Problem 61 - Chemistry The Central Science

Question

(a) In the Nernst equation, what is the numerical value of the reaction quotient, Q, under standard conditions? (b) Can the Nernst equation be used at temperatures other than room temperature?

Step-by-Step Solution

Answer

The short answer to the question is: (a) Under standard conditions, the numerical value of the reaction quotient, Q, is 1. (b) Yes, the Nernst equation can be used at temperatures other than room temperature, as it inherently includes temperature as one of its parameters (T in Kelvin), which can be adjusted accordingly for different temperatures.

Step 1: Question (a) - Numerical value of Q under standard conditions

Before we can find the numerical value of Q, we first need to review the Nernst equation, which is given by: \(E = E^0 - \frac{RT}{nF} \ln Q\) where: - \(E\) is the cell potential at any point in time, - \(E^0\) is the standard electrode potential, - \(R\) is the gas constant, - \(T\) is the temperature in Kelvin, - \(n\) is the number of electrons transferred in the redox reaction, - \(F\) is Faraday's constant, and - \(Q\) is the reaction quotient. Under standard conditions, the cell potential (\(E\)) is equal to the standard electrode potential (\(E^0\)) because the reaction is at equilibrium. As a result, the reactant and product activities are at their standard states, so the reaction quotient, Q, equals 1. Therefore, the numerical value of Q under standard conditions is 1.

Step 2: Question (b) - Applying the Nernst Equation at Other Temperatures

The Nernst equation is a general equation that relates the cell potential to the temperature, reaction quotient, and number of electrons transferred in a half-cell reaction. This means that the equation is not limited to a specific temperature, such as room temperature. In fact, one of the main uses of the Nernst equation is to be able to calculate the potential of an electrochemical cell under different temperatures and concentrations. The equation inherently includes temperature as one of its parameters, which means it can be applied to different temperatures as long as you adjust the value of T (temperature in Kelvin) accordingly.

Key Concepts

Reaction Quotient

In the Nernst equation, the reaction quotient (\( Q \)) is an expression that compares the concentrations of the reactants and products at any given point in the reaction. It plays a pivotal role in determining the cell potential. The reaction quotient is defined as:\[Q = \frac{\text{[products]}^{\text{coefficients}}}{\text{[reactants]}^{\text{coefficients}}}\]This means that \( Q \) is constructed like the equilibrium constant, \( K \), but at non-equilibrium conditions. \( Q \) informs us about how far the reaction has moved from equilibrium state. If \( Q = 1 \), the system is at standard state. This means all concentrations are at their standard values, which simplifies calculations and indicates that the driving force for the reaction is balanced. \( Q \) being equal to 1 under standard conditions is a key aspect that simplifies the Nernst equation, showing no difference between current and standard cell potential values.
Understanding this concept helps in grasping how cell potential changes with concentration and product/reactant distribution.

Standard Conditions

Standard conditions serve as a baseline for comparing reactions. They provide a common ground for measuring and predicting chemical behavior. For electrochemical reactions, standard conditions are defined as:

• A concentration of 1 mol/L for all solutions involved in the reaction.
• A pressure of 1 atm for any gases involved.
• A temperature of 298 K (25°C).

Under these conditions, the Nernst equation simplifies, and the standard cell potential (\( E^0 \)) can be directly applied because the reaction quotient \( Q \) is 1. When a reaction is at standard state, it indicates that all reactants and products are in their default forms, simplifying calculations.
It's important to recognize that standard conditions might not represent everyday lab or industrial conditions but offer a baseline for calculations and comparisons.

Cell Potential

Cell potential, denoted as \( E \), is a measure of the electrical potential difference between two electrodes in an electrochemical cell. It reflects the ability of a cell to drive an electric current through an external circuit. This potential is influenced by several factors including:

• The nature of the electrodes.
• The concentrations of the ionic solutions surrounding them.
• The temperature of the system.

The Nernst equation links these factors by correlating \( E \) with the reaction quotient (\( Q \)), the standard cell potential (\( E^0 \)), temperature (\( T \)), and the number of electrons transferred (\( n \)). This relationship is expressed as:\[E = E^0 - \frac{RT}{nF} \ln Q\]Where \( E^0 \) is constant for a given reaction at standard conditions, \( E \) varies based on non-standard conditions like changing concentrations, varying temperatures, or different surface areas of electrodes. Understanding cell potential is fundamental for predicting how cells will behave in real-world applications, such as batteries or electrolysis setups, illustrating why the Nernst equation is so vital.