Question

What is a concentration cell? Why is the \(E_{\text {cell }}^{\circ}\) equal to zero for such a cell?

Short answer

\(E_{\text {cell }}^{\circ}\) is equal to zero for a concentration cell because both electrodes are identical and have the same potential under standard conditions, so there is no net potential difference between them.

Step-by-step solution

Definition of a Concentration Cell

A concentration cell is a type of electrochemical cell where both the anode and the cathode are composed of the same material and immersed in solutions of the same solute, but with different concentrations. The driving force for the electrochemical reaction is the tendency to reach equilibrium by the transfer of ions from high to low concentration.

Determination of Standard Cell Potential

The standard cell potential, denoted as \(E_{\text {cell }}^{\circ}\), is determined under standard conditions, which include having all solutes at a concentration of 1 M. For a concentration cell, since both electrodes are the same material and would have the same potential under standard conditions, there is no potential difference between them, hence \(E_{\text {cell }}^{\circ} = 0\).

Reason for Zero Standard Cell Potential

\(E_{\text {cell }}^{\circ}\) is a measure of the potential difference between two half-cells under standard conditions. As concentration cells have the same electrode material and the same ions in solutions, just at different concentrations, their potentials would cancel each other out under standard conditions, leading \(E_{\text {cell }}^{\circ}\) to be zero.

Key concepts

Electrochemical Cell

An electrochemical cell is a device that generates an electric current from the chemical reactions occurring within it. In its simplest form, it consists of two different metals, known as electrodes, immersed in electrolytes where they undergo chemical reactions. One of these electrodes will act as an anode, losing electrons, while the other acts as the cathode, gaining electrons. The movement of electrons from one electrode to another through an external circuit is what generates electricity.

Electrochemical cells can be primary, meaning they are non-rechargeable, or secondary, which are rechargeable batteries like those found in cell phones and electric cars. Concentration cells form a special kind of electrochemical cell, where the difference in concentration between two solutions provides the energy for electron flow, rather than a difference in material.

Standard Cell Potential

Standard cell potential, represented as \(E_{\text {cell }}^{\circ}\), is a critical value in electrochemistry that tells us how capable a cell is at driving an electric current under standard conditions. These standard conditions typically mean that all the reactants and products are at a concentration of 1 molar, the temperature is 298 K (25°C), and the pressure is 1 atmosphere.

The standard cell potential is calculated by taking the difference between the potentials of the cathode and the anode\(—\)the higher the potential difference, the greater the cell's ability to do work. In a concentration cell, however, the electrodes are made of the same substance and the potential difference is derived from the concentration gradient of the electrolyte. Since the standard state requires equal concentrations, \(E_{\text {cell }}^{\circ}\) is zero, reflecting that there is no potential difference under these conditions.

Equilibrium in Electrochemistry

Equilibrium in electrochemistry refers to a state where the forward and reverse reactions occur at the same rate. At this point, there is no net change in the concentration of reactants and products over time, and the cell's voltage stabilizes. This principle is key to understanding concentration cells, as they rely on the natural tendency of ions to move from an area of higher concentration to one of lower concentration to achieve equilibrium.

A concentration cell functions because of this drive toward equilibrium. Initially, there's a voltage due to the concentration gradient; ions travel through the solution or across a permeable membrane to balance out the uneven concentrations. As this process unfolds, electricity is generated. Eventually, when the concentrations equalize on both sides of the cell, equilibrium is reached and the current stops flowing because there is no more driving force for the movement of ions and therefore no further potential difference.