Chapter 5.3, Problem 3TY

Interpretation Introduction

Interpretation:

The original concentration of ${\text{Na}}^{\text{+}}$ has to be calculated.

Concept Introduction:-

Standard addition:

Standard addition are the addition of known quantities of analyte to unknown solution, with the increase in linearity we can deduce that how much analyte present in the original unknown solution.

$\text{Standard}\text{addition}\text{equation=}\frac{{\left[\text{X}\right]}_{\text{i}}}{{\left[\text{S}\right]}_{\text{f}}\text{+}{\left[\text{X}\right]}_{\text{f}}}\text{=}\frac{{\text{I}}_{\text{X}}}{{\text{I}}_{\text{S+X}}}\mathrm{...}\text{(1)}$

Where,

${\left[\text{X}\right]}_{\text{i}}$= The concentration of analyte in initial solution.

${\left[\text{S}\right]}_{\text{f}}\text{+}{\left[\text{X}\right]}_{\text{f}}$= The concentration of analyte plus standard in final solution.

${\text{I}}_{\text{X}}$= Signal from the initial solution

${\text{I}}_{\text{S+X}}$=signal from the final solution.

For an initial volume ${\text{V}}_{\text{0}}$ of unknown and added volume ${\text{V}}_{\text{s}}$ of standard with concentration ${\left[\text{S}\right]}_{\text{i}}$,

The total volume is

${\text{V=V}}_{\text{0}}{\text{+V}}_{\text{s}}$

And the concentration of equation $\text{1}$ can be written as

$\begin{array}{l}{\left[\text{X}\right]}_{\text{f}}\text{=}{\left[\text{X}\right]}_{\text{i}}\left(\frac{{\text{V}}_{\text{0}}}{\text{V}}\right)\\ {\left[\text{S}\right]}_{\text{f}}\text{=}{\left[\text{S}\right]}_{\text{i}}\left(\frac{{\text{V}}_{\text{S}}}{\text{V}}\right)\end{array}$