## Approximating X

Michelle_Nguyen_3F
Posts: 40
Joined: Wed Sep 21, 2016 2:59 pm

### Approximating X

When trying to calculate the equilibrium compositions, how can we check to make sure that we can approximate x (by removing it from the denominator of the equilibrium constant calculation) and that is valid? I think Dr. Lavelle said something about it being valid if x was less than 5% of the initial concentration, but I'm not sure exactly what he said. Could someone please clarify how to ensure that approximating x is valid and how to tell if it can be approximated in the first place? Thank you!

Ethan Frankel 2C
Posts: 20
Joined: Wed Sep 21, 2016 2:56 pm

### Re: Approximating X

Hi!
If the K value that is initially given is less than 10-4, then you can assume that x will be less than 5% and therefore do not have to use the quadratic equation. However, if K=10-4 you have to check (and if it’s greater, you have to use the quadratic equation).

To check, you simply perform the steps you would do normally if K<10-4 (by using the ICE table and removing the x from the denominator).

Once you find the value for x, you divide by the initial concentration and multiply by 100. This is the percent protonation (for acids) or ionization (for bases), meaning the amount that dissociates.

If this value is less than 5%, you don’t need to go back and have the x in the denominator.
But if it is greater than 5%, you have to use the quadratic equation to solve for x. If K>10-4, you know right away that you'll be doing this.

Sorry if that’s a bit confusing, but I hope it helps!

Jenny2G
Posts: 31
Joined: Wed Sep 21, 2016 2:56 pm

### Re: Approximating X

The explanation is on page 161 on the course reader.

You can take X out when you know it is very small, so when K is a very small number. The example Lavelle said in class was that if you have a million dollars and you give away \$100 you still have around a million dollars and so when finding the concentration of the reactants and products when doing equilibrium equations you can take out x because it will be so small that it won't affect the answer drastically. To test if you can take x out you calculate the value of x you found divided by the initial concentration and multiply it by 100%. If the answer comes out to be less than 5% than it is okay to take out x when finding the concentrations.