Question

If the standard electrode potential of \(\mathrm{Cu}^{2}+/ \mathrm{Cu}\) electrode is \(0.34 \mathrm{~V}\), what is the electrode potential of \(0.01 \mathrm{M}\) concentration of \(\mathrm{Cu}^{2+}(T=298 \mathrm{~K}) ?\) (a) \(0.399 \mathrm{~V}\) (b) \(0.281 \mathrm{~V}\) (c) \(0.222 \mathrm{~V}\) (d) \(0.176 \mathrm{~V}\)

Short answer

The electrode potential of 0.01 M concentration of \(\mathrm{Cu}^{2+}\) at 298 K is \(0.399 \mathrm{V}\). Hence, option (a) is correct.

Step-by-step solution

Identify given and required values

The given values include \(\mathrm{Cu}^{2+}\) concentration as 0.01 M, the standard electrode potential of \(\mathrm{Cu}^{2+}/\mathrm{Cu}\) is \(0.34 \mathrm{V}\), and the temperature T as 298 K. The required value is the electrode potential of \(\mathrm{Cu}^{2+}\).

Apply the Nernst equation

Nernst's equation can be written as \(E=E^0-\frac{RT}{nF}lnQ\), where R is the gas constant (8.314 J/mol*K), E is the electrode potential, \(E^0\) is the standard electrode potential, n is number of electrons involved in the redox reaction (for \(\mathrm{Cu}^{2+} \rightarrow \mathrm{Cu}\), n=2), F is the Faraday's constant (96485 C/mol), and Q is the reaction quotient.

Calculate the potential E

Let's substitute given values into the Nernst equation, E = 0.34 V - ((8.314 J/mol*K * 298 K) / (2 * 96485 C/mol)) * ln(0.01 M). Simplifying, we obtain \(E = 0.34 \mathrm{V}-\frac{0.0257 \mathrm{V}}{2} ln(0.01)\). Solving this gives \(E = 0.34 \mathrm{V} + 0.059 V = 0.399 \mathrm{V}\), since \(ln(0.01)\) is negative.

Key concepts

Nernst Equation

The Nernst equation is a fundamental formula within the field of electrochemistry. It enables us to calculate the individual potential of an electrode in an electrochemical cell under non-standard conditions, meaning when concentrations, temperature, or pressure are different from the standard state. The equation is expressed as:
\[ E = E^0 - \left(\frac{RT}{nF}\right)\ln(Q) \]
In this expression, \( E \) represents the electrode potential we want to find, \( E^0 \) is the standard electrode potential, \( R \) is the universal gas constant (8.314 J/mol·K), \( T \) is the temperature in Kelvin, \( n \) is the number of moles of electrons exchanged in the electrochemical reaction, \( F \) is the Faraday constant (96485 C/mol), and \( Q \) is the reaction quotient, which represents the ratio of product activities to reactant activities. To solve for the electrode potential, you need known values for these variables, insert them into the equation, and calculate.
The Nernst equation is particularly beneficial in its ability to predict cell potential at any given concentration, thus bridging the gap between theory and practical application in lab settings or real-world scenarios. Understanding how to manipulate this equation is crucial for anyone delving into the intricacies of electrochemistry.

Standard Electrode Potential

Standard electrode potential, symbolized as \( E^0 \), is an essential concept in electrochemistry, representing the intrinsic tendency of a species to gain or lose electrons. This value is measured under standard conditions, which include a concentration of 1 M for aqueous species, a pressure of 1 bar for gases, and a reference temperature, often 298 K (25°C).
The standard electrode potential serves as a benchmark enabling chemists to predict the direction of electron flow in an electrochemical cell. Electrodes with higher standard potentials tend to gain electrons (act as cathodes), while those with lower potentials tend to lose electrons (act as anodes). These values are crucial for understanding the spontaneity of redox reactions and are tabulated for reference.
Moreover, when comparing two half-reactions, the one with the higher standard electrode potential will function as the reduction half-reaction in a spontaneous process. For example, in the exercise provided, the standard electrode potential of the \(\mathrm{Cu}^{2+}/\mathrm{Cu}\) electrode is given as 0.34 V. This value is a critical factor in determining the actual potential when conditions vary, such as in different concentrations of \(\mathrm{Cu}^{2+}\) ions.

Electrochemistry

Electrochemistry is a branch of chemistry that deals with the relationship between electrical energy and chemical changes. It covers a wide range of phenomena, such as batteries, fuel cells, corrosion, and electroplating, just to name a few. At the heart of electrochemistry are redox (reduction-oxidation) reactions, where the transfer of electrons occurs between substances.
These reactions can be split into two half-reactions: oxidation, where a species loses electrons, and reduction, where a species gains electrons. The flow of electrons from one electrode to another allows for the creation of electrical current, which can be harnessed for power or used to drive non-spontaneous chemical reactions. The principles of electrochemistry are grounded in thermodynamics and kinetics, governing how and why these electron transfers occur.
Understanding electrochemistry is vital for the development of new materials for batteries, creating methods for protecting metals from corrosion, and much more. It's an interdisciplinary field that merges chemistry with physics and materials science, crucial for various modern technologies.