As you know, the Virtual Titrator works by using interactive web technology to solve a set of equations and then plot the results. But "what equations?" you ask. Since solving the equations for a monoprotic acid is the easiest and shortest, that is what I give you as an example.
1) Equations involving acid-base equilibrium:
2) Charge balance equation:
3) Input the equilibrium expressions into the charge balance equation:
4) Solve for [H+]:
5) Find the roots and choose the only real, positive root for a pH value:
This step is possible for a monoprotic acid, only a 3rd order equation, but the equations for polyprotic acids scare me. The 4th to 8th order equations of the Virtual Titrator are much better being left alone for the computer to solve, both faster and more reliably.
6) Repeat step 5 at numerous pH's and graph to create a theoretical titration curve:
This final step is the single step that makes using a computer worthwhile. Solving the equations takes only five minutes once the method is known, but this step could take hours with just a calculator and a pencil, and probably days, months, or years without the calculator. So you could say modern technology lets us be lazy, or you could say it lets us skip the tedious calculations.