Question

Write the reaction and the corresponding \(K_{\mathrm{b}}\) equilibrium expression for each of the following substances acting as bases in water. a. aniline, \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{NH}_{2}\) b. dimethylamine, \(\left(\mathrm{CH}_{3}\right)_{2} \mathrm{NH}\)

Short answer

a. Aniline, C6H5NH2: Reaction: \(C_{6}H_{5}NH_{2} + H_{2}O \rightarrow C_{6}H_{5}NH_{3}^{+} + OH^{-}\) Kb expression: \(K_{b} = \frac{[C_{6}H_{5}NH_{3}^{+}][OH^{-}]}{[C_{6}H_{5}NH_{2}]}\) b. Dimethylamine, (CH3)2NH: Reaction: \((CH_{3})_{2}NH + H_{2}O \rightarrow (CH_{3})_{2}NH_{2}^{+} + OH^{-}\) Kb expression: \(K_{b} = \frac{[(CH_{3})_{2}NH_{2}^{+}][OH^{-}]}{[(CH_{3})_{2}NH]}\)

Step-by-step solution

Write the reaction of aniline with water

When aniline (C6H5NH2) acts as a base in water, it accepts a proton (H+) from a water molecule, forming its conjugate acid (C6H5NH3+) and hydroxide ion (OH-): C6H5NH2 + H2O -> C6H5NH3+ + OH-

Write the Kb equilibrium expression for aniline

For the given reaction, the Kb equilibrium expression is defined as: Kb = \(\frac{[C_{6}H_{5}NH_{3}^{+}] [OH^{-}]}{[C_{6}H_{5}NH_{2}]}\) b. Dimethylamine, (CH3)2NH:

Write the reaction of dimethylamine with water

When dimethylamine ((CH3)2NH) acts as a base in water, it accepts a proton (H+) from a water molecule, forming its conjugate acid ((CH3)2NH2+) and hydroxide ion (OH-): (CH3)2NH + H2O -> (CH3)2NH2+ + OH-

Write the Kb equilibrium expression for dimethylamine

For the given reaction, the Kb equilibrium expression is defined as: Kb = \(\frac{[(CH_{3})_{2}NH_{2}^{+}] [OH^{-}]}{[(CH_{3})_{2}NH]}\)

Key concepts

Kb equilibrium expression

The "Kb equilibrium expression" is vital in understanding how a base reacts in water to form an equilibrium state. For a base in the water, it demonstrates how the concentrations of the products relate to the concentration of the reactant at equilibrium. The general form of this expression for a base B, which accepts a proton from water to form its conjugate acid BH+ and hydroxide ion OH-, is denoted as:\[ K_b = \frac{[BH^+][OH^-]}{[B]} \]In this expression:

• \([BH^+]\) represents the concentration of the conjugate acid.
• \([OH^-]\) represents the concentration of hydroxide ions in the solution.
• \([B]\) denotes the concentration of the undissociated base.

The Kb value indicates the strength of the base; a higher Kb means a stronger base that dissociates more in water, producing more OH-. Kb values are particularly useful in predicting the extent to which a base will ionize in water, which is essential for calculations in chemistry.

Base reactions in water

"Base reactions in water" describe how bases interact with water molecules. A base, according to the Brønsted-Lowry theory, is a substance that can accept protons (H+ ions). When a base reacts with water, it takes a proton from a water molecule. This transfer generates a conjugate acid of the base and a hydroxide ion, OH-. For example:Reaction with AnilineAniline \((C_6H_5NH_2)\) when reacting with water behaves as follows:\(C_6H_5NH_2 + H_2O \rightarrow C_6H_5NH_3^+ + OH^-\)Reaction with DimethylamineDimethylamine \((CH_3)_2NH\) interacts with water similarly:\((CH_3)_2NH + H_2O \rightarrow (CH_3)_2NH_2^+ + OH^-\)In these reactions, the base transfers electrons to accept a proton from the water, promoting the formation of their respective conjugate acids and increasing the solution's pH due to OH- formation.

Proton acceptor

At the core of acid-base reactions, a "proton acceptor" is defined as a substance that can take up protons (H+ ions). In terms of the Brønsted-Lowry definition, bases are proton acceptors. This means that during a chemical reaction, they can capture hydrogen ions from other molecules.
When a base like aniline or dimethylamine is added to water, it operates as a proton acceptor. By accepting a proton from the water, the base shifts its balance:

• For aniline, accepting a proton forms the ion \(C_6H_5NH_3^+\).
• For dimethylamine, accepting a proton results in the ion \((CH_3)_2NH_2^+\).

These transformations highlight their behavior as proton acceptors in solution and are fundamental in analyzing the acid-base reactions' equilibrium. This capacity to accept protons is crucial in controlling pH levels in different solutions, illustrating the practical applications of understanding proton acceptors in chemical processes.