Calculate Percent Ionization

[Ashley Hiti 1K]

I have been trying to calculate the percent ionization for achieve but every problem instructs me to use the quadratic formula instead. How do I use the quadratic formula? Does this mean I need to use ICE tables?

[Kiku Shirakata 2A]

Hello,

Yes, an ICE table would be useful to visualize the problem. The quadratic formula is used when you are solving for 'x' in the Ka/b equation you set up. Usually, in the ice table, you will have the equilibrium concentrations as acid/base = (initial concentration) - x, conjugate base/acid = 'x', and [H+]/[H3O+]='x'. In this case, your Ka or Kb equation should be set up as Ka/Kb = x^2/((initial concentration) - x).

Sometimes, we are allowed to ignore the 'x' in the denominator when the Ka/b value is less than 10^-3. However, when it is not small enough to approximate, we need to include the 'x'. By adding that variable, you will need to solve a quadratic equation to find the value of x, which will then allow you to correctly calculate the percent ionization.

Hope this helps!

[Madison Nguyen 3L]

Percent ionization calculations require finding the initial concentration of acid/base and dividing it by the concentration of its conjugate species. Therefore, depending on if the Ka or Kb value is smaller than 10^-3, you may approximate the value of the initial concentration and disregard its x expression, enabling you to find the x values for the conjugate species concentration without quadratic equation. If the approximation is invalid, meaning x is greater than 5% of its initial concentration, then you must use the quadratic formula to solve for all x that belongs to the initial, conjugate, and H3O+ or OH- species, rather than taking the shortcut. This process is made simple with an ICE table, being that you could organize the expressions for your reactant and products easily.