CHEMISTRY COMMUNITY

When can we use approximations like making (x-0.89) become just x?

In regards to equilibrium equations, you must see the K value when making an assumption. If the K value is less than 10^-3, then you can proceed using x. However, make sure you check your assumption with the 5% condition.

You can use approximations if the Ka value is less than 1x10^-3. You should check to see that it was appropriate to use approximation by seeing if the equilibrium concentration is less than 5% of the initial concentration.

When the k value is small, 10^-3 , because so little of the reactants go to products it is negligable.

If the value of K is less than 10^-3, then we can assume that the value is too small to have any impact and therefore we can assume that X minus any number becomes just x.

When k is less than 10^-3

Given the K value, if K<<10^-3, then you may make the approximation. If K is not given, then make the approximation, but be sure to check if the value of x that you found is, indeed, less than 5% of the initial value(s)(concentration/partial pressure)of the components in the system. If x<5% of the initial value(s), then your approximation is valid. If you don't want to waste time verifying, you can always use the quadratic formula to solve for x without approximations(if you don't mind additional work, which might be less productive than the other method).

Also, if the initial value is 0, then the change, no matter how small, is significant, so no approximations should be made.

when the K is less than 1x10-3, so if the K ends with 10^-4 or smaller. Ex 1.9x10^4 approximate but 1.9x10^-3 don't approximate

When K is less than 10^-3

The approximation can only be used if K is very small.

Like everyone said, we make the approximation when K is small - less than 10^-3.

when K is less than 10^3

as a means to check if your approximations are correct,
remember the 5% rule at the end!

To add on, make sure to always verify at the end that your approximation was less than 5% otherwise the approximation won't hold and you need to use the formula for finding roots.

You can do this when your equilibrium constant value is less than 10^-3 because this value is extremely small.

When K is less than 10^-3, you can just approximate. Always remember to prove the approximation using the 5% rule.

When the k value is less than 10^-3

I think when k is less than 10^-3

when k is less than 10^-3, then we can assume that x is small enough to not have an effect in the math

If the value of K is less than 10^-3 then the assumption can be made that x is very small and would be negligible.

K has to be very small so you can assume that x is very small