91Ó°ÊÓ

The Nernst Equation is a powerful tool used in electrochemistry to determine the potential of an electrochemical cell under non-standard conditions. It provides insights into how cell potential changes with varying concentrations of ions. The equation is expressed as:- \[ E = E^0 - \frac{RT}{nF} \ln Q \]- Here:

• \( E \) is the cell potential under actual conditions.
• \( E^0 \) refers to the standard cell potential.
• \( R \) is the universal gas constant, \( 8.314 \) J/(molâ‹…K).
• \( T \) is the temperature in Kelvin.
• \( n \) denotes the number of moles of electrons involved in the reaction.
• \( F \) is Faraday's constant (approximately 96485 C/mol).
• \( Q \) is the reaction quotient, representing the ratio of product and reactant concentrations.

Breaking it down, the equation shows us how a difference in ion concentration can influence the voltage of the cell. For example, in our reaction, where the concentration of \( \mathrm{Zn}^{2+} \) is 10 times that of \( \mathrm{Cu}^{2+} \), the Nernst equation helps calculate the resulting cell potential, factoring in this concentration gradient.

The reaction quotient, \( Q \), is a crucial aspect in understanding the Nernst Equation's utility. It is a measure of the ratio of concentrations of products to reactants at any point in a reaction that is not necessarily at equilibrium. The expression for \( Q \) changes depending on the balanced chemical equation. For our zinc-copper cell system, the reaction is:- \[ \text{Zn}(s) + \text{Cu}^{2+}(aq) \rightarrow \text{Zn}^{2+}(aq) + \text{Cu}(s) \]- From this, \( Q \) is determined by:- \[ Q = \frac{[\text{Zn}^{2+}]}{[\text{Cu}^{2+}]} \]- Because the zinc ion concentration is provided as 10 times the copper ion concentration, this gives us \( Q = 10 \).
Reacting systems constantly aim to reach equilibrium. As such, the reaction quotient provides a snapshot of the reaction's status relative to equilibrium:

• If \( Q < K \) (equilibrium constant), the reaction proceeds forward.
• If \( Q = K \), the system is at equilibrium.
• If \( Q > K \), the reaction shifts backward.

In conjunction with the Nernst Equation, \( Q \) becomes a vital component in predicting cell potentials under varying conditions.

Gibbs Free Energy (\( \Delta G \)) is a term that combines enthalpy and entropy to determine the spontaneity of a reaction. It tells us whether a process can occur under constant pressure and temperature. When it comes to electrochemical cells, \( \Delta G \) can be directly linked to the cell potential by:- \[ \Delta G = -nFE \]- Where:

• \( \Delta G \) is the change in Gibbs Free Energy.
• \( n \) refers to the number of moles of electrons exchanged in the reaction.
• \( F \) stands for Faraday's constant.
• \( E \) is the cell potential.

By substituting the Nernst equation into this expression, we can understand how changes in ion concentration and temperature affect \( \Delta G \):- \[ \Delta G = -nF \left( E^0 - \frac{RT}{nF} \ln Q \right) \]- For our problem:- \[ \Delta G = -2F(1.1) + 2.303RT \ln(10) \]- This shows how increasing the concentration of \( \mathrm{Zn}^{2+} \) impacts the Gibbs Free Energy, ultimately affecting the reaction's spontaneity. When \( \Delta G \) is negative, the reaction is spontaneous, moving towards equilibrium naturally; a positive \( \Delta G \) indicates non-spontaneity under the given conditions.