Question

The Nernst equation \(E=E^{\circ}-R T / n F \ln Q\) indicates that the \(Q\) will be equal to equilibrium constant \(K_{c}\) when : (a) \(E=E^{\circ}\) (b) \(R T / n F=1\) (c) \(E=\) zero (d) \(E^{\circ}=1\)

Short answer

The Nernst equation indicates that the reaction quotient Q will be equal to the equilibrium constant Kc when E, the cell potential, is zero (c).

Step-by-step solution

Identify the Condition for Equilibrium

For a reaction to be at equilibrium, the cell potential, E, must be zero because there is no net reaction occurring and thus no potential difference. Therefore, we look for the condition where E is zero.

Apply the Condition to the Nernst Equation

We set E to zero in the Nernst equation: 0 = E^o - (RT/nF)ln Q. This dictates that E^o = (RT/nF)ln Q.

Solve for Q at Equilibrium

Under standard conditions at equilibrium, Q is equal to the equilibrium constant Kc. Therefore, when E = 0, we can deduce that ln Q = ln Kc, and hence Q = Kc.

Key concepts

Chemical Equilibrium

Chemical equilibrium is a state in which the rate of the forward chemical reaction equals the rate of the reverse reaction, resulting in no overall change in the concentrations of the reactants and products over time. It is a crucial concept in understanding how chemical reactions occur and how they can be manipulated in various processes, including biological systems and industrial synthesis.

At equilibrium, the quantities of reactants and products remain constant, but this does not imply that their amounts are equal, only that they are stable. This state is described by the equilibrium constant, represented by the symbol \( K_c \) for reactions in solution. The equilibrium constant is a ratio determined by the concentrations of products and reactants raised to their respective stoichiometric coefficients as shown by the equation \( K_c = \frac{[products]}{[reactants]} \). Importantly, in the context of the Nernst equation, at equilibrium \( E = 0 \), and \( Q \), the reaction quotient becomes equal to the equilibrium constant \( K_c \).

Electrochemistry

Electrochemistry is the branch of chemistry that deals with the relationship between electricity and chemical reactions. It involves the study of how chemical energy is converted to electrical energy and vice versa in electrochemical cells. There are two main types of electrochemical cells: galvanic (or voltaic) cells, which convert chemical energy into electrical energy, and electrolytic cells, which use electrical energy to induce chemical change.

In these cells, oxidation-reduction (redox) reactions occur at the electrodes. In a galvanic cell, the reaction that has a potential to spontaneously produce electric current is harnessed. The driving force of the electron flow in such a cell is known as cell potential (\( E \)), and it is measured in volts. Understanding how to calculate cell potential and its relationship with the concentration of reactants and products is crucial in electrochemistry, which is where the Nernst equation comes into play.

Cell Potential

Cell potential, often denoted as \( E \), is the measure of the potential difference between two half-cells in an electrochemical cell. It reflects the capacity of a chemical reaction to move electrons, that is, to do work through electric current. The cell potential is composed of two half-cell potentials, with each half-cell consisting of a metal electrode in a solution of its ions.

The standard cell potential \( E^\circ \), is the potential difference when all components are in their standard states, which usually means 1M concentration for soluble species, 1 bar pressure for gases, and pure solid or liquids for other substances. The Nernst equation provides a way to calculate the actual cell potential under non-standard conditions by accounting for the actual concentrations of the reacting species. The relevance of cell potential to chemical equilibrium is highlighted when the cell potential equals zero, indicating that the cell is at equilibrium and no net reaction occurs, linking electrical energy to the thermodynamics of chemical processes.