Black-and-white photographic film is coated with silver...

Black-and-white photographic film is coated with silver halides. Because silver is expensive, the manufacturer monitors the $\mathrm{Ag}^{+}$ content of the waste stream, $\left[\mathrm{Ag}^{+}\right]_{\text { waste }},$ from the plant with an Ag$^{+}$ -selective electrode at $25^{\circ} \mathrm{C}$ . A stream of known Ag$^{+}$ concentration, $\left[\mathrm{Ag}^{+}\right]_{\text { standard }},$ is passed over the electrode in turn with the waste stream and the data recorded by a computer. (a) Write the equations relating the nonstandard cell potential to the standard cell potential and $\left[\mathrm{Ag}^{+}\right]$ for each solution. (b) Combine these into a single equation to find [Ag $^{+} ]_{\text { waste }}$ (c) Rewrite the equation from part (b) to find [Ag' $]_{\text { waste }}$ in ng/L. (d) If $E_{\text { waste is }} 0.003$ V higher than $E_{\text { standard }},$ and the standard solution contains 1000 . ng/L, what is $\left[\mathrm{Ag}^{+}\right]_{\text { waste }} ?$ (e) Rewrite the equation from part (b) to find $\left[\mathrm{Ag}^{+}\right]_{\text { waste for a }}$ system in which $T$ changes and $T_{\text { waste }}$ and $T_{\text { standard }}$ may be different.

Black-and-white photographic film is coated with silver halides. Because silver is expensive, the manufacturer monitors the $\mathrm{Ag}^{+}$ content of the waste stream, $\left[\mathrm{Ag}^{+}\right]_{\text { waste }},$ from the plant with an Ag$^{+}$ -selective electrode at $25^{\circ} \mathrm{C}$ . A stream of known Ag$^{+}$ concentration, $\left[\mathrm{Ag}^{+}\right]_{\text { standard }},$ is passed over the electrode in turn with the waste stream and the data recorded by a computer.
(a) Write the equations relating the nonstandard cell potential to the standard cell potential and $\left[\mathrm{Ag}^{+}\right]$ for each solution.
(b) Combine these into a single equation to find [Ag $^{+} ]_{\text { waste }}$
(c) Rewrite the equation from part (b) to find [Ag' $]_{\text { waste }}$ in ng/L.
(d) If $E_{\text { waste is }} 0.003$ V higher than $E_{\text { standard }},$ and the standard solution contains 1000 . ng/L, what is $\left[\mathrm{Ag}^{+}\right]_{\text { waste }} ?$
(e) Rewrite the equation from part (b) to find $\left[\mathrm{Ag}^{+}\right]_{\text { waste for a }}$ system in which $T$ changes and $T_{\text { waste }}$ and $T_{\text { standard }}$ may be different.

Key Concepts

Temperature Dependence in Electrochemistry

Temperature plays a critical role in electrochemical measurements, as it directly affects the RT/nF term in the Nernst equation. Variations in temperature can lead to changes in the electrode potential, so accurate calibration and adjustment for temperature differences are necessary for precise determination of ion concentrations.

Calibration Curve Method

Calibration curves are used to relate the known concentrations of a standard solution to the measured electrode potential. By comparing the potential of an unknown sample with that of a standard, the concentration of the ion in the unknown sample can be accurately determined, forming the basis for quantitative analysis using ISEs.

Concentration Unit Conversion

In electrochemical analyses, it is often necessary to convert ion concentrations between different units, such as from molar concentrations (or ng/L) to other related units. Unit conversion is essential for ensuring that measurement data match regulatory standards or specific application requirements, and it involves using appropriate conversion factors and dimensions.

Standard Electrode Potential

The standard electrode potential is the intrinsic voltage measured under standard conditions (usually 25°C, 1 M concentrations, and 1 atm pressure) for a half-cell reaction. It serves as a baseline or reference point in the Nernst equation to determine deviations in potential due to changes in ion concentration or other experimental conditions.

Nernst Equation

The Nernst equation is a fundamental relation in electrochemistry that connects the electrode potential of a cell to its standard potential and the activities or concentrations of the reactants and products. It shows how the potential changes logarithmically with the ion concentration, typically expressed as E = E° + (RT/nF) ln([ion]), and is crucial for understanding and predicting the behavior of electrochemical cells.

Ion-Selective Electrodes

Ion-selective electrodes (ISEs) are specialized sensors designed to measure the activity of specific ions in a solution. They are tailored to respond primarily to one type of ion, offering a direct and selective means to monitor its concentration, and are widely used in environmental monitoring, clinical diagnostics, and industrial applications.

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