Cadmium is a toxic heavy metal. The U.S. Environmental Protection Agency limits the concentration of cadmium ions in drinking water to less than 4 * 10^-⁸ M. Assess the feasibility of monitoring of cadmium in drinking water using a voltaic cell based on the following half-reactions. $$\begin{array} { l l } \mathrm { Ag } ^ { + } ( a q ) + \mathrm { e } ^ { - } \longrightarrow \mathrm { Ag } ( s ) & E ^ { \circ } = + 0.7996 \mathrm {~V} \ \mathrm { Cd } ^ { 2 } + ( a q ) + 2 \mathrm { e } ^ { - } \longrightarrow \mathrm { Cd } ( s ) & E ^ { \circ } = - 0.4030 \mathrm {~V} \end{array}$$ If the silver ion concentration were 0.100 M, what cadmium ion concentration at 298 K would increase the cell potential by 10 mV from the standard cell potential?

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Quizplus · Accepted Answer

The standard cell potential is calculated as E° = E°(Ag⁺/Ag) - E°(Cd²⁺/Cd) = 0.7996 V - (-0.4030 V) = 1.2026 V. The Nernst equation is used to find the concentration of Cd²⁺ that increases the cell potential by 10 mV (0.01 V): E = E° - (RT/nF)ln(Q). With n = 2, T = 298 K, and using the given concentrations, solving for Cd²⁺ gives approximately 4.6 * 10⁻³ M.

Cadmium Is a Toxic Heavy Metal If the Silver Ion Concentration Were 0