(a) The general formulas for the homologous series of hydrocarbons are as follows: For alkenes (general formula): $$ \mathrm{C}_n\mathrm{H}_{2n} $$ For alkynes (general formula): $$ \mathrm{C}_n\mathrm{H}_{2n-2} $$ (b) To synthesize isopropyl alcohol from acetaldehyde, methyl iodide, magnesium, and water, we follow these steps: Step 1: Preparation of Grignard reagent Methyl iodide reacts with magnesium in the presence of dry ether to form methyl magnesium iodide (a Grignard reagent). $$ \mathrm{CH}_3\mathrm{I} + \mathrm{Mg} \xrightarrow{\text{dry ether}} \mathrm{CH}_3\mathrm{MgI} $$ Step 2: Reaction with acetaldehyde Methyl magnesium iodide reacts with acetaldehyde (ethanal) to form an addition product. $$ \mathrm{CH}_3\mathrm{CHO} + \mathrm{CH}_3\mathrm{MgI} \rightarrow \mathrm{CH}_3-\mathrm{CH}(\mathrm{OMgI})-\mathrm{CH}_3 $$ Step 3: Hydrolysis The addition product is then hydrolyzed with water to produce isopropyl alcohol (propan-2-ol). $$ \mathrm{CH}_3-\mathrm{CH}(\mathrm{OMgI})-\mathrm{CH}_3 + \mathrm{H}_2\mathrm{O} \rightarrow \mathrm{CH}_3-\mathrm{CH}(\mathrm{OH})-\mathrm{CH}_3 + \mathrm{Mg}(\mathrm{OH})\mathrm{I} $$