Sorry for the confusion - I want to calculate V_b from given values of pH (or [H^+ ]). In other words I know what pH I want to achieve from that I can get [H^+ ] because pH is simply -log([H^+ ]) and I need to calculate the V_b which will give me the desired pH.

I will need to be able to set different values for C_a, C_b, K_a, K_b and V_a. K_w is always constant. Thanks for your patience!