Problem 209 - A Complete Resource Book in Chemistry for JEE Main

Question

Considering the basic strength of amines in aqueous solution, which one has the smallest \(\mathrm{pK}_{b}\) value? [2014] (a) \(\left(\mathrm{CH}_{3}\right)_{3} \mathrm{~N}\) (b) \(\mathrm{C}_{6} \mathrm{H}_{3} \mathrm{NH}_{2}\) (c) \(\left(\mathrm{CH}_{3}\right)_{2} \mathrm{NH}\) (d) \(\mathrm{CH}_{3} \mathrm{NH}_{2}\)

Step-by-Step Solution

Answer

(c) \((\mathrm{CH}_3)_2\mathrm{NH}\) has the smallest \(\mathrm{pK}_{b}\) value.

Step 1: Understand pK_b and Basic Strength

The basic strength of an amine in aqueous solution is indicated by its pK_b value. A smaller pK_b value corresponds to a stronger base, as pK_b is the negative logarithm of the base dissociation constant (K_b). Therefore, the smaller the pK_b, the larger the K_b, indicating greater basic strength.

Step 2: Evaluate Methylated Amines

Examine the amines provided: - (a) Trimethylamine \((\mathrm{CH}_3)_3\mathrm{N}\) - (c) Dimethylamine \( (\mathrm{CH}_3)_2\mathrm{NH} \) - (d) Methylamine \( \mathrm{CH}_3\mathrm{NH}_2\)These amines enhance basicity as methyl groups push electron density towards the nitrogen, making it more basic. More methyl groups in amines generally correlate with higher basicity.

Step 3: Consider Aniline's Basicity

Examine (b) Aniline \( \mathrm{C}_6 \mathrm{H}_5 \mathrm{NH}_2\). Aniline is less basic than the aliphatic amines because the lone pair of electrons on nitrogen is delocalized into the aromatic ring, reducing its availability to accept protons. This results in a lower basicity compared to alkyl amines.

Step 4: Compare Between Aliphatic Amines

Among the remaining aliphatic amines: - Trimethylamine, with three methyl groups, has a lower tendency to release the nitrogen lone pair for hydrogen bonding due to steric hindrance and decreased solubility in water. - Dimethylamine typically has a higher basicity due to an optimal balance of electron donation and lack of hindrance.

Step 5: Conclusion on the Smallest pK_b

Comparing (c) Dimethylamine \( (\mathrm{CH}_3)_2\mathrm{NH} \) and (d) Methylamine \( \mathrm{CH}_3\mathrm{NH}_2 \), Dimethylamine is typically more basic due to additional electron donation from a second methyl group, thus generally having the smallest pK_b value among the options.

Key Concepts

pKb value

The pKb value is a crucial measure when discussing the basicity of amines. It indicates the strength of a base in a solution, specifically how easily an amine can attract and bond with protons in water. Let's break this down. The pKb is actually the negative logarithm of the base dissociation constant, expressed as follows:\[pK_b = -\log(K_b)\] In simple terms, the smaller the pKb number, the stronger the base is. This is because a lower pKb signifies a higher Kb, which means the base more readily accepts protons. Hence, if you are comparing the basic strength of different amines, you are essentially looking for the one with the lowest pKb value. This amine will be the strongest base in water among the options you are considering.

Amines in Aqueous Solution

When amines dissolve in water, they exhibit different levels of basicity. This is due to their ability to accept protons, thanks to the lone pair of electrons on the nitrogen atom. An amine's ability to do this in an aqueous solution depends on the presence of alkyl groups attached to the nitrogen. Let’s delve into how this works:

• Aliphatic Amines: These are amines with alkyl groups, such as methyl or ethyl, attached directly to the nitrogen. Aliphatic amines are typically more basic than aromatic amines because the alkyl groups push electron density toward the nitrogen atom, making it easier for the nitrogen to attract protons.
• Aromatic Amines (e.g., Aniline): These amines have the nitrogen atom attached to an aromatic ring, like a benzene ring. Here, the nitrogen's lone pair is delocalized into the aromatic system, making it less available to accept a proton. This delocalization reduces the basicity of aromatic amines compared to aliphatic ones.

Recognizing how different amines behave in water is key to understanding their basicity, hence facilitating correct identification of the strongest base based on their pKb values.

Electron Donation in Amines

Electron donation in amines is central to explaining their basicity. Alkyl groups like methyl groups are electron-donating, meaning they can push electron density toward the nitrogen. This increased electron density at the nitrogen atom enhances the amine's ability to accept protons. Let's explore this effect further:

• Methyl Groups: When attached to nitrogen, methyl groups increase the electron density on the nitrogen due to their electron-donating nature. This means that with each additional methyl group, the nitrogen becomes more electron-rich, increasing its proton-accepting ability.
• Effect on pKb: More methyl groups can lead to a lower pKb value, correlating with higher basicity. For instance, dimethylamine tends to have a smaller pKb than methylamine, highlighting its greater basic strength due to an extra methyl group enhancing electron donation.

Thus, the number and type of alkyl groups surrounding the nitrogen atom are crucial in determining an amine's basic strength. More electron donation means that the amine can engage more effectively with protons, strengthening its basic nature.