Titration curve equation/function
If $1$ liter $\ce{HCl} \pu{1 M}$ is gradually neutralized by adding $\pu{x mol }  \ce{NaOH}$, without change of volume, the pH of the obtained solution is given by : $$\mathrm{pH} = - \log(\frac{1-x}{2} + \frac{1}{2} \sqrt{(1-x)^2 + 4·10^{-14}})$$