X Approximations

[Daniel Hernandez 1G]

When given Ka or Kb, how can we determine whether or not the value is small enough to approximate the value or ‘x’ or assume that ‘x’ is near zero?

[Aaina 2D]

If Ka or Kb is < 10^-4, we can be certain that the value of x is small enough. You can also check by dividing your x value by the initial concentration (of a weak acid/base) given, and if it's <5%, your approximation is valid.

[Ashley Ko 3I]

Hi! I believe that Professor Lavelle said that if the value of Ka/Kb is less than 10^-4, then it is safe to assume that the value of x is small enough to approximate. However, to check if your approximation is valid, divide x by the initial concentration and then multiply by 100%. If x is less than 5% of the initial concentration then the assumption is valid. Otherwise, you have to use the quadratic equation. I hope this helps!

[Sean Wang 1F]

We can approximate that x is near 0 when the K value is less than 10^-4.

[Alexandra Ahlschlager 1L]

If the value of the equilibrium constant is less than 10^-4 you can assume that it will be small enough to approximate. You can also use the 5% rule, so if your x value is less than 5% of the initial concentration, you should be able to approximate. Hope this helps!

[Halle Villalobos 3E]

Hi! When values of Ka or Kb are < 10^-4, they are considered small enough that we can make the approximation of x equaling 0. I hope this helps!

[Sarah Huh 1K]

When Kb or Ka is less than 10^-4, we can approximate x to be 0.

[Kristina Krivenko 3I]

You can assume x value is small enough to approximate it when the equilibrium constant (whether it is Ka, Kb, etc) is smaller than or equal to .

You can also double check whether using the approximation in a given case was valid by using the 5% rule. If % ionization or protonation is less than 5%, then the answer you found using the approximation method should be correct. However, it is larger than 5%, you need to go back and solve the problem using the quadratic formula to get a more correct answer.

Hope this helps :)

[Kaili Valenzuela 2B]

Hey! When Ka or Kb is less than 10^ -4 then the values are considered to be very small and we can approximate that x will equal to 0.

[Rich Luong 1D]

It could sometimes depend on the initial concentration whether to approximate X as zero. If the initial concentration is very small and the Ka or Kb value is very near that value, I'd say X would still play a significant role in the solution. However, I'd say if the Ka or Kb value is 10^-4 smaller than the initial concentration value, X could be rounded off to 0.

[Stephen Min 1I]

To add on, you can verify your assumption that x is very small by dividing the x value by the initial concentration. If the result is less than 5 percent, than the assumption is valid.

[Sofia Lombardo 2C]

If Ka or Kb is less than 10^-4, then we can assume x to be negligible. We can check to make sure that x is negligible by using the percent protonation/ionized by seeing if it is less than 5%. If it is greater than 5% then we cannot assume x to be negligible.

[Alisa Nagashima 1B]

You can approximate when K_a or K_b < 10^-4. You can also double check by dividing x by the initial concentration given. If less than 5%, your approximation is valid.

[Javier Perez M 1H]

If the Ka or Kb is < 10^-4 then it is fine to ignore the -x from the initial mols.

[jasonfarrales3D]

Given your Ka or Kb value, you can approximate only if their values are less than 10^-4. Furthermore, if you find the percent protonation/ionization, and it is greater than 5%, then that approximation is invalid, and you would have to go through and use the quadratic formula. If the percent protonation/ionization is less than 5%, then the approximation is valid.

[Justin Zhang_1A]

If Ka or Kb is less than 10^-4, then you can approximate and ignore the -x.

[Sameer Chowdhury 3C]

So long as Ka or Kb is less than 1X10^-4 we can assume that the x is so small we can ignore the -x.

[Levon Grigoryan]

you can always assume and instead of solving the quadratic formula ignore the x for the B and solve the equation and squareroot it to get rid of the x^2. When you get the value of the x and divide it by the initial concentration. (keep in mind the 5 percent rule). So if the value less than 5% keep going. If it is more. You go back and solve the quadratic equation to get the actually values, instead of ignoring the x for the (B)

[Vivian_Le_1L]

You can approximate when your K value is less than 10^-4. We can assume that x is small enough that we can ignore -x. Remember that this does not mean we can ignore x^2 (I'm just adding this bit b/c someone asked about this on another post). The approximation can be checked by finding the % ionization/protonation. If it is less than 5%, then the approximation is acceptable.

[Nan_Guan_1L]

if you don't want to do the 5% test, you can check if Ka or Kb given is less than 10-4. usually we can use approximations if they are less than 10-4.

[Jared Limqueco 3E]

Ka and Kb has to be negligible, so generally < 10^-14 to omit x. Hopefully your approximation is valid if the percent ionization is <5%, otherwise you gotta do more work

[Agustina Santa Cruz 2F]

Usually if K is smaller than 10^-4, you can approximate and take it out of denominator so that you don't have to use the quadratic formula.

[Sahaj Patel Lec3DisK]

If Ka/Kb is less than 10^-4, it is deemed as small enough, however, afterwards you calculate the percent ionization, and if it is more than 5%, the approximation is invalid and you have to do the calculation again without the approximation. Hope this helps!

[Britney Tran IJ]

K is smaller than 10^-4, you can approximate and take it out of denominator