Coulometry: Videos & Practice Problems

Electrochemical cells can be classified based on spontaneity, determined by Gibbs free energy (ΔG), equilibrium constant (K), cell potential (E_cell), and entropy (ΔS). A spontaneous reaction (ΔG < 0) indicates a galvanic cell, while a non-spontaneous reaction (ΔG > 0) indicates an electrolytic cell, which requires an external energy source. At equilibrium (ΔG = 0), the cell behaves like a dead battery. In both cell types, the anode undergoes oxidation and the cathode reduction, but their charge roles differ in electrolytic cells, necessitating a battery to drive the reaction.

Coulometry

Electrochemical cells can be categorized based on their spontaneity, which is determined by several key variables: Gibbs free energy (ΔG), the equilibrium constant (K), cell potential (E), entropy (ΔS), and the reaction quotient (Q). Under standard conditions (25°C, pH 7, 1 M concentration), these variables help classify reactions as spontaneous, non-spontaneous, or at equilibrium.

When ΔG is less than 0, the reaction is spontaneous. In this case, K is greater than 1, the cell potential is positive, and ΔS (total entropy) is also positive. Here, Q is less than K, indicating that the reaction will shift forward towards equilibrium. This scenario corresponds to a galvanic or voltaic cell, which generates electricity.

Conversely, if ΔG is greater than 0, the reaction is non-spontaneous. In this situation, K is less than 1, the cell potential is negative, and ΔS is negative. Here, Q exceeds K, suggesting that the reaction will shift in the reverse direction. This indicates an electrolytic cell, which requires an external energy source (like a battery) to drive the reaction, consuming electricity in the process.

At equilibrium, all variables equal their respective values, indicating a state where the electrochemical cell is effectively a dead battery, having discharged all its electricity.

In electrolytic cells, the anode is positive and the cathode is negative, which is the opposite of galvanic cells where the anode is negative. This reversal occurs because electrolytic cells require a battery to force electrons from the anode to the cathode, overcoming the natural repulsion between like charges. The anode still undergoes oxidation while the cathode undergoes reduction, a consistent feature across both types of electrochemical cells.

Understanding these relationships between ΔG, K, E, ΔS, and Q is crucial for determining the nature of electrochemical reactions and the type of cell involved, whether it be spontaneous (galvanic) or non-spontaneous (electrolytic).

Here’s what students ask on this topic:

What is the difference between galvanic and electrolytic cells?

Galvanic (or voltaic) cells and electrolytic cells are both types of electrochemical cells, but they operate under different principles. A galvanic cell generates electrical energy from a spontaneous redox reaction, where ΔG < 0, K > 1, and E_cell > 0. In this cell, the anode is negative, and the cathode is positive. Conversely, an electrolytic cell requires an external energy source to drive a non-spontaneous reaction, where ΔG > 0, K < 1, and E_cell < 0. Here, the anode is positive, and the cathode is negative. Despite these differences, both types of cells involve oxidation at the anode and reduction at the cathode.

How does Gibbs free energy relate to the spontaneity of electrochemical cells?

Gibbs free energy (ΔG) is a key indicator of the spontaneity of a reaction in electrochemical cells. For a spontaneous reaction, ΔG is less than 0 (ΔG < 0), indicating that the reaction can proceed without external energy. This is typical of galvanic cells. For a non-spontaneous reaction, ΔG is greater than 0 (ΔG > 0), meaning the reaction requires an external energy source to proceed, as seen in electrolytic cells. At equilibrium, ΔG equals 0 (ΔG = 0), indicating no net reaction occurs, similar to a dead battery.

What role does the equilibrium constant (K) play in electrochemical cells?

The equilibrium constant (K) helps determine the direction and extent of a reaction in electrochemical cells. For a spontaneous reaction, K is greater than 1 (K > 1), indicating that the products are favored. This is typical in galvanic cells. For a non-spontaneous reaction, K is less than 1 (K < 1), meaning the reactants are favored, as seen in electrolytic cells. When K equals 1 (K = 1), the system is at equilibrium, and no net reaction occurs.

Why do electrolytic cells require an external energy source?

Electrolytic cells require an external energy source, such as a battery, because they drive non-spontaneous reactions where ΔG > 0. In these cells, the anode is positive, and the cathode is negative, which is opposite to galvanic cells. The external energy source forces electrons to move against their natural tendency, enabling the oxidation at the anode and reduction at the cathode. This process consumes electrical energy to make the reaction occur.

What happens at the anode and cathode in electrochemical cells?

In all electrochemical cells, the anode is where oxidation occurs, and the cathode is where reduction takes place. In a galvanic cell, the anode is negative, and the cathode is positive. In an electrolytic cell, the anode is positive, and the cathode is negative. Despite the difference in charge roles, the fundamental processes of oxidation at the anode and reduction at the cathode remain consistent across both types of cells.