Problem 98 - Chemistry: The Central Science

Question

Two important characteristics of voltaic cells are their cell potential and the total charge that they can deliver. Which of these characteristics depends on theamount of reactants in the cell, and which one depends on their concentration?

Step-by-Step Solution

Answer

In a voltaic cell, the cell potential depends on the concentration of the reactants, as described by the Nernst equation. However, the total charge that the cell can deliver depends on the amount of reactants in the cell, which is calculated using Faraday's law of electrolysis.

Step 1: Cell Potential and Concentration/Amount of Reactants

Cell potential, denoted as E_cell, is the difference in electrical potential between the cathode and the anode of a voltaic cell. It determines the cell's ability to generate an electric current. The cell potential is related to the concentration of the reactants by the Nernst equation: \[E_{cell} = E_{cell}^\circ - \frac{RT}{nF} \ln Q\] Where: - \(E_{cell}^\circ\) is the standard cell potential, - R is the gas constant, - T is the temperature, - n is the number of electrons exchanged in the redox reaction, - F is Faraday's constant, and - Q is the reaction quotient, which is determined by the concentrations of the reactants and products. From this equation, we can conclude that the cell potential depends on the concentration of the reactants, not on their amount.

Step 2: Total Charge and Concentration/Amount of Reactants

Meanwhile, the total charge that a voltaic cell can deliver is determined by the amount of reactants that can participate in the redox reaction. The total charge (Q_total) can be calculated using Faraday's law of electrolysis: \[Q_{total} = nF \times moles\] Where: - n is the number of electrons exchanged in the redox reaction, - F is Faraday's constant, and - moles represent the amount of reactant(s) available for the redox reaction. From this equation, we can conclude that the total charge depends on the amount of reactants in the cell, not on their concentration. In summary, the cell potential of a voltaic cell depends on the concentration of the reactants, while the total charge that the cell can deliver depends on the amount of reactants in the cell.

Key Concepts

Cell Potential

In the context of voltaic cells, cell potential (also known as electromotive force or EMF) is a vital element. This value indicates the difference in voltage between the two electrodes: the cathode and the anode. It essentially measures how strongly electrons will flow from one end of the cell to the other. A higher cell potential means a greater ability to do electrical work.
To determine the cell potential, we start with the standard cell potential, denoted by \(E_{cell}^\circ\), which is measured under standard conditions—where all solutions have concentrations of 1 M, gases are at 1 atm and the temperature is 25°C (298 K). Any changes in reactant concentration will affect this potential, which can be calculated using the Nernst Equation. This relationship highlights that cell potential is concentration-dependent, showing how reactants' levels impact the flow of electricity in a voltaic cell.

Nernst Equation

The Nernst Equation is a fundamental formula used to derive the cell potential under non-standard conditions. It connects the standard cell potential, \(E_{cell}^\circ\), with the actual conditions of concentration ratios of reactants and products. The equation is given by:

\[E_{cell} = E_{cell}^\circ - \frac{RT}{nF} \ln Q\]

Where:

• \(R\) is the universal gas constant \(8.314 \text{ J mol}^{-1} \text{ K}^{-1}\),
• \(T\) is the temperature in Kelvin,
• \(n\) represents the number of moles of electrons transferred in the balance reaction,
• \(F\) stands for Faraday's constant \(96485 \text{ C mol}^{-1}\),
• \(Q\) is the reaction quotient, calculated from the concentrations of products and reactants.

The Nernst Equation tells us how changes in concentration affect cell potential. If the concentration of reactants increases, it can increase \(Q\), thus affecting the second term of the equation, generally leading to a change in \(E_{cell}\). As a key tool in electrochemistry, it allows chemists to predict and measure the cell potential under various situations.

Faraday's Law of Electrolysis

Faraday's Law of Electrolysis is a principal concept that helps illustrate how much electrical charge is required to convert a set amount of matter during an electrochemical reaction. It shows the direct relationship between the amount of substance that reacts at an electrode and the quantity of electricity passed through the circuit. According to the formula:

\[Q = nF \times \text{moles}\]

where:

• \(Q\) is the total charge in coulombs,
• \(n\) is the number of electrons exchanged in the redox reaction,
• \(F\) is Faraday's constant,
• \(\text{moles}\) are the amount of the reacting substance.

This law indicates that the total charge that a voltaic cell delivers heavily depends on the amounts of reactants available for the redox reaction. It does not depend on concentration, making it essential for understanding how chemical amounts govern electricity production in electrochemistry.

Redox Reactions

Redox reactions, short for reduction-oxidation reactions, are chemical processes where the oxidation states of atoms are changed. They form the heart of voltaic cells and are vital for producing electricity. In these reactions, one substance gains electrons (is reduced) and another loses electrons (is oxidized). The site of reduction is the cathode, while oxidation occurs at the anode.
In a typical voltaic cell, the flow of electrons from the anode to the cathode through an external circuit generates electric current. Understanding these reactions is crucial as they explain how chemical energy transforms into electrical energy in cells. It's the balanced exchange of electrons that powers various devices by allowing controlled energy release. The efficiency and capacity of voltaic cells rely significantly on the substances involved and their ability to undergo these redox changes effectively.