Question

What conditions must be met for a cell potential \(E\) to qualify as a standard cell potential \(E^{\circ} ?\)

Short answer

For E to be E^{ ext{ extdegree}}, conditions: 1 M solutions, 1 atm gases, 298 K.

Step-by-step solution

Introduction to Standard Cell Potential

The standard cell potential ( E^{ ext{ extdegree}} ) is defined as the cell potential measured under standard conditions. The value of E^{ ext{ extdegree}} provides important information about the voltage a galvanic cell can provide.

Understanding Standard Conditions

Standard conditions refer to specific conditions set for measuring the standard cell potential. These conditions include: concentration of all solutions being 1 mol/L, pressure of all gases being 1 atm, and the temperature being 298 K (25°C).

Equality of Reactions and Products

When measuring standard cell potential, all reactants and products—excluding those in solid, liquid, or gas form—should be at standard state, i.e., 1 M for solutions or 1 atm for gases.

Balancing the Redox Reaction

The half-reactions involved in the cell must be correctly balanced in terms of mass and charge before calculating the standard cell potential. This ensures that the electron transfer is accurately represented.

Calculating Standard Cell Potential

Once the reactions are balanced, the standard cell potential ( E^{ ext{ extdegree}} ) can be determined using the standard reduction potentials of the cathode ( E^{ ext{ extdegree}}_{ ext{cathode}} ) and anode ( E^{ ext{ extdegree}}_{ ext{anode}} ): E^{ ext{ extdegree}} = E^{ ext{ extdegree}}_{ ext{cathode}} - E^{ ext{ extdegree}}_{ ext{anode}} .

Key concepts

Standard Conditions

When chemists refer to standard conditions in the context of a galvanic cell, they mean specific conditions under which measurements are consistent and comparable. These conditions include:

• Concentration of all solutions must be exactly 1 molar (1 M).
• Pressure of all gases needs to be maintained at 1 atmosphere (1 atm).
• The temperature has to be set at 298 Kelvin, which is equivalent to 25 degrees Celsius.

These controlled conditions ensure that the measurement of the cell potential is not influenced by external factors. By maintaining these specific conditions, results from different experiments or studies can be uniformly compared. It also ensures reproducibility of data across different laboratories.

Galvanic Cell

A galvanic cell is an electrochemical cell that generates electrical energy through a spontaneous redox reaction. This occurs when electrons are transferred from one substance to another, producing electric flow. The cell is composed of two half-cells, each containing an electrode and an electrolyte. These are typically:

• The anode, where oxidation occurs and electrons are released.
• The cathode, where reduction occurs and electrons are gained.

Within a galvanic cell, the movement of electrons from the anode to the cathode via an external circuit provides the energy needed to do work, like lighting a bulb or powering a small device. This makes galvanic cells highly valuable in everyday technology, from batteries to fuel cells.

Redox Reaction

Redox reactions, or oxidation-reduction reactions, are fundamental in chemistry for transferring energy. In a redox reaction:

• Oxidation involves the loss of electrons by a molecule, atom, or ion.
• Reduction involves the gain of electrons by a substance.

These two processes are coupled; as one species oxidizes, another reduces. For galvanic cells, this electron transfer is harnessed to generate electricity. Balancing redox reactions is important to ensure that the number of atoms and charges are equal on both sides, which allows accurate calculation of cell potentials. Understanding redox processes is crucial for working with any systems involving electron exchange and energy transformation.

Standard Reduction Potential

The standard reduction potential is a key measure used to determine how much voltage a specific electrode reaction contributes in a cell. Each half-cell reaction within a galvanic cell has a standard reduction potential, which represents the tendency of the species to gain electrons. It is denoted by the symbol:\(E^{\circ}\) and measured in volts (V).To calculate the overall standard cell potential, the standard reduction potentials of both the cathode and the anode are used:\[E^{\circ} = E^{\circ}_{\text{cathode}} - E^{\circ}_{\text{anode}}\]This formula helps determine whether a reaction is spontaneous. A positive \(E^{\circ}\) value indicates a spontaneous reaction that can generate electrical power without external energy inputs. Understanding and using standard reduction potentials is essential for designing batteries and other electrochemical systems.