[Products] over [Reactants] cancellations

[kimberlyrose1G]

Why is it that you can sometimes cancel the x on the reactants portion before using the quadratic formula to solve for x in ICE tables?

[Chase Yonamine 1J]

In the cases with weak acids we can assume that Ka is very small and does not affect the reaction. (if Ka is less than 10^-3 or 10^-4 to be safe). It is important to remember that x is not 0, it just very small relative to the initial molar concentration that it has not affect on the reaction.

[Nicole Lee 4E]

It is a tool to make calculations easier. The concentration of the reactant is not significantly changed by subtracting the small x. Dr. Lavelle gave an example in class about a millionaire. If a millionaire gives $1000 to someone, it does not really affect the total amount of money the millionaire still has since it is still almost a million.

[Deepika Pugalenthi 1A]

Think about the million dollar example Professor Lavelle gave during lecture. If a millionaire gives a poor man a thousand dollars, it seems like a lot to the poor man but doesn't seem that substantial to the millionaire. This is due to the fact that a thousand dollars doesn't make a significant difference in the total amount of money the millionaire has.
Similar to this, when setting up ICE tables, when the equilibrium constant is less than 10^-3, you can assume the change in the reactants will be small and can cancel the x in the reactants portion. However, for the products side, the x is required as the products start off as zero and the x defines how much is created as the reaction proceeds.