Chapter 19, Problem 19.15P

Interpretation Introduction

Interpretation:

Values of $\left[\text{A}\right]$ and $\left[\text{B}\right]$ have to be calculated.

Concept Introduction:

Molar absorptivity is a coefficient that appears in Beers’ law. It measures the extent of light absorbed at a certain wavelength. Molar absorptivity is denoted by the symbol $\epsilon$. SI unit for Molar absorptivity is ${\text{M}}^{-1}{\text{cm}}^{-1}$.

Relation between path length and dimension is as follows:

  $D=b\left(\text{ε}{\text{'}}_{\text{X}}\text{ε}{"}_{\text{Y}}-\text{ε}{\text{'}}_{\text{Y}}\text{ε}{"}_{\text{X}}\right)$

Here,

$\epsilon$ denotes molar absorptivity in ${\text{M}}^{-1}{\text{cm}}^{-1}$.

$b$ denotes path length in centimeters.

$D$ denotes dimension.

Expression to compute absorbance from transmittance is as follows:

  $A=-\log T$

Formula to calculate molar absorptivity from absorbance is as follows:

  $\text{ε}=\frac{A}{b\cdot c\cdot l}$

Here,

$b$ denotes path length in centimeters.

$c$ denotes concentration of species capable to absorb.

$A$ denotes absorbance.

$T$ denotes transmittance.