Approximating to Zero

[Alyssa Gates 1H]

Are we better off approximating x as 0 when it 10^-5 or 10^-3? I heard we can do it both ways but is 10^-3 better?

[Alex Baugh 2I]

I am assuming that you mean this regarding the ICE tables and approximating x to 0 when the K values are really small. In that case, you should only approximate it when the K is 1000 times smaller, and you can always use the 5% check at the end of your calculations to see if approximating x was the right move.

[Megan Wang 3D]

I usually use the 5% rule when approximating as the K value could be small but your initial concentration and x could also be small too.

[jennacostello8]

Anytime x is 10^-4 or less, I use the 5% rule to check if I can cancel it out in the denominator. Hope this helps.

[Titania Le [2F]]

Depending on how close the value is to 10^-3, I will make the value of x negligible. Typically, 10^-4 is a safe bet. Regardless, the <5% rule can be used to check your answer.

[Maya_Panozzo_2D]

I would use 10^-5. Sometimes even then the 5% rule doesn't work out so it's safe to use the quadratic formula. But I would definitely follow the 5% rule which means that when you calculate the percent yield the value is less than 5%.

[James Yu 3C]

I believe in the Achieve solutions, it says we can use 10^-3 but I would definitely always double check with the 5% rule!

[906023369]

While it is stated that 10^-3 is the rule on deciding whether you can approximate, there are instances where you have a K value or equilibrium constant of 10^-4 where approximation doesn't work. I went to TA office hours to get clarification on this question and I was told that it is always a safe bet to approximate when your K is less than 10^-5. You can still approximate if your K is less than 10^-3 or 10^-4 you just have to be careful because it is not surefire that it will work. Also you can check to see if the approximation was the correct step by using the 5% rule with your answer. The 5% rule states that your x value over the initial concentration of the molecule times 100 is less than 5% (x/initial conce. X 100 < 5%).

Hope this helps!

[Ashwin Kumar 3D]

I think it would be safest to use 10^-5 when approximating the value of x to zero. I remember when doing the achieve problems, they sometimes used x = 0 when the value was 10^-3, however, I'm pretty sure that this will not always work. On the final, I think it would be best if you just stuck to using the quadratic equation since that would be the safest way to get the right answer, however, if you are uncomfortable with that method, I would just use 10^-5 as the value where you can approximate x as zero.

[charlotteweymer_2H]

Technically there is no correct answer and is really just based off of personal choice. Lavelle and the textbook say 1x10^-3 but some UAs have said they generally use 1x10^-5. Ultimately, if you always solve using the quad equation you will be guaranteed to get the correct answer without having to worry about approximation. Additionally, since our exams are multiple choice, odds are that you will be close enough to the correct answer despite any rounding or approximations.