For a spontaneous reaction the \(\Delta \mathrm{G}\), equilibrium constant \((\mathrm{K})\) and \(\mathrm{E}_{\text {oell }}^{\circ}\) will be respectively: (a) \(-\mathrm{ve},>1,+\mathrm{ve}\) (b) \(+\) ve, \(>1,-\mathrm{ve}\) (c) \(-\mathrm{ve},<1,-\mathrm{ve}\) (d) \(-\mathrm{ve},>1,-\mathrm{ve}\)

Gibbs free energy, noted as \( \Delta G \), is a thermodynamic quantity that can predict the direction of a chemical reaction under constant temperature and pressure conditions. When \( \Delta G \ < 0 \) for a process or reaction, it is considered spontaneous, meaning it can proceed without any external energy input. This is a crucial concept for understanding why certain reactions occur naturally.

For instance, when water flows downstream or ice melts on a warm day, these are examples of spontaneous processes where the Gibbs free energy is negative. It is an indicator that the reactions or processes are thermodynamically favorable. A negative \( \Delta G \), reflecting the spontaneous nature of a reaction, is typically associated with an increase in entropy, or disorder, in the system.

Connection with Equilibrium

When a reaction has reached equilibrium, it means that the forward and reverse reactions are happening at the same rate and \( \Delta G \) is zero. In other words, there is no net change in the composition of the system. In the context of equilibrium, Gibbs free energy also helps determine the position of the equilibrium, favoring either reactants or products, based on whether \( \Delta G \)'s sign is negative or positive.

• If \( \Delta G < 0 \), the equilibrium will favor the formation of products (spontaneous).
• If \( \Delta G > 0 \), the equilibrium will favor the reactants (non-spontaneous).
• If \( \Delta G = 0 \), the system is at equilibrium.

Therefore, for a spontaneous reaction, we are looking for conditions where \( \Delta G \ < 0 \), suggesting that the process is thermodynamically favorable at standard conditions.

The equilibrium constant, represented by \( K \), is a dimensionless number that expresses the ratio of product concentrations to reactant concentrations at equilibrium, with each concentration raised to the power of its stoichiometric coefficient. A larger equilibrium constant, \( K > 1 \), signifies that at equilibrium, the products are favored over the reactants.

A clear understanding of \( K \) helps predict how far a reaction will proceed before reaching equilibrium. This quantitative measure is invaluable when comparing the extents of different reactions under the same conditions.

Relationship Between ΔG and K

The link between Gibbs free energy (\( \Delta G \) and the equilibrium constant is encapsulated in the equation \( \Delta G = -RT \ln(K) \), where \( R \) is the universal gas constant and \( T \) is the absolute temperature. This equation illustrates how the sign of \( \Delta G \) is influenced by the magnitude of \( K \)：

• If \( K > 1 \), the reaction is product-favored, and \( \Delta G \) is negative, indicating a spontaneous process.
• If \( K < 1 \), the reaction is reactant-favored, and \( \Delta G \) is positive, indicating a non-spontaneous process.

For a spontaneous chemical reaction in NEET chemistry, the condition \( K > 1 \) confirms that the products are predominantly formed at equilibrium, thereby manifesting the reaction's natural tendency to proceed.

Cell potential, denoted by \( E_{\text{cell}}^{\circ} \), is the electrical potential difference between the cathode and anode in an electrochemical cell when they are at standard conditions. It is a measure of the cell’s ability to drive an electric current through an external circuit.

In the context of spontaneous reactions for NEET chemistry, a positive standard cell potential (\(\ E_{\text{cell}}^{\circ} > 0 \)) indicates that the reaction can spontaneously generate electrical energy, much like a battery.

ΔG and E_cell° Relationship

The connection between Gibbs free energy and cell potential is given by the formula \( \Delta G = -nFE_{\text{cell}}^{\circ} \), where \( n \) is the number of moles of electrons transferred in the reaction and \( F \) is Faraday's constant, which represents the charge per mole of electrons. When electrons move through the cell from the anode to the cathode, this movement generates electrical work, corresponding to a positive \( E_{\text{cell}}^{\circ} \) and a negative \( \Delta G \).

• A positive \( E_{\text{cell}}^{\circ} \) means the cell can do work on the surroundings (spontaneous).
• A negative \( E_{\text{cell}}^{\circ} \) means work must be done on the cell to cause the reaction (non-spontaneous).
• If \( E_{\text{cell}}^{\circ} = 0 \), there is equilibrium, and no net movement of electrons occurs.

Positive cell potential is an essential requirement for a spontaneous reaction, and it provides the driving force for the chemical change, reinforcing the answer to the original exercise, which is option (a) \( (-\text{ve},>1,+\text{ve}) \).