Understanding the microscopic origin of the acid base behavior of mineral surfaces in contact with water is still a challenging task, for both the experimental and the theoretical communities. Even for a relatively simple material, such as silica, the origin of the bimodal acidity behavior is still a debated topic. In this contribution we calculate the acidity of single sites on the humid silica surface represented by a model for the hydroxylated amorphous surface. Using a thermodynamic integration approach based on ab initio molecular dynamics, we identify two different acidity values. In particular, some convex geminals and some type of vicinals are very acidic (pK(a) = 2.9 and 2.1, respectively) thanks to a special stabilization of their deprotonated forms. This recalls the behavior of the out-of-plane silanols on the crystalline (0001) alpha-quartz surface, although the acidity here is even stronger. On the contrary, the concave geminals and the isolated groups present a quite high pK(a) (8.9 and 10.3, respectively), similar to the one of silicic acid in liquid water.