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ICE tables are often used when you're asked to find equilibrium concentrations, and when you're given initial concentrations and a Kc value. However, you can also be asked to do the other way around: find initial concentrations from equilibrium concentrations and a Kc value. So, no, the concentration of the products will not always start at 0.
For ICE tables, you also want to consider where the reaction is if it not at its initial state in terms of which way the reaction will proceed. For example, if you are given the concentrations of some of the reactants and some of the products in the midst of the reaction, you want to calculate Q and compare it to K to see which way the reaction should shift. This matters for the "change in concentration" row and whether reactants or products will have the - or + x values.
ICE tables are typically used when finding the equilibrium concentrations of weak acids and bases. This is because with weak acids and bases, they don't fully dissociate and we have to calculate the specific concentrations of each reactant and product.
ICE Tables are specifically used to find the equilibrium concentration of products and reactants when given the initial concentration. The value of the products will not always be zero. It will be values given from the question.
Eruchi Okpara 2E wrote:When using ICE tables, how do you know when its better to use the quadratic formula to find X or the 5% rule?
If you're given a weak acid or base with an equilibrium constant less than 10^-3 you can assume that the x in the (number-x) is negligible and you can just get rid of that x. If it's not a weak acid or base then you should use the quadratic formula.
Also, the quadratic formula will always work it's just unnecessary at times and you can save time by doing it the other way.
If you really want to be sure you can always just check the percent ionization after you solve the problem. If the concentration of the conjugate base/acid divided by the initial concentration of the acid/base is less than 5%, then you're good.