Chapter 19.1, Problem 1TY

Interpretation Introduction

Interpretation:

The concentration of $\left[\text{X}\right]$ at the given absorbance and wavelengths have to be calculated.

Concept Introduction:

When spectra is resolved, the analysis of a mixture is solved using the equation,

$\left[\text{X}\right]\text{=}\frac{\left|\begin{array}{l}{\text{A}}^{\text{'}}{\text{ξ}}_{{\text{γ}}^{\text{''}}}\text{b}\\ {\text{A}}^{\text{''}}{\text{ξ}}_{{\text{γ}}^{\text{''}}}\text{b}\end{array}\right|}{\left|\begin{array}{l}{\text{ξ}}_{{\text{x}}^{\text{'}}}\text{b}{\text{ξ}}_{{\text{γ}}^{\text{''}}}\text{b}\\ {\text{ξ}}_{{\text{x}}^{\text{''}}}\text{b}{\text{ξ}}_{{\text{γ}}^{\text{''}}}\text{b}\end{array}\right|}\left[\text{Y}\right]\text{=}\frac{\left|\begin{array}{l}{\text{ξ}}_{{\text{x}}^{\text{'}}}\text{b}{\text{A}}^{\text{'}}\\ {\text{ξ}}_{{\text{x}}^{\text{''}}}\text{b}{\text{A}}^{\text{''}}\end{array}\right|}{\left|\begin{array}{l}{\text{ξ}}_{{\text{x}}^{\text{'}}}\text{b}{\text{ξ}}_{{\text{γ}}^{\text{''}}}\text{b}\\ {\text{ξ}}_{{\text{x}}^{\text{''}}}\text{b}{\text{ξ}}_{{\text{γ}}^{\text{''}}}\text{b}\end{array}\right|}$

In the above equation , each symbol $\left|\begin{array}{l}\text{a}\text{b}\\ \text{c}\text{d}\end{array}\right|$ is determinant

The shortest representation can be given as $\left(\text{a×d}\right)\text{-}\left(\text{b×c}\right)$.

To calculate the concentration of $\left[\text{X}\right]$ at the given absorbance and wavelengths