We report a first principles molecular dynamics (FPMD) study of surface acid chemistry of the two growth surfaces of quartz, (101̄0) (including Alpha and Beta terminations) and (101̄1) facets. The interfacial hydration structures are characterized in detail and the intrinsic pKas of surface silanols are evaluated using the FPMD based vertical energy gap method. The calculated acidity constants reveal that every surface termination shows a bimodal acid-base behavior. It is found that all doubly-protonated forms (i.e. SiOH2) on the three terminations have pKas lower than -2.5, implying that the silanols hardly get protonated in a common pH range. The pKas of surface silanols can be divided into 3 groups. The most acidic silanol is the donor SiOH on the (101̄0)-beta surface (pKa = 4.8), the medium includes the germinal silanol on (101̄0)-alpha and the outer silanol on (101̄1) (pKa = 8.5-9.3) and the least acidic are inner silanols on the (101̄1)-facet, acceptor SiOH on (101̄0)-beta, and the secondly-deprotonated OH (i.e. Si(O-)(OH)) on (101̄0)-alpha (pKa > 11.0). With the pKa values, we discuss the implication for understanding metal cations complexing on quartz surfaces.