Question

(a) Under what circumstances is the Nernst equation applicable? (b) What is the numerical value of the reaction quotient, \(Q\), under standard conditions? (c) What happens to the emf of a cell if the concentrations of the reactants are increased?

Short answer

The Nernst equation is applicable when there is a redox reaction at the electrodes and the reaction is at equilibrium or close to it, and the temperature is constant. Under standard conditions, the numerical value of the reaction quotient, \(Q\), is 1. When the concentrations of the reactants are increased, the emf of the cell will decrease.

Step-by-step solution

Understanding the Nernst Equation and its Applicability

The Nernst equation is used to calculate the emf (electromotive force) of an electrochemical cell under non-standard conditions. It takes into account the concentrations or activities of the reactants and products involved in the electrochemical process. The Nernst equation is applicable when there is a redox reaction at the electrodes and the reaction is at equilibrium or close to it. Additionally, the temperature should be constant during the reaction.

Determining the Reaction Quotient, \(Q\), under Standard Conditions

The reaction quotient, \(Q\), is a dimensionless number that describes the ratio of the concentrations of the products to the concentrations of the reactants in a reversible chemical reaction at a given point in time. Standard conditions refer to 25°C (298.15 K) temperature, 1 atm pressure, and all species present at 1 M concentration. Under standard conditions, since all species have an equal concentration of 1 M, the concentration terms in the reaction quotient will cancel out, leaving: \[Q = \frac{[C]^c [D]^d}{[A]^a [B]^b}\] \[Q = \frac{[1]^c [1]^d}{[1]^a [1]^b}\] Therefore, under standard conditions, Q = 1.

Effect of Increasing Reactant Concentrations on the emf of a Cell

According to the Nernst equation, the emf of a cell (\(E_{cell}\)) is given by: \[E_{cell} = E_{cell}^0 - \frac{RT}{nF} \ln Q\] Where \(E_{cell}^0\) is the standard cell potential, R is the gas constant, T is the temperature, n is the number of electrons transferred in the redox reaction, F is the Faraday constant, and Q is the reaction quotient. When the reactant concentrations are increased, the value of the reaction quotient, \(Q\) will decrease because the concentration of the products remains unchanged. Since the term \(-\frac{RT}{nF} \ln Q\) contributes negatively to the Nernst equation, a decrease in Q will cause an increase in the magnitude of the negative term and, therefore, a decrease in the emf of the cell. In conclusion, when the concentrations of the reactants of an electrochemical cell are increased, the emf of the cell will decrease.

Key concepts

Reaction Quotient

The reaction quotient, denoted by \( Q \), is a crucial part of understanding chemical reactions at any point. It signifies the ratio of the concentrations (or partial pressures) of the products raised to their respective stoichiometric coefficients, divided by the reactants raised to their coefficients. This is generally represented as:\[ Q = \frac{[C]^c [D]^d}{[A]^a [B]^b} \]In the context of electrochemical cells, \( Q \) helps in assessing the cell potential under different conditions using the Nernst equation. When the reaction is at standard conditions, which we'll discuss in the next section, the concentrations of the reactants and products are typically equal, making \( Q = 1 \).
Understanding the value of \( Q \) helps predict the direction in which a reaction will naturally proceed towards equilibrium.

Standard Conditions

Standard conditions are specific reference points that allow chemists to compare different reactions under the same baseline. These conditions include:

• Temperature of 25°C or 298.15 K.
• Pressure of 1 atm.
• Concentrations of all solutes at 1 M.

When an electrochemical reaction is under standard conditions, like those mentioned above, it simplifies calculations because the reaction quotient \( Q \) equals 1, thus having no logarithmic impact in the Nernst equation: \[ E_{cell} = E_{cell}^0 - \frac{RT}{nF} \ln Q \]Under these standard sets, you can focus on other variables that might affect the cell's performance without worrying about concentration impacts.

Electrochemical Cell

An electrochemical cell is a device that generates electrical energy from chemical reactions—either through spontaneous reactions in galvanic cells or by inputting energy to drive non-spontaneous reactions in electrolytic cells.
A basic electrochemical cell consists of two electrodes, the anode (where oxidation occurs) and the cathode (where reduction takes place), submerged in separate solutions that facilitate ion transfer.
The role of an electrochemical cell is crucial in industries for galvanization and energy generation. For students, understanding this cell is critical when applying the Nernst equation to calculate the cell's electromotive force (emf) during reactions.

Cell EMF

Electromotive force, abbreviated as emf, refers to the potential difference that drives the flow of electrons from the anode to the cathode in an electrochemical cell. It’s measured in volts and can be calculated using:\[ E_{cell} = E_{cell}^0 - \frac{RT}{nF} \ln Q \]This formula emphasizes how the emf is impacted by the standard cell potential \( E_{cell}^0 \), temperature \( T \), and the reaction quotient \( Q \). Under standard conditions, \( Q \) equals 1, hence the emf aligns closely with the standard cell potential.
A higher emf indicates a stronger driving force for the electron flow, critical for the efficiency of batteries and electrochemical sensors.

Redox Reaction

Redox reactions, short for reduction-oxidation reactions, entail the transfer of electrons between chemical species. The overarching principle is that one species loses electrons (oxidation) while another gains electrons (reduction).
These reactions are pivotal in the operation of electrochemical cells. For instance, your flashlight batteries rely on redox reactions to generate electronic power.
In the context of the Nernst equation, recognizing which redox reactions occur at the electrodes, and how they impact the reaction quotient \( Q \), helps in attaining accurate calculations for the cell emf and understanding how changes in conditions affect the reaction dynamics.