Basicity order of the following amines in aqueous medium
i) N-Methylaniline i
i) N, N-Dimethylaniline
iii) Aniline
In aqueous medium, the electron-donating groups (such as alkyl groups) attached to the nitrogen atom increase the basicity of the amine.
In this case, N, N-Dimethylaniline (ii) has the highest basicity, followed by N-Methylaniline (i), and Aniline (iii) with the lowest basicity.
The presence of two methyl groups on the nitrogen in N, N-Dimethylaniline makes it more basic than N-Methylaniline, which has only one methyl group. Aniline has the least basicity due to the lack of any alkyl groups on the nitrogen.
Amines have a lone pair of electrons on the nitrogen atom, due to which they behave as Lewis bases. Greater the value of \( K_b \) or smaller the value of \( pK_b \), stronger is the base. Amines are more basic than alcohols, ethers, esters, etc. The basic character of aliphatic amines should increase with the increase of alkyl substitution. However, it does not occur in a regular manner, as a secondary aliphatic amine is unexpectedly more basic than a tertiary amine in aqueous solutions. Aromatic amines are weaker bases than ammonia and aliphatic amines. Electron-releasing groups such as \( -CH_3 \), \( -NH_2 \), etc., increase the basicity, while electron-withdrawing substituents such as \( -NO_2 \), \( -CN \), halogens, etc., decrease the basicity of amines. The effect of these substituents is more pronounced at the para-position than at the meta-position.
Arrange the following in increasing order of their basic character. Give reason:
A 3 kg block is connected as shown in the figure. Spring constants of two springs \( K_1 \) and \( K_2 \) are 50 Nm\(^{-1}\) and 150 Nm\(^{-1}\) respectively. The block is released from rest with the springs unstretched. The acceleration of the block in its lowest position is ( \( g = 10 \) ms\(^{-2}\) )
Evaluate the integral: \[ \int \frac{3x^9 + 7x^8}{(x^2 + 2x + 5x^9)^2} \,dx= \]