Abstract It has frequently been observed that the shapes of titration curves closely resemble those of inverse hyperbolic or trigonometric functions. Here we show that there exists not only a resemblance, but that, for simple titration reactions, we can derive expressions which represent the change in a solution property with the volume of titrant added, in terms of inverse hyperbolic or trigonometric functions. The general mathematical form of the expressions so obtained is then used to model these and other, more complicated titrations. Copyright © 2002 John Wiley & Sons, Ltd.