We present a measurement of the mass dependence of the forward-backward charge asymmetry (AFB) for e+e− pairs produced via an intermediate Z/γ∗ with mass Mee>40  GeV/c2. We study the constraints on the Z-quark couplings imposed by our measurement. We analyze an integrated luminosity of 72  pb−1 collected by the CDF-II detector in pp collisions at s√=1.96  TeV at the Fermilab Tevatron. A comparison of the uncorrected AFB between data and standard model Monte Carlo gives good agreement with a χ2/DOF of 15.7/15. The couplings measurements are also consistent with standard model predictions.