Faraday's Law of Electrolysis
Faraday's Law of Electrolysis is a fundamental principle that enables us to understand and quantify the process of electrolysis, such as the production of hydrogen and oxygen gas from water. In essence, it establishes the link between electrical charge and chemical change. According to this law, the amount of a substance that undergoes oxidation or reduction at each electrode is proportional to the total electric charge passed through the substance.
For water electrolysis, the formation of hydrogen gas can be represented by the reaction \(2H_2O(l) \rightarrow 2H_2(g) + O_2(g)\). Faraday's first law quantifies this reaction; it tells us that the mass of hydrogen (\(m_{H_2}\)) produced is proportional to the amount of charge (\(Q\)) passed through the water, as shown in the equation \(m_{H_2} = (Q/F) \times (M_{H_2}/z)\) where \((F\)) is Faraday's constant, representing the charge of one mole of electrons (\(96,485 C \cdot mol^{-1}\)), \((M_{H_2}\)) is the molar mass of hydrogen, and \((z\)) is the valence number of the reaction which, for hydrogen production, is 2 because two electrons are transferred per hydrogen molecule formed.
Electrolysis applications range from industrial processes to innovative concepts like the proposed raising of the Titanic, where hydrogen gas production through electrolysis could provide the necessary buoyancy.
Nernst Equation
The Nernst Equation is critical for predicting the behavior of electrochemical cells under non-standard conditions. While the standard reduction potentials provide info for reactions at standard conditions (\(1M\) concentration, \(298 K\) temperature, and \(1 atm\) pressure), real-world applications often operate differently. The Nernst Equation allows us to calculate the actual cell potential (\(E_{cell}\)) when the concentrations, temperature, or pressure differ from the standard state.
The formula \[E_{cell} = E_{cell}^0 - \frac{RT}{nF} \ln Q\] incorporates \((E_{cell}^0\)), the standard cell potential, \((R\)), the universal gas constant, \((T\)), the temperature in Kelvin, \((n\)), the number of moles of electrons transferred, \((F\)), Faraday's constant, and \((Q\)), the reaction quotient indicating the ratio of product and reactant activities or concentrations when not at standard conditions.
When applied to electrolysis under pressures vastly different from \(1 atm\), such as the depth at which the Titanic lies, the Nernst equation can determine the minimum voltage necessary to carry out the electrolysis while considering the increased gases' pressure. The resulting voltage accounts for real pressures and confirms that electrolysis can occur under the specified conditions.
Electrochemical Cell Potential
Electrochemical cell potential, often simply called cell potential (\(E_{cell}\)), is the driving force behind the movement of electrons in an electrochemical cell. It determines if a redox reaction will occur spontaneously. The cell potential is measured in volts (V) and is essentially the difference in potential energy between the anode and the cathode within the cell.
For the electrolysis of water, the cell potential must be positive, and sufficient to cause the decomposition of water into hydrogen and oxygen gases. The standard cell potential is calculated under standard conditions (all reactants and products at \(1M\) concentrations, a temperature of \(298 K\), and a pressure of \(1 atm\)), and reflects the inherent tendency of the reaction to proceed. In situations where conditions are non-standard (like at the ocean's depths), the actual cell potential may differ and must be determined using adjustments such as the Nernst Equation.
Understanding the electrochemical cell potential is critical for designing systems to harness chemical reactions to produce electricity or, conversely, to use electrical energy to drive chemical changes, as in the case of electrolysis for hydrogen gas production.
Standard Reduction Potential
The standard reduction potential (\(E^0_{red}\)) is a measure of the tendency of a chemical species to gain electrons and thereby be reduced. Each half-reaction in an electrochemical cell has a standard reduction potential, and these values are key in predicting the direction of electron flow and the feasibility of a reaction. Tabulated values for standard reduction potentials are determined at standard conditions, which include a temperature of \(298 K\), a pressure of \(1 atm\), and \(1M\) concentration for all the aqueous species involved.
Within the context of water electrolysis, two half-reactions occur: one where water is reduced to produce hydrogen gas (with an \(E^0_{red}\) of \(0 V\) for \(2H^+ + 2e^- \rightarrow H_2\)) and another where water is oxidized to produce oxygen gas (with an \(E^0_{red}\) for the converse of \(4OH^- \rightarrow O_2 + 2H_2O + 4e^-\), which is typically \(1.229 V\)). By understanding and using standard reduction potentials, scientists and engineers can calculate the standard cell potential and make predictions about the energy requirements for chemical processes.
