Cometary ices have remained largely unaltered since their accretion from protoplanetary ice and dust, so studying their compositions provides unique information on the chemical conditions prevalent during the birth of the solar system. Comets are also believed to have delivered volatiles and organic molecules to planets during impact events, so understanding their compositions provides insight into the chemical regents that may be present to drive prebiotic chemistry on young planetary surfaces. Cometary ice abundances are derived primarily through remote observations of their volatile atmospheres (comae). However, previous coma mapping observations have revealed that some well-known cometary molecules (such as C2, HNC and H2CO) are not released directly from the nucleus — instead, they are produced in the coma as a result of thermal/photolytic processes. It is commonly assumed that several of the more complex organic molecules observed in cometary comae at radio wavelengths are released directly from ices stored inside the nucleus, but this is largely unproven. In fact, our latest chemical/hydrodynamic coma models show that several complex organic molecules can be produced in the coma via gas-phase (neutral-neutral) chemistry. Here we present chemical model calculations for cometary HC3N and NH2CHO, demonstrating that coma synthesis is indeed possible for these species. The production rates of HC3N and NH2CHO are found to be sensitive to the overall coma density, as well as to the production rates of specific reagents — in particular, the CN radical. Our chemical/hydrodynamic model shows that by adopting a CN/HCN ratio consistent with the inner-coma CN abundance identified by Rosetta in comet 67P, it is possible to obtain HC3N and NH2CHO abundances similar to those previously observed in bright Oort cloud comets. Consequently, the abundances of these molecules inside cometary nuclei could be less than previously thought.