Primary alcohols are oxidized by aqueous \(\mathrm{H}_{2}\) CrO \(\mathrm{O}_{4}\) to give carboxylic acids in a process that involves initial aldehyde formation, followed by conversion to an aldehyde hydirate that is further cxidized to the casboxylic acid.

The primary alcohol is the starting compound that will undergo oxidation to eventually form carboxylic acid. In this case, the oxidizing agent is aqueous \(\mathrm{H}_{2}\mathrm{CrO}_{4}\), which will facilitate the oxidation of the primary alcohol.

In the first step of the reaction, the primary alcohol loses a hydrogen atom from its hydroxyl group (-OH) and a hydrogen atom from the adjacent carbon atom. This results in the formation of an aldehyde with a double bond between the carbon and oxygen atoms. The general reaction can be written as: $$ \textrm{R-CH}_{2}\textrm{OH} \xrightarrow[]{\mathrm{H}_{2}\mathrm{CrO}_{4}} \textrm{R-CHO} $$ Where R represents the rest of the alkyl group.

The aldehyde formed in the previous step undergoes further reaction with water, leading to the formation of an aldehyde hydrate. This is a result of the attack of a water molecule on the electrophilic carbon atom of the aldehyde, creating a new bond between the oxygen atom of water and the carbon atom of the aldehyde. This leads to the formation of a tetrahedral intermediate, in which the positive charge resides on the oxygen atom. After the transfer of a proton from one oxygen atom to another, we obtain the aldehyde hydrate. The general reaction can be written as: $$ \textrm{R-CHO} + \textrm{H}_{2}\textrm{O} \rightleftharpoons \textrm{R-CH(OH)\(_{2}\)} $$

In the final step, the aldehyde hydrate undergoes oxidation by losing another hydrogen atom from the carbon atom adjacent to the -OH group and one of the hydrogen atoms bonded to the oxygen of the -OH group. This results in the formation of a double bond between the carbon and oxygen, leading to the carboxylic acid. The general reaction can be represented as: $$ \textrm{R-CH(OH)\(_{2}\)} \xrightarrow[]{\mathrm{H}_{2}\mathrm{CrO}_{4}} \textrm{R-COOH} $$ In conclusion, the process of oxidizing primary alcohols to carboxylic acids using aqueous \(\mathrm{H}_{2}\mathrm{CrO}_{4}\) involves the initial formation of an aldehyde, followed by its conversion to an aldehyde hydrate, and finally, its further oxidation to produce the carboxylic acid.