Question

How to get new concentration from percent transmittance?

Answer 1

Transmittance and absorbance are related as follows.

`A = -log(T)`

Evidently, percent transmittance is simply some fraction of `T`. Absorbance is known to be related to concentration:

`A = epsilonbc`

where `epsilon` is the molar absorptivity, `b` is the path length, and `c` is the concentration in `"M"`. `epsilon` and `b` are CONSTANTS for the same substance.

Therefore:

`-log(T_1) = epsilonbc_1`

`-log(T_2) = epsilonbc_2`

And we have:

`c_2/c_1 = log(T_2)/(log(T_1)`

Thus, the new concentration is:

`color(blue)(c_2) = c_1log(T_2)/log(T_1)`

`= ("26 mg/L")log(0.617)/log(0.528)`

`=` `color(blue)("19.66 mg/L")`

This should make sense... if it transmits more, it absorbs less. It absorbs less if less particles are in solution that block the path of the incoming light.