Approximation Valid?

[Mia Glinn 1I]

Hi, can someone help explain the reasoning behind approximating when X is less than 5% of the initial concentration? What are we approximating, X or just the general calculation of K? Thanks in advance!

[Caden Ciraulo 1J]

The approximation for when x is less than 5% of the initial value is utilized to make the calculations easier. The approximation basically means that if x is 5% or less than the initial value, then it won't have any effect compared to the initial value. As Lavelle was saying, if you have $1,000,000, and you give away $10, and someone asks how much money you have, you're still going to say you have $1,000,000. In other words, 5% is our base number to say that x will have little enough effect on the large amount of concentration we already have that we can say it basically has no effect.

[tim_villasenor 1k]

Is this applied when for weak acids you approximate x=0 for when the Ka is less than 10^-3?

[briana lay 3c]

Is this applied when for weak acids you approximate x=0 for when the Ka is less than 10^-3?

That would be correct! Same would apply for Kb values as well.

[Mia Glinn 1I]

The approximation for when x is less than 5% of the initial value is utilized to make the calculations easier. The approximation basically means that if x is 5% or less than the initial value, then it won't have any effect compared to the initial value. As Lavelle was saying, if you have $1,000,000, and you give away $10, and someone asks how much money you have, you're still going to say you have $1,000,000. In other words, 5% is our base number to say that x will have little enough effect on the large amount of concentration we already have that we can say it basically has no effect.

How do you know to approximate X to make the calculations easier if you haven't calculated X yet? Does that mean you have to calculate X twice?

[Jake 1F]

You know you can approximate when the K value is greater than 10^3 or less than 10^-3. After you finish the calculations you can make sure that it was okay to approximate by finding the percent of the initial value that x represents. If it's less than 5% it means that it was small enough that the approximation was valid. If it's greater than 5% it means their either an error in calculations or that the change was too significant to approximate. So you should only need to find x once, because you know whether or not to approximate from the k value.

[Hannah Chang 1F]

You know you can approximate when the K value is greater than 10^3 or less than 10^-3. After you finish the calculations you can make sure that it was okay to approximate by finding the percent of the initial value that x represents. If it's less than 5% it means that it was small enough that the approximation was valid. If it's greater than 5% it means their either an error in calculations or that the change was too significant to approximate. So you should only need to find x once, because you know whether or not to approximate from the k value.

I believe you can only approximate when K < 10^-3, and if K is any larger than that (i.e., K > 10^3), then that means that the change in the initial concentration of reactant, -x, is so large that it is significant. For instance, lets say that the initial reactant concentration is 1 M, and if the reaction only uses 0.0001 M of reactant to form products, then you would subtract 0.0001 from 1 to get 0.9999, which essentially rounds to 1. Thus, the initial reactant concentration basically doesn't change because so little reactant was used to form product. But you are only able to subtract such a small number if the K value is small, because a small K means that not much product is formed, so not much of the reactants would be used, hence leading to a very small change in the reactant concentration. But if K is really large, then that means that a lot of product will be formed, so, much of the initial reactant concentration will be used to make product, resulting in a significant change in the initial reactant concentration (which would not allow us to approximate).