In UV-Vis spectrophotometry, absorbance is defined as $A=-{\log }_{10}\left(\frac{I}{I_0}\right)$. What units are absorbance measured in?

• A. Percent (% transmittance)
• B. Inverse centimeters (${\mathrm{cm}}^{\mathrm{-1}}$)
• C. Molar ($\mathrm{mol}\cdot L^{\mathrm{-1}}$)
• D. No units (dimensionless; sometimes reported as absorbance units, AU)

Answer: (D)

Verified step by step guidance

1. Understand the definition of absorbance in UV-Vis spectrophotometry, which is given by the equation: \(A = -\log_{10}\left( \frac{I}{I_0} \right)\), where \(I_0\) is the intensity of the incident light and \(I\) is the intensity of the transmitted light.
2. Recognize that absorbance is calculated as the logarithm of a ratio of two intensities, \(I\) and \(I_0\), which have the same units (usually power or intensity of light).
3. Since absorbance is the logarithm of a unitless ratio, it itself has no physical units; it is a dimensionless quantity.
4. Note that although absorbance is dimensionless, it is sometimes reported with arbitrary units called absorbance units (AU) for convenience, but these are not true physical units.
5. Conclude that absorbance is not measured in percent transmittance, inverse centimeters, or molar units, but is fundamentally unitless.