The present work simulates the transport of oxygen, carbon dioxide, and carbon monoxide between a fetus’s circulatory system and the mother’s. The organ responsible for this exchange is the placenta. Carbon monoxide is a common air pollutant, and it impacts the physiological conditions even in low concentration. The impacts of carbon monoxide are especially dangerous for pregnant women, fetuses, and newborn babies. A model of carbon monoxide transport, from the literature, is modified to simulate a pregnant woman (original model was a male), therefore changing some parameters to express the adjusted respiratory system. It was considered the gas exchange in the placenta, to evaluate the concentration of these different gases in the fetus arterial and venous blood. Three methods of the exergy analysis are implemented for both mother and fetus respiratory systems, aiming at the comparison with the respiratory system of a male adult. The destroyed exergy of the literature did not have the same trend as the models proposed in this article, taking into consideration the hemoglobin reactions. In contrast, the entropy generation associated only with the diffusion transport phenomena was one order of magnitude lower than the other methods. The placenta destroyed exergy rate is significantly higher compared to the irreversibilities of the mother’s respiratory system. One possible explanation is the fact that the placenta has other physiological functions than gas transportation.