After recognizing the reagents given, we know we need to begin with an alcohol. The alcohol choices differ only by how substituted they are.

For a carboxylic acid to form from a reaction with sodium dichromate and sulfuric acid, a primary alcohol needs to be available. Therefore, 1-pentanol is the correct answer.

The malonic ester is deprotonated at the most acidic hydrogen, the one on the carbon between the two oxygens. The electrons from that bond to the hydrogen form a carbon-carbon double bond while electrons from the oxygen-carbon double bond go to the oxygen atom. This is the enolate form. The chlorine leaves the 3-chloroheptane and the electrons from the carbon-carbon double bond bond to the carbon that the chlorine left. At the same time, the carbonyl is reformed. After deesterfication, 3-ethylheptanoic acid is formed.

Aldehyde is not a derivative of carboxylic acid. Esters can be derived from carboxylic acids by reacting them with  to form an acid chloride. From there, react it with an  to form an ester. Amides can be derived from carboxylic acids by reacting them with  to form an acid chloride. From there, react it with  to form an amide.

As a general rule, any carboxylic acid derivative can be converted into al carboxylic acid when reacting with 

The hydrolyzation of a nitrile with hydronium leads to a carboxylic acid. Only one choice is a carboxylic acid.

 is the only strong oxidizing agent listed. It is strong enough to oxidize the primary alcohol even further to a carboxylic acid product. The rest of the compounds listed are weak oxidizing agents or reducing agents.

This reaction is an electrophilic addition reaction with an alkene. This is one of many alkene addition reactions that can add an -OH group onto your starting material. The key aspect of an hydroboration-oxidation reaction is the anti-Markovinikov addition to the double bond. The -OH group should be on the least substituted of the two carbons that originate from the double bond. In light of this information, the answer is 2-cyclohexanol.

This reaction involves a very strong reducing agent in lithium aluminum hydride, . LAH converts ketones, aldehydes, esters, and acid chlorides into alcohols. This reaction changes the carbonyl group into a hydroxyl group. As a result, the final answer is 2-butanol.

This is an example of a Grignard reaction that requires the use of an ester or acid chloride, and more than one equivalent of an organometallic. The second step would be to react the product of the first step in an acidic source.

In the HVZ reaction of a carboxylic acid, a bromine is added to the alpha carbon. Phosphorus catalyzes the reaction and allows for the formation of an acyl halide. Acyl halides readily undergo enol-ketone tautomerization. The enol form uses electrons from the carbon-carbon double bond to bond to the bromine. In water, the two bromine molecules convert back to a carboxylic acid with one bromine on the alpha carbon.