Closed-form expressions for monoprotic weak acid aqueous solutions

A general closed-form expression for [H3O+] of solutions of a weak acid and a weak acid buffer, as well as their titration with a strong base, has been obtained and mathematically analyzed with the aid of computer algebra systems. This expression is used to evaluate, without the use of numerical approximations, the precision and accuracy of different approximations commonly employed in general chemistry and chemical analysis courses. The closed-form expression for [H3O+] of a buffer solution is used to obtain an analytical expression for the pH stability when a strong base is added. Finally, it is shown that the [H3O+] expressions for all the systems under study can be obtained from a general closed-form expression in terms of an effective weak acid constant and an effective acid concentration. The formulas found in this work do not display numerical rounding errors and do not require the use of numerical or graphical methods for their evaluation.

Automated summary

A general closed-form expression for [H3O+] in weak acid solutions and buffers, as well as their titration with a strong base, has been mathematically analyzed using computer algebra systems. The expression is used to evaluate the precision and accuracy of different approximations commonly used in general chemistry and chemical analysis courses, without numerical approximations. The stability of pH when a strong base is added to a buffer solution is determined using the closed-form expression for [H3O+]. Furthermore, it is shown that the [H3O+] expressions for all systems can be obtained from a general closed-form expression using effective weak acid constants and concentrations, without any numerical or graphical methods.