A brief outline of the mathematical issues faced by chemistry students.
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
Can you work out how to produce the right amount of chemical in a temperature-dependent reaction?
Water naturally dissociates into an equilibrium mixture of $H^+$ and $OH^-$ ions and $H_2O$ molecules $$ H_2O \rightleftharpoons^{K_W} H^++OH^-\,, $$ where the concentrations of $H^+$ and $OH^-$ ions, written as $[H^+]$ and $[OH^-]$ are related by the expression $$ K_W = [H^+][OH^-]. $$ $K_W$ is called the dissociation constant, and depends on the temperature of the water. The following table of data shows the dissociation constant for water at various temperatures and standard pressure.
From this table, work out an estimate for the temperature at which water has a $pH$ of exactly 7, 6.8 and 7.2. Recall that the $pH$ is defined as $pH=-\log_{10}([H^+])$