The reaction sequence is as follows:
Step 1: Reaction of ethanamine with \(\text{NaNO}_2\) and \(\text{HCl}\)
Ethanamine (\(\text{CH}_3\text{CH}_2\text{NH}_2\)) reacts with \(\text{NaNO}_2\) and \(\text{HCl}\) to form an unstable diazonium salt (\(\text{CH}_3\text{CH}_2\text{N}_2^+\text{Cl}^-\)):
\[\text{CH}_3\text{CH}_2\text{NH}_2 + \text{NaNO}_2 + \text{HCl} \rightarrow \text{CH}_3\text{CH}_2\text{N}_2^+\text{Cl}^- + \text{NaCl} + \text{H}_2\text{O}.\]
Step 2: Hydrolysis of the diazonium salt
The diazonium salt decomposes upon hydrolysis, liberating \(\text{N}_2\), \(\text{HCl}\), and ethanol (\(\text{CH}_3\text{CH}_2\text{OH}\)):
\[\text{CH}_3\text{CH}_2\text{N}_2^+\text{Cl}^- + \text{H}_2\text{O} \rightarrow \text{CH}_3\text{CH}_2\text{OH} + \text{N}_2 + \text{HCl}.\]
Step 3: Calculation of the mass of ethanamine
The reaction generates \(0.2\) moles of \(\text{HCl}\), which neutralizes \(0.2\) moles of \(\text{NaOH}\). From the stoichiometry of the reaction, 1 mole of ethanamine produces 1 mole of \(\text{HCl}\). Therefore, the moles of ethanamine (\(\text{CH}_3\text{CH}_2\text{NH}_2\)) required are \(0.2\) moles.
The molar mass of ethanamine is:
\[\text{Molar mass of } \text{CH}_3\text{CH}_2\text{NH}_2 = 12 + 3 + 3 + 12 + 2 + 14 + 1 = 44 \, \text{g/mol}.\]
The mass of ethanamine is:
\[\text{Mass} = \text{Moles} \times \text{Molar mass} = 0.2 \times 44 = 8.8 \, \text{g} \, (\text{Nearest Integer to } 9).\]
Final Answer: \(X = 9\).
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.
(a) Arrange the following in increasing order of their basic character. Give reason:
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If \[ \frac{dy}{dx} + 2y \sec^2 x = 2 \sec^2 x + 3 \tan x \cdot \sec^2 x \] and
and \( f(0) = \frac{5}{4} \), then the value of \[ 12 \left( y \left( \frac{\pi}{4} \right) - \frac{1}{e^2} \right) \] equals to: