When scientists analyze a chemical sample, they need to understand how the substance interacts with light. This process, known as spectroscopy, involves shining a beam of light through a sample and measuring the intensity of the light that emerges. This measurement is typically performed using a spectrophotometer, which compares the initial intensity of the light entering the sample to the final intensity exiting it. Two primary metrics are derived to quantify the light’s interaction with the sample: transmittance and absorbance.
Understanding Transmittance and Percent Transmittance
Transmittance (\(T\)) is the direct measure of the light that travels through a sample. It is mathematically defined as the ratio of the light intensity transmitted through the sample (\(I_t\)) to the intensity of the light incident on the sample (\(I_0\)): \(T = I_t / I_0\). This ratio is a fraction with a value always between 0 and 1. A transmittance value of 1 means all the light passed through, indicating no absorption, while 0 means no light passed through. Percent Transmittance (\(\%T\)) is this fractional value expressed as a percentage: \(\%T = T \times 100\).
Understanding Absorbance
Absorbance (\(A\)), sometimes called optical density, represents the flip side of transmittance. Instead of measuring the light that passes through, absorbance quantifies the amount of light that the sample retains or blocks. A higher absorbance value indicates a greater amount of light was absorbed by the material. The amount of light absorbed is directly related to the concentration of the light-absorbing molecules and the distance the light travels through the solution. Unlike percent transmittance, absorbance is a non-linear, unitless value defined to simplify later calculations.
The Logarithmic Connection
The algebraic relationship between absorbance and transmittance is defined by a negative logarithm. This mathematical connection is what converts the physically measured light ratio (transmittance) into the more analytically useful metric (absorbance). The fundamental algebraic definition is that absorbance (\(A\)) is the negative logarithm (base 10) of the transmittance (\(T\)): \(A = -\log_{10}(T)\). Since \(T\) is the fraction \(I_t / I_0\), this equation is often written as \(A = \log_{10}(I_0 / I_t)\). Because percent transmittance (\(\%T\)) is \(T \times 100\), the relationship can also be stated in terms of \(\%T\) as \(A = 2 – \log_{10}(\%T)\). This logarithmic function ensures that as transmittance decreases, absorbance increases. For example, a transmittance of \(T = 0.1\) (\(10\%T\)) results in an absorbance of \(A = 1\). If the sample’s concentration doubles, the transmittance drops to \(T = 0.01\) (\(1\%T\)), but the absorbance simply increases by a factor of two, to \(A = 2\).
Why Absorbance is Preferred in Measurement Calculations
Absorbance is the preferred measurement for quantitative analysis because it exhibits a linear relationship with the concentration of the absorbing substance. This linearity is a direct consequence of the logarithmic definition of absorbance. The principle known as the Beer-Lambert Law states that absorbance is directly proportional to both the concentration of the sample and the path length of the light. This proportionality means that if the concentration of a solution is doubled, the absorbance value will also double. This simple, direct relationship makes it significantly easier to create calibration curves and calculate the concentration of an unknown sample. Another practical advantage is that absorbance values are additive. If two different light-absorbing substances are mixed, the total absorbance of the mixture is the sum of the individual absorbances.