the stomach's acidic environment.
Evaluating the balance between hydronium concentrations and the ionization properties of compounds is key to predicting their solubility and reactivity in different conditions.