The quantum equation of state of the electron-ion-plasmas in thermal equilibrium is derived; the pressure until the third virial coefficient is calculated. We consider only the thermal equilibrium plasma in the case of nλ3 ab  1 where λ2 ab = 2 mabKT is the thermal De Broglie wavelength. The formulas contain the contributions of the exchange effects. Our equation of state is compared with result of Ebeling et al. who calculated the pressure until the second virial coefficient only and in the case of χλee  1 where χ is the Debye length. Upon comparison with Ebeling et al. one observes that the considerable contribution of the third virial coefficient in the region of high temperatures.