Chapter 22, Problem 22.18QAP

Interpretation Introduction

(a)

Interpretation:

A spreadsheet should be created to calculate the standard electrode potential for the Ag-AgCl electrode.

Concept introduction:

$\text{AgCl(s) + e }\rightleftharpoons {\text{ Ag(s) + Cl}}^{-}$

${\text{H}}^{+}\text{ + e }\rightleftharpoons \frac{1}{2}{\text{ H}}_2\text{(g)}$

Overall equation: $\text{AgCl(s) + }\frac{1}{2}{\text{ H}}_2\text{(g)}\to {\text{Ag(s) + Cl}}^{-}{\text{ + H}}^{+}$

${\text{E}}_{cell}={\text{E}}_{cell}^0-0.0592\log \frac{{\gamma }_{H^{+}}{\gamma }_{C{l}^{-}}{c}_{HCl}^2}{P_{H_2}^{1/2}}$

Activity coefficient of ions can be calculated by Debye-Huckel equation,

$-\log {\gamma }_x=\frac{0.509Z_x^2\sqrt{\mu }}{1+3.28{\alpha }_x\sqrt{\mu }}$

Z_x − charge on the species X

$\mu$ - ionic strength of the solution

${\alpha }_x$ - the effective diameter of the hydrated ion in nanometers.

Ionic strength is defined by the equation,

$\mu =\frac{1}{2}\left(c_1{Z}_1^2+c_2{Z}_2^2+c_3{Z}_3^2+\mathrm{.....}\right)$

C₁, C₂, C₃ − molar concentrations of various ions in the solution

Z₁, Z₂, Z₃ − charges on the ions.

For the electrolyte A_mB_n, the mean activity coefficient is given by

${\gamma }_{\pm }={\left({\gamma }_A^m.{\gamma }_B^n\right)}^{\frac{1}{\left(m+n\right)}}$

Interpretation Introduction

(b)

Interpretation:

The values obtained in part (a) for the activity coefficients and standard potential should be compared with those of MacInnes and if there are any differences, a possible reason for the discrepancies should be suggested.

Concept introduction:

$\text{AgCl(s) + e }\rightleftharpoons {\text{ Ag(s) + Cl}}^{-}$

${\text{H}}^{+}\text{ + e }\rightleftharpoons \frac{1}{2}{\text{ H}}_2\text{(g)}$

Overall equation: $\text{AgCl(s) + }\frac{1}{2}{\text{ H}}_2\text{(g)}\to {\text{Ag(s) + Cl}}^{-}{\text{ + H}}^{+}$

${\text{E}}_{cell}={\text{E}}_{cell}^0-0.0592\log \frac{{\gamma }_{H^{+}}{\gamma }_{C{l}^{-}}{c}_{HCl}^2}{P_{H_2}^{1/2}}$

Interpretation Introduction

(c)

Interpretation:

The mean, standard deviation, 95 % confidence interval, and other useful statistics for the standard potential of the Ag-AgCl electrode should be found by using descriptive statistics function of Excel.

Concept introduction:

$\text{AgCl(s) + e }\rightleftharpoons {\text{ Ag(s) + Cl}}^{-}$

${\text{H}}^{+}\text{ + e }\rightleftharpoons \frac{1}{2}{\text{ H}}_2\text{(g)}$

Overall equation: $\text{AgCl(s) + }\frac{1}{2}{\text{ H}}_2\text{(g)}\to {\text{Ag(s) + Cl}}^{-}{\text{ + H}}^{+}$

${\text{E}}_{cell}={\text{E}}_{cell}^0-0.0592\log \frac{{\gamma }_{H^{+}}{\gamma }_{C{l}^{-}}{c}_{HCl}^2}{P_{H_2}^{1/2}}$

Interpretation Introduction

(d)

Interpretation:

The analysis results and the quality of the MacInne’s results should be compared and discussed.

Concept introduction:

$\text{AgCl(s) + e }\rightleftharpoons {\text{ Ag(s) + Cl}}^{-}$

${\text{H}}^{+}\text{ + e }\rightleftharpoons \frac{1}{2}{\text{ H}}_2\text{(g)}$

Overall equation: $\text{AgCl(s) + }\frac{1}{2}{\text{ H}}_2\text{(g)}\to {\text{Ag(s) + Cl}}^{-}{\text{ + H}}^{+}$

${\text{E}}_{cell}={\text{E}}_{cell}^0-0.0592\log \frac{{\gamma }_{H^{+}}{\gamma }_{C{l}^{-}}{c}_{HCl}^2}{P_{H_2}^{1/2}}$