Problem 69 - Chemistry The Central Science

Question

Write the chemical equation and the \(K_{b}\) expression for the reaction of each of the following bases with water: (a) dimethylamine, \(\left(\mathrm{CH}_{3}\right)_{2} \mathrm{NH} ;(\mathbf{b})\) carbonate ion, \(\mathrm{CO}_{3}^{2-} ;(\mathbf{c})\) formate ion, \(\mathrm{CHO}_{2}^{-} .\)

Step-by-Step Solution

Answer

(a) Dimethylamine reacts with water: \((\mathrm{CH}_{3})_{2} \mathrm{NH} + \mathrm{H}_{2} \mathrm{O} \leftrightarrow (\mathrm{CH}_{3})_{2} \mathrm{NH}_{2}^{+} + \mathrm{OH}^{-}\), with \(K_{b} = \frac{[ (\mathrm{CH}_{3})_{2} \mathrm{NH}_{2}^{+}] [\mathrm{OH}^{-}]}{[(\mathrm{CH}_{3})_{2} \mathrm{NH}]}\) (b) Carbonate ion reacts with water: \(\mathrm{CO}_{3}^{2-} + \mathrm{H}_{2} \mathrm{O} \leftrightarrow \mathrm{HCO}_{3}^{-} + \mathrm{OH}^{-}\), with \(K_{b} = \frac{[\mathrm{HCO}_{3}^{-}] [\mathrm{OH}^{-}]}{[\mathrm{CO}_{3}^{2-}]}\) (c) Formate ion reacts with water: \(\mathrm{CHO}_{2}^{-} + \mathrm{H}_{2} \mathrm{O} \leftrightarrow \mathrm{CHO}_{2}\mathrm{H} + \mathrm{OH}^{-}\), with \(K_{b} = \frac{[\mathrm{CHO}_{2}\mathrm{H}] [\mathrm{OH}^{-}]}{[\mathrm{CHO}_{2}^{-}]}\)

Step 1: (a) Reaction of dimethylamine with water

Dimethylamine reacts with water to form dimethylammonium ion and hydroxide ion. The chemical equation of this reaction is: \((\mathrm{CH}_{3})_{2} \mathrm{NH} + \mathrm{H}_{2} \mathrm{O} \leftrightarrow (\mathrm{CH}_{3})_{2} \mathrm{NH}_{2}^{+} + \mathrm{OH}^{-}\)

Step 2: (a) \(K_{b}\) expression for the reaction of dimethylamine with water

Based on the chemical equation, the \(K_{b}\) expression can be written as: \[K_{b} = \frac{[ (\mathrm{CH}_{3})_{2} \mathrm{NH}_{2}^{+}] [\mathrm{OH}^{-}]}{[(\mathrm{CH}_{3})_{2} \mathrm{NH}]}\]

Step 3: (b) Reaction of carbonate ion with water

Carbonate ion reacts with water to form bicarbonate ion and hydroxide ion. The chemical equation of this reaction is: \(\mathrm{CO}_{3}^{2-} + \mathrm{H}_{2} \mathrm{O} \leftrightarrow \mathrm{HCO}_{3}^{-} + \mathrm{OH}^{-}\)

Step 4: (b) \(K_{b}\) expression for the reaction of carbonate ion with water

Based on the chemical equation, the \(K_{b}\) expression can be written as: \[K_{b} = \frac{[\mathrm{HCO}_{3}^{-}] [\mathrm{OH}^{-}]}{[\mathrm{CO}_{3}^{2-}]}\]

Step 5: (c) Reaction of formate ion with water

Formate ion reacts with water to form formic acid and hydroxide ion. The chemical equation of this reaction is: \(\mathrm{CHO}_{2}^{-} + \mathrm{H}_{2} \mathrm{O} \leftrightarrow \mathrm{CHO}_{2}\mathrm{H} + \mathrm{OH}^{-}\)

Step 6: (c) \(K_{b}\) expression for the reaction of formate ion with water

Based on the chemical equation, the \(K_{b}\) expression can be written as: \[K_{b} = \frac{[\mathrm{CHO}_{2}\mathrm{H}] [\mathrm{OH}^{-}]}{[\mathrm{CHO}_{2}^{-}]}\]

Key Concepts

Understanding Dimethylamine

Dimethylamine is a simple secondary amine, commonly represented by the formula \((\mathrm{CH}_3)_2 \mathrm{NH}\). It's a base that reacts with water to produce dimethylammonium ions and hydroxide ions. This occurs because dimethylamine can accept a proton from water, which increases the water's hydroxide concentration:

• Chemical Reaction: \((\mathrm{CH}_3)_2 \mathrm{NH} + \mathrm{H}_2 \mathrm{O} \leftrightarrow (\mathrm{CH}_3)_2 \mathrm{NH}_2^+ + \mathrm{OH}^-\)
• Kb Expression: \[K_{b} = \frac{[ (\mathrm{CH}_3)_2 \mathrm{NH}_2^+] [\mathrm{OH}^-]}{[(\mathrm{CH}_3)_2 \mathrm{NH}]}\]

Dimethylamine is frequently used in the synthesis of various chemicals and pharmaceuticals. Its behavior in water is crucial for understanding its role in such chemical reactions. Understanding its nature helps in predicting its behavior in complex reactions, where it often serves as a proton acceptor. By looking at its Kb expression, we understand the strength of dimethylamine as a base relative to water.

Inside the Carbonate Ion Reaction

The carbonate ion, \(\mathrm{CO}_3^{2-}\), is an interesting polyatomic ion whose chemistry is essential in many environmental and biological processes. When carbonate ion reacts with water, it forms bicarbonate ions and hydroxide ions:

• Chemical Reaction: \(\mathrm{CO}_3^{2-} + \mathrm{H}_2 \mathrm{O} \leftrightarrow \mathrm{HCO}_3^- + \mathrm{OH}^-\)
• Kb Expression: \[K_{b} = \frac{[\mathrm{HCO}_3^-] [\mathrm{OH}^-]}{[\mathrm{CO}_3^{2-}]}\]

This base ionization is significant in processes such as the buffering of blood pH and the oceanic carbon cycle. By accepting a proton, carbonate ions form bicarbonate ions, contributing to the alkalinity of a solution. The Kb expression provides insight into how effectively carbonate ions can raise the pH of a solution by generating hydroxide ions.A solid grasp of how carbonate ions interact with water can illuminate broader environmental and industrial processes where they play a critical role.

Exploring the Formate Ion

The formate ion, \(\mathrm{CHO}_2^-\), represents the simplest carboxylate anion, derived from formic acid. Known for its simplicity, the formate ion reacts with water to produce formic acid and hydroxide ions:

• Chemical Reaction: \(\mathrm{CHO}_2^- + \mathrm{H}_2 \mathrm{O} \leftrightarrow \mathrm{CHO}_2\mathrm{H} + \mathrm{OH}^-\)
• Kb Expression: \[K_{b} = \frac{[\mathrm{CHO}_2\mathrm{H}] [\mathrm{OH}^-]}{[\mathrm{CHO}_2^-]}\]

Formate ions exhibit weak base behavior. They can accept protons from water, a reaction that produces small amounts of hydroxide and increases basicity slightly. Understanding the Kb expression for the formate ion helps us comprehend its role in various chemical and biological processes.They often serve in deicing applications or as a biodegradable pesticide, showcasing their versatility and importance in today’s chemistry and environmental science spheres. Knowing how formate ions react with water contributes to this understanding and can facilitate advances in handling and utilizing formate ion-related compounds.