I confronted a problem, stating that we have a solution of potassium hydroxide. By adding extra water, when the volume of solution reaches 630 mL, the pH decreases by 0.5 units. How much extra water have we added to the solution?
And I know this is a simple problem, but I wondered, when we add water to the strong basic solution, the volume increases, which means a decrease in $[OH^-]$. and a decrease in $[OH^-]$ means an increase in $[H^+]$, and therefore a decrease in pH.
Everything sounds good in a macroscopic view, but what really happens to $[H^+]$ when we add more water? Why doesn't it decrease just like $[OH^-]$ when we increase the volume of soultion? What happens to $[H^+][OH^-] = constant$ from a microscopic view?