Problem 89 - Chemistry and Chemical Reactivity

Question

The base ethylamine \(\left(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{NH}_{2}\right)\) has a \(K_{\mathrm{b}}\) of \(4.3 \times 10^{-4} .\) A closely related base, ethanolamine \(\left(\mathrm{HOCH}_{2} \mathrm{CH}_{2} \mathrm{NH}_{2}\right),\) has a \(K_{\mathrm{b}}\) of \(3.2 \times 10^{-5}\). (a) Which of the two bases is stronger? (b) Calculate the \(\mathrm{pH}\) of a \(0.10 \mathrm{M}\) solution of the stronger base.

Step-by-Step Solution

Answer

(a) Ethylamine is stronger. (b) pH is 11.82.

Step 1: Identify the Base Strength using Kb

Compare the given values of the base dissociation constant \( K_b \) for each base. The larger the \( K_b \), the stronger the base is, because it means it dissociates more in solution.

Step 2: Compare Kb values

Ethylamine \((\mathrm{CH}_3\mathrm{CH}_2\mathrm{NH}_2)\) has a \( K_b = 4.3 \times 10^{-4} \), while Ethanolamine \((\mathrm{HOCH}_2\mathrm{CH}_2\mathrm{NH}_2)\) has a \( K_b = 3.2 \times 10^{-5} \). Since \(4.3 \times 10^{-4} > 3.2 \times 10^{-5}\), ethylamine is the stronger base.

Step 3: Calculate the Concentration of Hydroxide Ions

For ethylamine, use the equation for the equilibrium of a base: \[ \mathrm{CH}_3\mathrm{CH}_2\mathrm{NH}_2 + \mathrm{H}_2\mathrm{O} \rightleftharpoons \mathrm{CH}_3\mathrm{CH}_2\mathrm{NH}_3^+ + \mathrm{OH}^- \] Apply the expression for \( K_b \): \[ K_b = \frac{[\mathrm{CH}_3\mathrm{CH}_2\mathrm{NH}_3^+][\mathrm{OH}^-]}{[\mathrm{CH}_3\mathrm{CH}_2\mathrm{NH}_2]} \] Assuming \([\mathrm{OH}^-] = x\) and \([\mathrm{CH}_3\mathrm{CH}_2\mathrm{NH}_2] \approx 0.10 - x \approx 0.10\): \[ K_b = \frac{x^2}{0.10} \] Substitute \( K_b = 4.3 \times 10^{-4} \) and solve for \(x\).

Step 4: Solve for x

Set up the equation: \[ 4.3 \times 10^{-4} = \frac{x^2}{0.10} \] Thus, \[ x^2 = (4.3 \times 10^{-4}) \times 0.10 = 4.3 \times 10^{-5} \] Solve for \(x\): \[ x = \sqrt{4.3 \times 10^{-5}} \approx 0.00656 \] This is the concentration of \( \mathrm{OH}^- \) ions.

Step 5: Calculate pOH

Use the concentration of hydroxide ions to find \( \mathrm{pOH} \): \[ \mathrm{pOH} = -\log [\mathrm{OH}^-] = -\log (0.00656) \approx 2.18 \]

Step 6: Convert pOH to pH

Since pH and pOH are related by the equation \( \mathrm{pH} + \mathrm{pOH} = 14 \): \[ \mathrm{pH} = 14 - \mathrm{pOH} = 14 - 2.18 = 11.82 \]

Key Concepts

Ethylamine

Ethylamine, chemically denoted as \( ext{C}_2 ext{H}_5 ext{NH}_2\), is a simple aliphatic amine. Amines are organic derivatives of ammonia (\( ext{NH}_3\)), where one or more hydrogen atoms are replaced by carbon-containing groups. In ethylamine, this substitution involves an ethyl group \((\text{-CH}_2\text{CH}_3)\).One key property of ethylamine, which comes into focus in chemistry, is its ability to act as a base. A base, by definition, is a substance that can accept protons (\( ext{H}^+\)) or donate electron pairs. Ethylamine is a weak base, meaning it does not fully ionize in water. It can moderately accept protons, forming the ethylammonium ion \((\text{C}_2 ext{H}_5 ext{NH}_3^+)\).The strength of a base in solution can often be gauged by its base dissociation constant \(K_b\). This constant helps in understanding how completely a base dissociates in water. Ethylamine has a relatively high \(K_b\) value of \(4.3 \times 10^{-4}\), which indicates it is a stronger weak base compared to many others with lower \(K_b\) values.

Ethanolamine

Ethanolamine \((\text{HOCH}_2\text{CH}_2\text{NH}_2)\) is another fascinating compound that combines the structure of both an alcohol and an amine. In its structure, it has a hydroxyl group \((\text{-OH})\) attached alongside the amino group \((\text{-NH}_2)\). This dual functionality contributes to its unique chemical properties.Ethanolamine, like ethylamine, acts as a weak base when dissolved in water. It can attract and bind to hydrogen ions, partly dissociating into ethanolammonium ions \((\text{HOCH}_2\text{CH}_2\text{NH}_3^+)\). While it's also a weak base, its base dissociation constant \(K_b\) is \(3.2 \times 10^{-5}\), making it weaker than ethylamine in terms of base strength.The presence of the hydroxyl group in ethanolamine affects its hydrophilicity, meaning it is quite soluble in water. Such properties have implications for its use in various industrial and chemical applications, including as a surfactant and in the production of detergents.

Hydroxide Ion Concentration

Understanding the concept of hydroxide ion \([\text{OH}^-]\) concentration is crucial when dealing with basic solutions. In any aqueous base solution, the dissociation process results in the formation of hydroxide ions. For example, when you dissolve ethylamine in water, it reacts following the equilibrium:
\[ \text{CH}_3\text{CH}_2\text{NH}_2 + \text{H}_2\text{O} \rightleftharpoons \text{CH}_3\text{CH}_2\text{NH}_3^+ + \text{OH}^- \]The concentration of \([\text{OH}^-]\) is a key factor in calculating the pH and pOH of the solution. In our case, the concentration of hydroxide ions can be determined by setting up the equation based on the known \(K_b\) value. Solving for \([\text{OH}^-]\) involves using mathematical manipulation to ultimately obtain that \(x \approx 0.00656\), where \(x\) is the concentration of hydroxide ions.

pOH and pH Calculation

The concepts of pOH and pH are vital for understanding the acidity or basicity of a solution. \[ \text{pOH} = -\log(0.00656) \approx 2.18 \]

\[ \text{pH} + \text{pOH} = 14 \]Substituting the pOH value, you can find:
\[ \text{pH} = 14 - 2.18 = 11.82 \]This indicates that the solution is basic, as expected when dealing with bases like ethylamine. Understanding these relationships helps you predict the behavior of solutions in various chemical contexts.