Physics-Informed Neural Networks (PINNs) have emerged as a promising alternative to purely data-driven neural networks (NNs) for surrogate modeling, particularly in data-scarce scenarios. This study evaluates the performance of hybrid-PINNs against traditional NNs for modeling the adsorption step of a Direct Air Capture (DAC) process. As the complexity of the modeled system increases, larger datasets and longer computational times are required for numerical methods. Therefore, the study aims to develop approaches that minimize data requirements while maintaining accuracy, which is crucial for efficient modeling of complex physical systems. While both AI models can achieve high accuracy with abundant data, the advantages of hybrid-PINNs become more evident as data becomes scarce. In the intermediate and low-data regimes, the physics constraints embedded in hybrid-PINNs significantly improves generalization and predictive accuracy. For extreme low-data conditions, a curriculum learning strategy is implemented, progressively enforcing physics constraints to mitigate underfitting and enhance model stability. Despite these benefits, hybrid-PINNs exhibit a computational cost approximately one order of magnitude higher than traditional NNs, as enforcing physics constraints increases training complexity. The results suggest that PINNs hold potential for modeling complex multi-physics problems in DAC and beyond, provided challenges related to gradient balancing and computational efficiency are addressed.