Calculating pH of Weak Acids and Bases

[Dustin Shin 2I]

In the notes, there was a moment where after writing out the ICE chart, the equation Ka = x^2/0.10-x was given. However, because it was a weak acid, the x became negligible and was not considered. Can someone explain why? And can this apply to equations for strong acids and bases or just weak ones?

[Gillian Murphy 2C]

Basically, the reason for this is that with such a low Ka, subtracting x won't have that much of an affect on the original concentration. If you were to subtract 1x10^-5 from .1, you would end up with .09999, which is still essentially .1 (especially when you would eventually round for sig figs). Lavelle said that anything smaller than 10^-3 is small enough to assume that it won't make a difference and the x in the denominator can be discarded, but to check at the end you should make sure that the percent deprotonation/protonation is less than 5%. It makes the math so much easier to do this so I would definitely recommend it. Make sure that you still keep the x's in the numerator though! Without those, there would be nothing to solve for. It can only be neglected when it is small compared to the concentration it is being subtracted from.

[Rachel-Weisz3C]

I think that is totally correct, and Dr. Lavelle mentioned the metaphor that if a person has a million dollars giving away a couple thousand doesn't make much of a difference to them, because they are still very close to a million. So basically even though we don't know x, we know it is going to be small and therefore it is not needed to solve the problem.