Question

Cell reaction is spontaneous when (a) \(E_{\text {red }}^{\circ}\) is +ve (b) \(\Delta G^{\circ}\) is -ve (c) \(\Delta G^{\circ}\) is +ve (d) \(E_{\text {red }}^{\circ}\) is +ve

Short answer

A cell reaction is spontaneous when \(E_{\text {red }}^{\circ}\) is positive and \(\Delta G^{\circ}\) is negative. So, options (a) and (b) are correct.

Step-by-step solution

Understanding Standard Reduction Potential

The standard reduction potential \(E_{\text {red }}^{\circ}\) is a measure of the tendency of a chemical species to be reduced, i.e., to gain electrons. A positive standard reduction potential indicates a strong tendency to be reduced - which is favorable for the reaction to be spontaneous.

Understand Standard Gibbs Free Energy

The standard Gibbs free energy \(\Delta G^{\circ}\) is a thermodynamic potential that measures the maximum reversible work that a system can perform at constant temperature and pressure. If \(\Delta G^{\circ}\) is negative, it means that the system loses energy, which is favorable for a spontaneous reaction.

Answer the question

So for a cell reaction to be spontaneous, \(E_{\text {red }}^{\circ}\) should be positive and \(\Delta G^{\circ}\) should be negative.

Key concepts

Standard Reduction Potential

The concept of Standard Reduction Potential (E_red°) is fundamental to understanding spontaneous reactions in electrochemistry. It provides a quantitative way to assess the tendency of a chemical species to gain electrons, a process known as reduction. A positive E_red° value signifies that a species is more likely to be reduced. Consequently, when comparing two half-reactions in an electrochemical cell, the one with the higher E_red° will act as the cathode, accepting electrons, and driving the cell towards a spontaneous reaction.

In simpler terms, think of E_red° as a 'desire meter' for electrons—the higher the value, the greater the desire of a substance to 'accept' electrons. If you come across a positive E_red° in a problem, you can be confident you're dealing with a reaction that has the potential to occur on its own, under standard conditions.

Gibbs Free Energy

Moving onto Gibbs Free Energy (abla G°), this thermodynamic quantity can be compared to a balance sheet for the energy exchange in a reaction. It predicts whether a process will proceed spontaneously at constant pressure and temperature. A negative value of abla G° indicates that a reaction is 'spontaneously profitable', energetically speaking, and the reaction will likely proceed without external input.

One crucial aspect to remember is that a spontaneous reaction isn't necessarily a rapid one. For example, a diamond turning into graphite has a negative abla G°, making it thermodynamically favorable, yet you won't see diamonds turning into pencil lead because the rate at which this process naturally occurs is exceptionally slow. In summary, negative abla G° is akin to having a green light for a reaction to occur spontaneously, but it doesn't comment on the 'speed limit'—the kinetics of the reaction.

Thermodynamics

The field of Thermodynamics is the backbone behind the ideas of Standard Reduction Potential and Gibbs Free Energy. It's the study of heat, energy, and work, allowing scientists and engineers to predict the direction and extent of chemical reactions as well as designing systems that convert heat energy into work, like engines.

Thermodynamics tells us that energy cannot be created or destroyed, only converted from one form to another. This principle underlies the concept of abla G°, where we assess the energy available to do work in a system. Spontaneous reactions will always move a system towards a state of lower free energy, in accordance with the second law of thermodynamics. In essence, systems love laziness; they spontaneously tend towards the lowest energy state available—their own form of 'couch potato' mode.

Electrochemistry

Lastly, Electrochemistry is the study of chemical processes that cause electrons to move, which creates an electrical current. It links electricity with chemical change, allowing us to use chemical reactions to generate electricity, or vice versa. A spontaneous cell reaction is the bedrock upon which batteries and electroplating are built.

A common real-world example is a battery in a remote control. Inside the battery, a spontaneous electrochemical reaction occurs, releasing energy that powers the remote. The Standard Reduction Potential tells us if it's favorable for this reaction to happen, while Gibbs Free Energy ensures that the reaction has a 'profit' of energy, enough to be usable. Electrochemistry is, therefore, not just an academic topic, but the practical force behind many everyday technologies.