Question

In \(\text{A}=\text{A}_{1\%}^{1\,\text{cm}} \cdot b \cdot c\), \(\text{A}_{1\%}^{1\,\text{cm}}\) is defined as __________.

• A. Absorbance of a 1 mol/L solution in a 1 cm path length cell
• B. Absorbance of a 0.1% w/v solution in a cell of 1 cm path length
• C. Absorbance of a 1% w/v solution in a cell of 10 cm path length
• D. Absorbance of a 1% w/v solution in a cell of 1 cm path length

Hint:

To convert between specific absorbance (\(\text{A}_{1\%}^{1\,\text{cm}}\)) and molar absorptivity (\(\epsilon\)), use the mathematical relationship involving the Molecular Weight (\(\text{MW}\)) of the compound: \[ \epsilon = \frac{\text{A}_{1\%}^{1\,\text{cm}} \times \text{MW}}{10} \]

Answer 1

The Correct Option is D

Concept: Spectrophotometric quantification relies fundamentally on the Beer-Lambert Law, which dictates that absorbance (\(\text{A}\)) is directly proportional to both the path length of the light beam (\(b\)) and the concentration of the absorbing chemical species (\(c\)). The equation can be stated in two common formats: \[ \text{A} = \epsilon \cdot b \cdot c \quad (\text{where } c \text{ is in moles/liter, and } \epsilon \text{ is the molar absorptivity}) \] \[ \text{A} = \text{A}_{1\%}^{1\,\text{cm}} \cdot b \cdot c \quad (\text{where } c \text{ is expressed in standard percentage weight-in-volume units, \% w/v}) \]

Step 1: Breakdown the specific notation \(\text{A}_{1\%}^{1\,\text{cm}}\) The standard notation contains explicit structural indicators:
• The subscript \(1\%\) refers strictly to the concentration standard of the solute, which means a solution containing 1 gram of solute per 100 mL of solution (1% w/v).
• The superscript \(1\,\text{cm}\) defines the path length of the optical sample cell (cuvette), which is exactly 1 centimeter.

Step 2: Synthesize the full definition Therefore, \(\text{A}_{1\%}^{1\,\text{cm}}\) (also termed the specific absorptivity or extinction coefficient) is explicitly defined as the total measured absorbance when a 1% w/v solution is measured inside an optical cell possessing a path length of exactly 1 cm.