Question

Consider the following half-reactions: $$\begin{array}{cc}\mathrm{IrCl}_{6}{ }^{3-}+3 \mathrm{e}^{-} \longrightarrow \mathrm{Ir}+6 \mathrm{Cl}^{-} & \mathscr{E}^{\circ}=0.77 \mathrm{~V} \\ \mathrm{PtCl}_{4}{ }^{2-}+2 \mathrm{e}^{-} \longrightarrow \mathrm{Pt}+4 \mathrm{Cl}^{-} & \mathscr{E}^{\circ}=0.73 \mathrm{~V} \\ \mathrm{PdCl}_{4}{ }^{2-}+2 \mathrm{e}^{-} \longrightarrow \mathrm{Pd}+4 \mathrm{Cl}^{-} & \mathscr{E}^{\circ}=0.62 \mathrm{~V} \end{array}$$ A hydrochloric acid solution contains platinum, palladium, and iridium as chloro-complex ions. The solution is a constant \(1.0 \mathrm{M}\) in chloride ion and \(0.020 \mathrm{M}\) 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

In order to determine the feasibility of separating platinum, palladium, and iridium from the given solution by electrolysis, we first calculate the reaction quotient (Q) for each half-reaction using the formula \(Q = \frac{[\text{M}] [\text{Cl}^-]^{m}}{[\text{MCl}_m]}\). Then, we use the Nernst equation \(\mathcal{E} = \mathcal{E}^{\circ} - \frac{RT}{nF} \ln Q\) to find the cell potential for each metal complex under the given conditions. Next, we order the calculated voltages from highest to lowest and determine the potential difference between each adjacent half-reaction. Finally, we compare the potential differences with the required potential difference for 99% deposition of one metal before the next one starts depositing to assess the feasibility of separation.

Step-by-step solution

Identify the Nernst equation

The Nernst equation helps us determine the cell potential under non-standard conditions. The equation is given by: \[ \mathcal{E} = \mathcal{E}^{\circ} - \frac{RT}{nF} \ln Q \] where \(\mathcal{E}\) is the cell potential, \(\mathcal{E}^{\circ}\) is the standard cell potential, R is the gas constant, T is the temperature, n is the number of electrons involved, F is the Faraday constant, and Q is the reaction quotient.

Calculate Reaction Quotient (Q) for each half-reaction

For each half-reaction, the reaction quotient (Q) can be calculated as follows: \[Q = \frac{[\text{M}] [\text{Cl}^-]^{m}}{[\text{MCl}_m]}\] where M represents the metal of interest, and m is the number of chloride ions in the complex.

Calculate the cell potentials for each half-reaction at the given conditions.

Using the Nernst equation, we can find the cell potential for each metal complex in the solution under these specific conditions (1.0 M Cl⁻ and 0.020 M in each complex ion).

Determine the ordering of cell potentials

Order the calculated voltages from highest to lowest and determine the potential difference between each adjacent half-reaction. This ordering will help us understand the sequence of deposition of the metals during electrolysis.

Evaluate the feasibility of separating the metals

To decide if it is feasible to separate these metals, we must look at the potential difference between each half-reaction. If there is a sufficient potential difference, the metal with the higher cell potential will deposit 99% before the next metal starts depositing. When we compare the calculated cell potentials with the required potential difference for 99% deposition, we can conclude if it is feasible or not to separate these three metals through electrolysis under the given conditions.

Key concepts

Nernst Equation

The Nernst equation is crucial when it comes to understanding electrochemical reactions taking place in non-standard conditions. In essence, this equation allows us to calculate the cell potential that exists when concentrations of reactants and products are not at standard state, which is typically 1 M for solutions.

Mathematically, it is represented as:
\[\mathcal{E} = \mathcal{E}^{\circ} - \frac{RT}{nF} \ln Q\]
Here, \(\mathcal{E}\) is the cell potential under non-standard conditions, \(\mathcal{E}^\circ\) is the standard cell potential, \(R\) is the universal gas constant, \(T\) is the temperature in Kelvin, \(n\) is the number of electrons transferred in the half-reaction, \(F\) is Faraday’s constant, and \(Q\) is the reaction quotient, which gauges the relative amounts of products and reactants present during the reaction. Understanding the Nernst equation is vital for predicting how changes in concentration will influence the voltage of an electrochemical cell, such as in the electrolysis of metals.

Cell Potential

Cell potential, often denoted as \(\mathcal{E}\), is the measure of the driving force behind an electrochemical cell. It's the voltage produced by the two half-reactions in an electrochemical cell when connected by an external circuit. The larger the cell potential, the greater the ability of the reacting species to transfer electrons.

In the context of our exercise, if the cell potential for one metal to deposit is much higher than for another, we can expect that the metal to begin plating out first, assuming other factors like overpotential do not come into significant play. This difference in potential is exploited during electrolysis for metal separation.

Reaction Quotient

The reaction quotient (\(Q\)) serves as a predictor to determine the direction in which a reaction will proceed to reach equilibrium.

For our half-reactions, it is calculated using the concentration of metal ions and chloride ions, as shown:
\[Q = \frac{[\text{M}] [\text{Cl}^-]^{m}}{[\text{MCl}_m]}\]
In this formula, \([\text{M}]\) is the concentration of the metal ion, \([\text{Cl}^-]\) is the concentration of chloride ions, and \([\text{MCl}_m]\) is the concentration of the metal chloro-complex ion. By calculating the reaction quotient for each metal, we can use the Nernst equation to calculate the cell potential under the specific conditions present in the system.

Standard Cell Potential

The standard cell potential (\(\mathcal{E}^\circ\)) provides a reference point by which we gauge the tendency of a reaction to occur under standard conditions, which is when all solutes are at a concentration of 1 M, gases are at 1 atm, and the temperature is 298 K (25°C).

This property is intrinsic to each half-reaction and is determined experimentally. When we have two dissimilar metals, as in our exercise, each will have its unique standard cell potential. By comparing these potentials, we can predict which metal will start to deposit onto an electrode first in the course of electrolysis. This selection is made clearer when combined with the Nernst equation, which considers actual reaction conditions.

Selective Metal Deposition

Selective metal deposition is a process that allows us to selectively separate and recover metals from a solution through electrolysis. It targets specific metals based on differences in their cell potentials, allowing us to plate one metal out of solution before another.

This technique requires a sufficiently large potential difference to ensure that nearly all (99%) of one metal is deposited before the next metal begins to plate. It's based on both the Nernst equation, which tells us the potentials at which metals will begin to plate out, and the kinetics of the electrodeposition process. In practice, this is not just about thermodynamics but also involves the consideration of kinetics, such as overpotentials and the rate at which electron transfer occurs at the electrode surfaces. If properly managed, selective metal deposition can be a very effective method of metal purification and separation.