# How to calculate transmittance from concentration?

Im not sure how to do these

3. A 10 mM solution has a transmittance of 45%. Calculate the transmittance of a 20mM solution at the same wavelength and optical pathlength.

4. Two colored solution, C and D contain different dyes. Let the transmittances of these two solutions be TC and TD respectively, when measured in a 1-cm cell at a given wavelength. Express the transmittance TCD of the mixture of equal volumes of C and D, measured under the same conditions, in terms of TC and TD.

Relevance

First question...

Using the Beer-Lambert Law,

A = ebc and A = -log T

where

**e = molar absorptivity (which is wavelength-dependent)

**b = optical pathlength

**c = concentration

**T = transmittance

Equating both A...

ebc = -log T [Eq.1]

or eb = (-log T)/c

If in both cases they have the same b and same e...

Thus, (-log T)/c of the first case is equal to (-log T)/c of the second case

(-log 0.45)/10 = (-log T)/20

>>> T = 20.25%

Second question...

We use the equation:

A(sol'n) = A(C) + A(D)

-log TCD = -log TC + -log TD

-log TCD = -log (TC*TD)

>>> TCD = TC*TD

Hope that helps! :)

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