A solution that has a transmittance of 1.0 %T would have an absorbance of:

To determine the absorbance of a solution based on its transmittance, we use the relationship defined by the Beer-Lambert law. The equation that connects transmittance (T) and absorbance (A) is expressed as:

[ A = -\log(T) ]

In this equation, T is the transmittance expressed as a fraction (not a percentage), where 100% transmittance corresponds to a value of 1. Therefore, a transmittance of 1.0 %T is equivalent to 0.01 when converted to a fraction (1% divided by 100).

Now, substituting this value into the equation gives:

[ A = -\log(0.01) ]

Using logarithm properties, we know that:

[ \log(0.01) = -2 ]

Thus, we can calculate:

[ A = -(-2) = 2.0 ]

This shows that a solution with a transmittance of 1.0 %T would have an absorbance of 2.0. This understanding reinforces the direct relationship between absorbance and the logarithm of the transmittance, clarifying why, as transmittance decreases, absorbance