I have been using a way to verify the assumptions. For example lets say, If we add 200 mL of NaOH to 400 mL of HNO2 2M, The pH become 1.5 + (##pH_i##) calculate the concentration of NaOH. The usual way of doing is this: ## K_a = (0.02+x)[H^+]/(4/3-x) ## then find the x which most of the time is equal to the initial concentration of OH- after addition which you can convert back to the original solution and find the required information. But the way I see how these approximations work is that you have to also think about how the additional OH can interact with H+ (or H3O+ if you like) to form water. So you really need simultaneous equations ##K_w = ([H+]_i -y)([OH-]_i-x-y) ## Where X is from the original acid reaction and Y comes from forming water reaction. Now usually Y is negligible so I can assume the OH- fully reacts with the acid but here in this situation Y isn't I did the math and found that x = 0.41345 and y = 0.01917811 which is not negligible ( about 4.63% mistake, However I am talking about more extreme version of this) . Is this way of thinking is true?