Surface-enhanced Raman scattering (SERS) is a promising analytical technique with applications in environmental monitoring, healthcare, and the biopharmaceutical industry. While SERS has been successfully applied to molecules such as 4-mercaptobenzoic acid and other thiol- and amine-containing compounds, there is limited research on its detection capabilities for molecules rich in carboxyl groups or unsaturated bonds, such as citric acid. This study investigates the SERS enhancement of Au@Ag core-shell nanoparticles in response to citric acid and other molecules with carboxyl and unsaturated bonds. We compare the SERS behavior of nanoparticles in freshly prepared and aged sodium citrate solutions to identify differences in Raman peak enhancement. Our findings show that the Au@Ag core-shell nanoparticles exhibit significant SERS enhancement when exposed to citric acid and other related compounds. The enhancement varies based on the age of the sodium citrate solution, which influences the structural properties of the nanoparticles. This work opens avenues for further research and applications in biological monitoring, environmental testing, and the pharmaceutical industry.