Question

What information do you need in order to determine the standard voltage of a voltaic cell?

Short answer

To determine the standard voltage of a voltaic cell, first identify the two half-reactions occurring at the anode and cathode and note their standard reduction potentials (Eº). Ensure the reactions follow the correct direction, with oxidation at the anode and reduction at the cathode. Calculate the standard cell potential (Eº_cell) by subtracting the reversed standard reduction potential from the standard reduction potential occurring as written: Eº_cell = Eº_cathode - Eº_anode. A positive Eº_cell indicates a spontaneous flow of electrons under standard conditions.

Step-by-step solution

Identify the half-reactions

In the given voltaic cell, identify the two half-reactions occurring at the anode and cathode. Note down their respective standard reduction potentials (Eº).

Determine the direction of the reactions

Ensure that the oxidation (loss of electrons) occurs at the anode and that the reduction (gain of electrons) occurs at the cathode. Remember that the more positive standard reduction potential will occur as written (i.e., as a reduction) while the more negative one will be reversed (i.e., as an oxidation).

Calculate the standard cell potential

Subtract the reversed standard reduction potential from the standard reduction potential occurring as written. This will give you the standard cell potential (Eº_cell) of the voltaic cell: Eº_cell = Eº_cathode - Eº_anode Make sure to use the appropriate signs for the standard reduction potentials, as found in step 2.

Interpret the result

Ensure that the calculated standard cell potential (Eº_cell) is positive. A positive value indicates that the voltaic cell can produce a spontaneous flow of electrons (i.e., electrical energy) under standard conditions. If the value is negative, the cell reaction is non-spontaneous, and it would require an external energy source to drive the reaction.

Key concepts

Standard Reduction Potentials

Understanding the standard reduction potentials in electrochemistry is akin to learning how a battery's power is determined. A standard reduction potential, often represented as Eº, is the voltage or electric potential that a half-reaction develops under standard conditions, which include a solute concentration of 1 M, a gas pressure of 1 atm, and a temperature of 25°C (298 K).

The standard reduction potential is a half-reaction measure of the tendency of a chemical species to acquire electrons and thus be reduced. Each half-reaction has its unique Eº value, which is measured relative to the standard hydrogen electrode (SHE), which is arbitrarily given a potential of 0 volts. The values for various substances can be found in an electrochemical series, which orders substances from highest to lowest standard reduction potentials.
When trying to determine the standard voltage of a voltaic cell, you need to look up the standard reduction potential for both the anode and the cathode. This information is essential because the cell potential is directly calculated from these potentials. The substance with the higher reduction potential tends to gain electrons and function as the cathode, while the other becomes the anode.

Half-Reactions in Electrochemistry

In electrochemistry, a voltaic cell, or galvanic cell, is composed of two half-cells, each of which is responsible for one half of the overall reaction. A half-reaction is simply one part of a redox (reduction-oxidation) reaction whereby electrons are either gained or lost. Every electrochemical cell consists of two half-reactions: one where oxidation occurs (loss of electrons) at the anode, and another where reduction takes place (gain of electrons) at the cathode.

For clarity, let's dissect the two types of half-reactions:

• Oxidation half-reaction: Occurs at the anode where a substance loses electrons, thereby increasing its oxidation state.
• Reduction half-reaction: Happens at the cathode where a substance gains electrons and its oxidation state is reduced.

Identifying these half-reactions is imperative because they provide vital information about which substances are involved in electron transfer, how many electrons are transferred, and the direction in which the electrons flow through the external circuit in a voltaic cell.
This electron movement is the very essence of the electric current generated by the cell. Moreover, by reversing the half-reaction with a negative standard reduction potential (making it oxidation), students can then use these half-reactions to calculate the cell potential.

Calculating Cell Potential

Once you have the standard reduction potentials and have identified the half-reactions at the anode and cathode, the next step is to calculate the cell potential. This value, known as the electromotive force (EMF) of the cell, can be obtained by using the formula:

Eº_cell = Eº_cathode - Eº_anode

Here, Eº_cathode is the standard reduction potential for the half-reaction at the cathode, and Eº_anode is the potential for the half-reaction at the anode after it has been reversed to represent oxidation. It is crucial to subtract the anode potential from the cathode potential because the anode potential represents the tendency to lose electrons (oxidation), which counters the cathode's tendency to gain electrons (reduction).
A positive standard cell potential indicates a spontaneous reaction, meaning the cell can generate electrical energy without external input. Conversely, a negative cell potential implies that the reaction is non-spontaneous and would require external energy to proceed.
For students, understanding these steps breaks down a seemingly complex electrochemical calculation into manageable parts, aiding in problem-solving and a deeper comprehension of how voltaic cells operate.