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### Approximating -x

Posted: Thu Jan 16, 2020 3:29 pm
When can we approximate x when expressing K(a) or K(b)

i.e. when (x)(0.10+x)/(0.10 - x)

can be approximated to

(x)(0.10 + x)/(0.10)

### Re: Approximating -x

Posted: Thu Jan 16, 2020 4:37 pm
You can approximate if the x value is less than or equal to 10^-3 I believe.

### Re: Approximating -x

Posted: Thu Jan 16, 2020 4:41 pm
You can approximate by considering x insignificant any time it seems like x is extremely small compared to the initial concentration. Dr Lavelle gave an example where the K value was around 10^-4. Since the inital concentration was 0.10, it would be fair to assume the x in the equation would be really small in comparison (since it yields a K value that is so small). I would advise that whenever you approximate you double check that the x you have approximated is less than 5% of the initial value. If you approximate and x is 0.01 and the initial is 0.10, then x is 10% of the initial value, so it is actually too big to approximate. In that case you have to use a different method (probably the quadratic formula).
Hope this helps!

### Re: Approximating -x

Posted: Thu Jan 16, 2020 4:42 pm
You can approximate x only if the Ka or Kb value is small enough (less than 10^-3) since this will give you a very small x that would be an insignificant amount to remove from the bigger initial concentration of the weak acid or base they give you.