Using your roadmaps as a guide, show how to convert acetaldehyde into racemic 3-hydroxybutanal. You must use acetaldehyde as the source of all carbon atoms in the target molecule. Show all reagents and all molecules synthesized along the way.

First, we need to increase the carbon chain from two carbons to four. We can achieve this through an aldol condensation reaction. In this reaction, we'll use sodium hydroxide (NaOH) as a base to promote the formation of an enolate intermediate from acetaldehyde. The enolate will then react with another molecule of acetaldehyde, joining the carbon chains together. The final product will be 3-hydroxy-2-methyl-2-propenal. \[ \text{Acetaldehyde} + \mathrm{NaOH} \rightarrow \text{3-Hydroxy-2-methyl-2-propenal} \]

Now, we need to reduce the alpha,beta-unsaturated carbonyl group in the 3-hydroxy-2-methyl-2-propenal molecule to form 3-hydroxybutanal. We can accomplish this via catalytic hydrogenation using a catalyst, such as palladium on carbon (Pd/C), and a hydrogen source, such as hydrogen gas (H2). This reaction will form the desired 3-hydroxybutanal product. \[ \text{3-Hydroxy-2-methyl-2-propenal} + \mathrm{H_2} + \mathrm{Pd/C} \rightarrow \text{racemic 3-Hydroxybutanal} \] To summarize the process of converting acetaldehyde into racemic 3-hydroxybutanal, follow these steps: 1. Perform an aldol condensation reaction with acetaldehyde and sodium hydroxide (NaOH) to form 3-hydroxy-2-methyl-2-propenal. 2. Reduce the alpha,beta-unsaturated carbonyl group of 3-hydroxy-2-methyl-2-propenal using catalytic hydrogenation with palladium on carbon (Pd/C) and hydrogen gas (H2) to obtain racemic 3-hydroxybutanal.