Chapter 5, Problem 5.23P

(a)

Interpretation Introduction

Interpretation:

An expression for the final concentration ${\left[{\text{Cu}}^{\text{2+}}\right]}_{\text{f}}$ after dilution has to be expressed.

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

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

Answer to Problem 5.23P

The expression for the final concentration ${\left[{\text{Cu}}^{\text{2+}}\right]}_{\text{f}}$ after dilution was expressed as $\text{0}\text{.950}{\left[{\text{Cu}}^{\text{2+}}\right]}_{\text{i}}$

Explanation of Solution

Given,

An unknown sample of ${\text{Cu}}^{\text{2+}}$ gave an absorbance of 0.262.  $\text{1}\text{.00}\text{mL}$ Of a solution had $\text{100}\text{.0}\text{ppm}$ ${\text{Cu}}^{\text{2+}}$ and the mixture is diluted to $\text{100}\text{.0}$ in a volumetric flask. The new solution absorbance was $\text{0}\text{.500}$

${\left[\text{X}\right]}_{\text{f}}\text{=}{\left[\text{X}\right]}_{\text{i}}\left(\frac{{\text{V}}_{\text{0}}}{\text{V}}\right)$

${\left[{\text{Cu}}^{\text{2+}}\right]}_{\text{f}}\text{=}{\left[{\text{Cu}}^{\text{2+}}\right]}_{\text{i}}\left(\frac{{\text{V}}_{\text{i}}}{{\text{V}}_{\text{f}}}\right)\text{=0}\text{.950}{\left[{\text{Cu}}^{\text{2+}}\right]}_{\text{i}}$

Conclusion

An expression for the final concentration ${\left[{\text{Cu}}^{\text{2+}}\right]}_{\text{f}}$ after dilution was expressed.

(b)

Interpretation Introduction

Interpretation:

An expression for the final concentration of standard ${\text{Cu}}^{\text{2+}}\text{designated}\text{as}{\left[\text{S}\right]}_{\text{f}}$ after dilution has to be expressed.

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

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

Answer to Problem 5.23P

The expression for the final concentration of standard ${\text{Cu}}^{\text{2+}}\text{designated}\text{as}{\left[\text{S}\right]}_{\text{f}}$ after dilution was expressed as $\text{1}\text{.00}\text{ppm}$

Explanation of Solution

Given,

An unknown sample of ${\text{Cu}}^{\text{2+}}$ gave an absorbance of 0.262. $\text{1}\text{.00}\text{mL}$ Of a solution had $\text{100}\text{ppm}$ ${\text{Cu}}^{\text{2+}}$ was mixed with $\text{95}\text{.0}\text{mL}$ of unknown and the mixture is diluted to $\text{100}\text{.0}$ in a volumetric flask. The new solution absorbance was $\text{0}\text{.500}$

${\left[\text{S}\right]}_{\text{f}}\text{=}{\left[\text{S}\right]}_{\text{i}}\left(\frac{{\text{V}}_{\text{i}}}{{\text{V}}_{\text{f}}}\right)$= $\left(\text{100}\text{.0}\text{ppm}\right)\left(\frac{\text{1}\text{.00}\text{mL}}{\text{100}\text{.0}\text{mL}}\right)\text{=1}\text{.00}\text{ppm}$

Conclusion

An expression for the final concentration of standard ${\text{Cu}}^{\text{2+}}\text{designated}\text{as}{\left[\text{S}\right]}_{\text{f}}$ after dilution was expressed.

(c)

Interpretation Introduction

Interpretation:

The concentration of ${\left[{\text{Cu}}^{\text{2+}}\right]}_{\text{i}}$ in the unknown 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

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

Answer to Problem 5.23P

The concentration of ${\left[{\text{Cu}}^{\text{2+}}\right]}_{\text{i}}$ in the unknown was calculated as $\text{1}\text{.04ppm}$ .

Explanation of Solution

Given,

An unknown sample of ${\text{Cu}}^{\text{2+}}$ gave an absorbance of 0.262.  $\text{1}\text{.00}\text{mL}$ Of a solution had $\text{100}\text{ppm}$ ${\text{Cu}}^{\text{2+}}$ was mixed with $\text{95}\text{.0}\text{mL}$ of unknown and the mixture is diluted to $\text{100}\text{.0}$ in a volumetric flask. The new solution absorbance was $\text{0}\text{.500}$

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

$\frac{{\left[{\text{Cu}}^{\text{2+}}\right]}_{\text{i}}}{\text{1}\text{.00 ppm +0}\text{.950}{\left[{\text{Cu}}^{\text{2+}}\right]}_{\text{i}}}\text{=}\frac{\text{0}\text{.262}}{\text{0}\text{.500}}\text{=1}\text{.04ppm}$

Conclusion

The concentration of ${\left[{\text{Cu}}^{\text{2+}}\right]}_{\text{i}}$ in the unknown was calculated.