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When in a problem are we supposed to use the quadratic formula when solving for equilibrium? I know Dr. Lavelle in lecture showed we are supposed to get the terms in relation to ax^2+bx+c but what I am confused about is what type of problem requires this type of calculation in which we have to apply the quadratic formula.
The quadratic formula ends up being used most often when we use ICE tables. While we place the concentrations of the products over the concentrations of the reactants at equilibrium over each other, we do not know the change in concentration from their initial molarities. Ultimately, the quadratic formula is used to find the positive value for x in the equation, which indicates the changes in R and P during a chemical reaction as it approaches equilibrium and gives us a completed K expression.
The quadratic formula is used most commonly in problems where changes to the initial molarity of the reactant are significant and usually when K is greater than 10^-3. When we get to acid and base equilibria, some K values will be so small that we will be able to use the assumption rule, which allows us to calculate concentrations at equilibrium without the quadratic formula. (This is because changes to initial molarity of the reactants are so small that they are insignificant.)
Going off from the response above, if the value of Kc is not less than 10^-4, then you must solve for the x value using the quadratic equation (cannot use shortcut). Dr. Lavelle included the rule about quadratic and cubic to help us when dealing with math equations with these properties.
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