Calculating concentration using the quadratic formula

[Mahnoor_Wani_1I]

I understand how to use the ice/rice table to calculate the value of x to find the concentrations. Hypothetically, what if both the values of x we get from the quadratic formula are positive, then which one would we use to calculate concentrations?

[Marylyn Makar 1B]

Hi! I think that usually you will get a positive and negative value from the quadratic formula, so you do not have to worry about getting 2 positive values.

[IsaacLaw1E]

Usually one of the equilibrium concentrations will be something like 3.0 - x, and x will have two values where one is greater than three and one is less than 3. x cannot equal the one that is greater than three, because 3.0 - x will be negative and concentrations can't be negative. So x must be the one less than three. So when you get multiple x values, check each of them to see if they can actually occur.

[Lillian Ma 1I]

I think most of the time one of the values will be impossible to be the right concentration (either negative or larger than the initial concentration) so you can easily tell which one is the right answer. I don't think we would be given a problem that had two possible concentrations and be told to choose one.

[Nathan Lao 2I]

It depends on the initial concentrations of the reactants and products. There's no such thing as negative concentration/partial pressure; the lowest it would be is zero. When finding the x value using the quadratic formula, it's important to plug the values into the equilibrium equations for each reactant/product. Whichever x value produces a negative concentration will not be correct.

[Michael Cardenas 3B]

Usually if you get two positive values for x one of them is larger than the initial concentration and therefore cannot be used. For example if the initial concentration was 3.0 you would get one value that is less than 3 and another that is greater. You would then use the value that is less than 3.

[Taylor Newville 1C]

A good example of this concept is question 3 of the Week 1 Sapling Assignment. I'm not sure if everyone has the same questions with the same values on sapling, but for the question I was given, you solve for x using the quadratic equation and get two positive values. However, one is bigger than the initial concentration value it needs to be subtracted from so you must use the other answer to solve the question.