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When using an ice box, should you always use the approximation method where x additions are removed first? In other words, how can you tell when or when not to use the quadratic equation? Toolbox 5I.1 explains this, but I don't understand it in their words.
if the K value is less than 10^-3, then you can assume x is very small relative to the initial concentration. this makes sense when you think about the formula for K (the concentration of reactants is much greater than that of products). if this is the case, you can disregard the x (that is subtracted from the reactant)
Approximation is okay when the K value is less than 10^-3. To check if your approximation was appropriate at the end of the problem, you can calculate the percent ionization. If this percent is less than 5%, approximation was acceptable.
anjali41 wrote:Approximation is okay when the K value is less than 10^-3. To check if your approximation was appropriate at the end of the problem, you can calculate the percent ionization. If this percent is less than 5%, approximation was acceptable.
Just in case you need the equation for percent ionization, it's [H+ at equilibrium]/[initial concentration of acid] x 100%
Use approximation when value of K is less than 10^-3. Always verify your answer by plugging the concentrations to check if you still get the same K. My TA recommended using the quadratic equation every time just to be safe.
When K is less than 10^-3 it essentially means that the acid or base dependent on the given problem is so weak that it barely disassociates. So any protonation or deprotonation can be ignored and we can approximate x to be a small value and ignore it in either the Ka or Kb expression calculation.
Again, in addition to the small (<10-3) approximation, you can find the percent ionization to test if you can use the approximation. If the percent ionization is less than 5%, your approximation is acceptable. Remember that to find percent ionization, you take the equilibrium concentration of the conjugate acid/base and divide it by the initial concentration of the base/acid, then multiply by 100%. This 5% rule should make sense because if the equilibrium concentration of the conjugate is smaller than 5% of the initial base/acid concentration, there was little dissociation and the equilibrium concentration of the base/acid is about the same.
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