In this paper, we numerically study pool boiling of a binary (water and nitrogen) mixture on a surface endowed with a combination of hydrophobicity and hydrophilicity (i.e., the so called biphilic surface). Here we adopt a numerical approach based on the phase field theory, where the vapor-liquid interface is assumed to be of a finite thickness (hence diffusive in nature) and requires no explicit tracking schemes. The theoretical modeling of two-phase heat and mass transfer in water diluted with nitrogen demonstrates the signiant impact of impurities on bubble dynamics. The simulations show that locally high concentrations of nitrogen gas within the vapor bubble is essential to weakening the condensation effect, which results in sustained bubble growth and ultimately (partial) departure from the surface under the artificially enlarged gravity. Simply increasing the solubility of nitrogen in water, however, turns out to be counterproductive because possible re-dissolution of the aggregated nitrogen by the bulk water could deprive the bubble of vital gas contents, leading instead to continuous bubble shrinkage and collapse. Additionally, it is found that with the significant accumulation of nitrogen, the bubble interface is increasingly dominated by a strong interfacial thermocapillary flow due to the Marangoni effect.