Achieve week 2, #3

[605823283]

On problem #3 the K value is 8.4*10^-4, but we couldn't assume out the denominator x. Why is that?
Cause the K value is small enough that we shouldn't have to do quadratic formula, but we do?

[Hannah Joo 2D]

I'm not sure what the specific reason is, but I usually use the quadratic formula and solve everything out unless the K value is super super small on achieve because some people have mentioned that slight differences in rounding will get you marked as wrong.

[Lisa Ramos 1C]

Hi, this is becaus even with the K value being less than 1 x 10^-3, x can still be greater than 5% of the solution concentration. Thus, the percent ionization should be calculated via quadratic equation as even a K value like 8.4*10^-4 can still cause an impact.

[Marleena]

I'm not sure what the specific reason is, but I usually use the quadratic formula and solve everything out unless the K value is super super small on achieve because some people have mentioned that slight differences in rounding will get you marked as wrong.

Can you explain what you got for the quadratic formula /your steps for getting the answer for the quadratic formula? I keep getting the wrong answer for this and am unsure why. Thanks so much!

[Nicola Higgins 14B]

I thought this rule applies for the x value being small and therefore insignificant (as it wouldn't have an impact,) rather than the K value as K is constant over constant temperature?

[Viduttam Dutt 2H]

The rule that I generally follow is that if K is less than 10^-3, then it should be safe to assume that the -x in the denominator is too small to be considered. Although another important thing to remember is that in your final result for percent ionization, if the value is greater than 5%, then it means the -x cannot be neglected. So overall there might be times when you solve the whole problem only to learn that the percentage ionization is too high for you to neglect -x in the denominator, but it usually doesn't take too long for that.

[Kai Tokiyeda 2K]

Based on the textbook, you can try assuming the Ka is small enough to where you can simplify everything. But if you plug in the values for the percent ionization and it comes out larger than 5%, you have to do the quadratic equation in order to find the actual percent ionization. If the number was less than 5%, then you can leave it as is.

[Hannah Choi 1K]

The rule of thumb is that if you get an X value that is above 5%, of the initial concentration of the reactants, you cannot make the assumption that the effect of the change in concentration is very small (basically you can't ignore the -X in the denominator of the Ka expression and find the X value that way). This means you have to find X by using the quadratic formula.

[Holly Do 2J]

Although sometimes you can ignore the quadratic and cubics when the K value is smaller than 10^-3 but when you do that you must check whether it is less than 5% of the initial concentration. If it is over, that means that the change would have been great enough to effect the concentration and must not be ignored. You can calculate this by calculating the precent ionization after you find your "x" value.

[Ruben Adamov 1E]

sometimes even when the Ka is smaller than 10^-3, it can still make an impact, which is why making a habit of checking for the 5% rule is a good idea in my opinion.
Hope this helps!!