Approximations

[Andrew Nguyen 2K]

I am confused as to why approximations are valid if x is less than 5 percent of the initial concentration. Can someone please explain this to me and how to properly use these approximations?

[Sunny Xiao 1A]

Because it's annoying to go through the quadratic formula to solve the K expressions, we can typically "cheat" and simplify so instead of (for example) 0.35-x in the denominator of the k expression, we consider the x as negligible and solve from there. Upon getting the value of x, you can divide that answer by the initial concentration of the weak acid/base. If it's less than 5%, the approximation is good enough.

This is possible because the percent protonation/deprotonation is so small for weak acids and bases, so we can just consider it negligible.

[Amy Wong 2F]

With Ka/Kb values that are extremely small, we know that the acid/base will not dissociate to a large degree. If x is less than 5% of the initial concentration, the change in concentration of the weak acid/base is so small that it can be considered negligible. I think 5% is a general benchmark to indicate that the amount of dissociation that occurs is small enough for the change in concentration of the weak acid/base to be considered zero.
Like Dr. Lavelle gave as an example in class, if someone has a million dollars and they lose 1 dollar, we don't say they have 999,999 dollars. We just say they have around a million dollars.

[Cassidy Chiong 2J]

If the percent ionization/deprotonation of an acid/base is less than 5%, that means that less than 5% of that acid or base will dissociate to gain/lose an H+ ion. As a result, since such a small percentage of that acid/base will change, its change in the ice table is so small that we can regard that "-x" as 0.

[Michelle Gong]

To further add on, you can always go back and check and not rely on the rule. While the rule is good for most cases, it never hurts to check by doing the assumption and then seeing if when you subtract the value by the x if it is the same value, if it is then your assumption is okay and that is the true value, if not, you must do quadratic formula.

[Kailin Mimaki 2K]

You need to use the 5% rule in order to determine how much of a weak acid or base will disassociate. If it is a really small amount, it won’t matter if you disregard it when calculating x. So in order to calculate this, take the amount of X, divide it by the initial amount, then multiply this amount by 100. Hope this helped!