Question

Consider the following half-reactions: $$ \begin{aligned} \mathrm{IrCl}_{6}{ }^{3-}+3 \mathrm{e}^{-} \longrightarrow \mathrm{Ir}+6 \mathrm{Cl}^{-} & \mathscr{E}^{\circ}=0.77 \mathrm{~V} \\ \mathrm{PtCl}_{4}{ }^{2-}+2 \mathrm{e}^{-} \longrightarrow \mathrm{Pt}+4 \mathrm{Cl}^{-} & \mathscr{E}^{\circ}=0.73 \mathrm{~V} \\ \mathrm{PdCl}_{4}{ }^{2-}+2 \mathrm{e}^{-} \longrightarrow \mathrm{Pd}+4 \mathrm{Cl}^{-} & \mathscr{E}^{\circ}=0.62 \mathrm{~V} \end{aligned} $$ A hydrochloric acid solution contains platinum, palladium, and iridium as chloro-complex ions. The solution is a constant \(1.0 M\) in chloride ion and \(0.020 M\) in each complex ion. Is it feasible to separate the three metals from this solution by electrolysis? (Assume that \(99 \%\) of a metal must be plated out before another metal begins to plate out.)

Short answer

It is not feasible to separate the three metals (platinum, palladium, and iridium) from the hydrochloric acid solution by electrolysis, as their reduction potentials become infinite under the given conditions, making it impossible to achieve 99% plating of one metal before the other metals plate out.

Step-by-step solution

Write the Nernst Equation

The Nernst equation relates the reduction potential of a half-cell reaction at non-standard conditions to the standard reduction potential, concentration of the reactants, and the number of electrons exchanged in the reaction. It can be expressed as: \(E = E^\circ - \dfrac{0.0592}{n} \log Q\) where \(E\) is the reduction potential at non-standard conditions, \(E^\circ\) is the standard reduction potential, \(n\) is the number of electrons involved in the reaction, and \(Q\) is the reaction quotient.

Calculate the Reaction Quotient for Each Half-Reaction

For each half-reaction, we need to determine the reaction quotient Q, which can be calculated using the concentrations of the species involved in the reaction. For IrCl₆³⁻: \(Q_{\mathrm{Ir}} = \dfrac{[\mathrm{Ir}][\mathrm{Cl}^-]^6}{[\mathrm{IrCl}_{6}^{3-}]}\) For PtCl₄²⁻: \(Q_{\mathrm{Pt}} = \dfrac{[\mathrm{Pt}][\mathrm{Cl}^-]^4}{[\mathrm{PtCl}_{4}^{2-}]}\) For PdCl₄²⁻: \(Q_{\mathrm{Pd}} = \dfrac{[\mathrm{Pd}][\mathrm{Cl}^-]^4}{[\mathrm{PdCl}_{4}^{2-}]}\) With given concentrations: [Cl⁻] = 1.0 M, [IrCl₆³⁻] = [PtCl₄²⁻] = [PdCl₄²⁻] = 0.020 M. Initially, as no metal is plated out, we assume [Ir] = [Pt] = [Pd] = 0. Therefore, the reaction quotients are: \(Q_{\mathrm{Ir}} =\dfrac{0 \cdot (1.0)^6}{0.020} = 0\) \(Q_{\mathrm{Pt}} =\dfrac{0 \cdot (1.0)^4}{0.020} = 0\) \(Q_{\mathrm{Pd}} =\dfrac{0 \cdot (1.0)^4}{0.020} = 0\)

Calculate the Reduction Potentials at Non-Standard Conditions

Use the Nernst equation to calculate the reduction potentials for the half-reactions at the given conditions: For IrCl₆³⁻: \(E_{\mathrm{Ir}} = \mathscr{E}^{\circ}_\mathrm{Ir} - \dfrac{0.0592}{3} \log Q_{\mathrm{Ir}} = 0.77\mathrm{~V} - \dfrac{0.0592}{3} \log 0\) For PtCl₄²⁻: \(E_{\mathrm{Pt}} = \mathscr{E}^{\circ}_\mathrm{Pt} - \dfrac{0.0592}{2} \log Q_{\mathrm{Pt}} = 0.73\mathrm{~V} - \dfrac{0.0592}{2} \log 0\) For PdCl₄²⁻: \(E_{\mathrm{Pd}} = \mathscr{E}^{\circ}_\mathrm{Pd} - \dfrac{0.0592}{2} \log Q_{\mathrm{Pd}} = 0.62\mathrm{~V} - \dfrac{0.0592}{2} \log 0\)

Evaluate the Feasibility of Separation

We can now compare the calculated reduction potentials to determine if it is possible to separate the three metals through electrolysis. Flipping the sign of the logarithms (as it goes to negative infinity) will result in the following potentials: \(E_{\mathrm{Ir}} = 0.77\mathrm{~V} + \infty\) \(E_{\mathrm{Pt}} = 0.73\mathrm{~V} + \infty\) \(E_{\mathrm{Pd}} = 0.62\mathrm{~V} + \infty\) As the potentials become infinite due to each metal not being initially plated, it is impossible to achieve 99% plating of one metal before plating of the other metals begins. Thus, it is not feasible to separate the three metals from this solution by electrolysis in the given scenario.

Key concepts

Understanding the Nernst Equation

The Nernst equation is a fundamental principle in electrochemistry that helps us understand what happens inside an electrochemical cell.
Think of it as a mathematical equation that predicts the voltage, or electrical potential, of an electrochemical reaction under non-standard conditions. The standard conditions imply standard concentrations (1 M), pressure (1 atm), and a temperature of 25 degrees Celsius. When these factors change, the Nernst equation comes into play to adjust the reaction's potential accordingly.

The equation looks like this: \(E = E^\circ - \dfrac{0.0592}{n} \log Q\), where:

• \(E\) is the cell potential under the non-standard conditions,
• \(E^\circ\) is the standard reduction potential,
• \(n\) is the number of moles of electrons transferred in the reaction,
• \(Q\) is the reaction quotient, a measure of the ratio of concentrations of reactants and products at any point in time.

In simplifying this concept, the equation tells us how the voltage will change if we alter the concentration of the chemicals in the reaction or the pressure and temperature of the environment. By substituting these variables into the equation, we can calculate the new cell potential.

Calculating the Reaction Quotient

To fully grasp the electrochemical cell reactions, it's crucial to understand the reaction quotient \(Q\). This term plays a pivotal role in the Nernst equation and hence in the study of reaction dynamics.

The reaction quotient is, essentially, a snapshot of a reaction at a specific instant. It's calculated by taking the concentration of the products divided by the concentration of the reactants, each raised to the power of its coefficient in the balanced equation. When a reaction has yet to start or has just begun, and no products have formed, the reaction quotient \(Q\) is zero. This is because the concentration of the products is effectively zero, making the fraction's value zero. This concept is used in electrochemistry to understand how far the reaction has progressed from equilibrium and to adjust the reduction potential accordingly using the Nernst equation.

For example, in the textbook problem mentioned, we're looking at the potential to separate metals from a solution by electrolysis. The reaction quotient calculations help us quantify how feasible this separation is, by considering the current concentrations of the metal ions and chloride ions in solution.

Deciphering Reduction Potential

Reduction potential, often symbolized as \(E^\circ\), is a measurement that determines the ease with which a chemical species can be reduced – that is, gain electrons. In simpler terms, it's the 'willingness' of a compound to acquire electrons and thus reduce in chemical context.

It is measured in volts and normally presented under standard conditions, which is why you'll often see it as \(E^\circ\). The more positive the reduction potential, the greater the species' tendency to be reduced. Reduction potentials are intrinsic values for each substance and play a critical role in predicting the direction of electron flow in an electrochemical cell.

Relation to Electrochemical Cell Separation

When attempting to separate metals in a solution through electrolysis, like in the provided exercise, their individual reduction potentials inform us which metal will be deposited (reduced) at the cathode first. However, the actual experimental conditions can modify the theoretical reduction potential we start with, and this is where the Nernst equation comes into play, adapting the standard reduction potential to reflect the real-life scenario. Understanding these concepts is key to deciphering the complex processes taking place within electrochemical cells and for achieving successful separation of metals through electrolysis.