Cell Potential: Standard: Videos & Practice Problems

In an electrochemical cell, the standard cell potential (E^°_cell) is a crucial measure of the cell's ability to produce an electric current. It is defined by the difference in standard reduction potentials (E^°_red) of the cathode and anode, expressed in volts (V), which also equate to joules per coulomb (J/C). A positive E^°_cell indicates a spontaneous reaction, typical of galvanic or voltaic cells, where the cathode has a higher E^°_red than the anode. Conversely, in an electrolytic cell, the cathode has a lower E^°_red, resulting in a negative E^°_cell, signifying non-spontaneity. Understanding the relationship between cathode and anode potentials is key to determining the cell's standard potential and its type—galvanic/voltaic or electrolytic.

Standard Cell Potential

The standard cell potential, denoted as \( E^\circ_{\text{cell}} \), is a crucial concept in electrochemistry, representing the measure of the reduction potential between two half-cells: the cathode and the anode. This potential is expressed in volts (V), which quantifies the work done as electrons move from one electrode to another. It is important to note that the term "standard" indicates that the concentrations of ions in the half-cells are at 1 molar, the pressure is at 1 atmosphere, and the pH is equal to 7.

In terms of units, volts can be defined as joules per coulomb, where the coulomb (C) is the SI unit for electric charge. To calculate the standard cell potential of an electrochemical cell, the formula used is:

\[ E^\circ_{\text{cell}} = E^\circ_{\text{cathode}} - E^\circ_{\text{anode}} \]

This equation highlights that the standard cell potential is determined by subtracting the standard reduction potential of the anode from that of the cathode. Understanding which half-cell serves as the cathode and which as the anode is essential for applying this formula correctly. The cathode is where reduction occurs, while oxidation takes place at the anode. By accurately identifying these components, one can effectively calculate the standard cell potential and gain insights into the electrochemical behavior of the cell.

Standard Cell Potential Example

To determine the standard cell potential for a voltaic cell involving copper and zinc electrodes, we start by analyzing the two half-reactions. The first half-reaction involves zinc ions (Zn²⁺) gaining two electrons (2e^-) to form solid zinc (Zn), with a standard reduction potential (E^°) of -0.7621 volts. The second half-reaction features copper ions (Cu²⁺) accepting two electrons to become solid copper (Cu), which has a standard reduction potential of 0.3394 volts.

In this voltaic cell, the copper electrode acts as the cathode, while the zinc electrode serves as the anode. The standard cell potential (E^°_cell) can be calculated using the formula:

E^°_cell = E^°_cathode - E^°_anode

Substituting the values into the equation gives:

E^°_cell = 0.3394 V - (-0.7621 V)

Since subtracting a negative is equivalent to addition, this simplifies to:

E^°_cell = 0.3394 V + 0.7621 V

Calculating this results in a standard cell potential of:

E^°_cell = 1.1015 V

Thus, the standard cell potential for this voltaic cell is 1.1015 volts, indicating a spontaneous electrochemical reaction under standard conditions.

Standard Cell Potential and Spontaneity

In electrochemistry, understanding the types of electrochemical cells is crucial for predicting the spontaneity of reactions. A standard cell potential greater than 0 indicates a spontaneous reaction. There are two primary types of electrochemical cells: galvanic (or voltaic) cells and electrolytic cells, which operate under different principles.

In a galvanic (voltaic) cell, the cathode is the half-cell compartment with the higher standard reduction potential, while the anode has the lower standard reduction potential. This configuration results in a standard cell potential that is greater than 0, confirming that galvanic cells are spontaneous electrochemical cells. The relationship can be expressed as:

Standard Cell Potential (E_cell) = E_cathode - E_anode

Conversely, in an electrolytic cell, the roles of the cathode and anode are reversed. Here, the cathode has the lower standard reduction potential, and the anode has the higher standard reduction potential. Consequently, the standard cell potential in electrolytic cells is less than 0, indicating that these cells require an external energy source to drive the non-spontaneous reaction.

Recognizing the type of electrochemical cell is essential for determining the expected standard cell potential. This understanding is key to solving problems related to electrochemical reactions and predicting their behavior in various applications.

Standard Cell Potential of a Redox Reaction Example

In a redox reaction involving cerium solid and aluminum ions, the process of determining the standard cell potential is essential for understanding the electrochemical behavior of the system. The reaction can be summarized as cerium solid plus aluminum ion producing aluminum solid plus cerium in aqueous form. To find the standard cell potential, we first identify which species is oxidized and which is reduced. This is crucial because the cathode is where reduction occurs, while the anode is where oxidation takes place.

In this case, cerium solid is oxidized as its oxidation state increases from 0 to +3, indicating it loses electrons. Therefore, cerium acts as the anode. Conversely, aluminum ions are reduced as their oxidation state decreases from +3 to 0, meaning they gain electrons and function as the cathode.

To calculate the standard cell potential, we use the formula for standard cell potential:

$$E^\circ_{\text{cell}} = E^\circ_{\text{cathode}} - E^\circ_{\text{anode}}$$

Substituting the given values, we have:

$$E^\circ_{\text{cell}} = -1.677 \, \text{V} - (-2.336 \, \text{V})$$

This simplifies to:

$$E^\circ_{\text{cell}} = -1.677 \, \text{V} + 2.336 \, \text{V} = 0.659 \, \text{V}$$

Thus, the standard cell potential for this redox reaction is 0.659 volts, indicating a spontaneous reaction under standard conditions.

Calculate the standard cell potential of an electrolytic cell when given the following half reactions. 
Standard Reduction Potentials
Fe³⁺ (aq) + e ^– →  Fe²⁺ (aq)        E°_red = + 0.769 V
Li⁺ (aq) + e ^– →  Li (s)                  E°_red = – 3.04 V

• A. –2.271 V
• B. –1.551 V
• C. –3.060 V
• D. –3.809 V

Answer: (D)

Use the standard half-cell potentials listed below to calculate the standard cell potential for the following reaction occurring in an electrochemical cell at 25°C.  
3 Cl_2­ (g) + 2 Fe (s)  →  6 Cl ^– (aq) + 2 Fe³⁺ (aq)
Standard Reduction Potentials
Cl₂ (g) + 2 e^– →  2 Cl ^– (aq)                      E°_red = + 1.396 V
Fe³⁺ (aq) + 3 e^– →  Fe (s)                         E°_red = – 0.040 V

• A. 1.024 V
• B. 1.436 V
• C. 1.356 V
• D. 0.999 V

Answer: (B)

Predict whether the following reaction will occur as written based on the calculated E^ºcell. 
Ag⁺ (aq) + Au (s)  →  Ag (s) + Au³⁺ (aq)
Standard Reduction Potentials
Ag⁺(aq) + e^– →  Ag (s)                         E°_red = + 0.80 V
Au³⁺ (aq) + 3 e^– →  Au (s)                    E°_red = + 1.50 V

• A. +0.70 V
• B. +2.30 V
• C. -0.70 V
• D. -2.30 V

Answer: (C)

Here’s what students ask on this topic:

How do you calculate standard cell potential?

To calculate the standard cell potential, you need to use the standard reduction potentials of the half-reactions occurring at the cathode and anode in an electrochemical cell. Here's how you do it:

1. Write down the half-reactions for the cathode and anode. Identify which substances are being reduced and which are being oxidized.
2. Look up the standard reduction potentials (E^°) for each half-reaction in a table of standard electrode potentials. These values are typically given in volts and are measured under standard conditions (1 M concentration, 1 atm pressure, and 25°C).
3. Assign the reduction potential to the cathode (since reduction occurs at the cathode) and the oxidation potential to the anode. Remember that the oxidation potential is the negative of the standard reduction potential for the anode reaction.
4. Calculate the standard cell potential (E^°_cell) by subtracting the anode potential from the cathode potential:

E^°_cell = E^°_cathode - E^°_anode

The result is the electromotive force (emf) of the cell under standard conditions, and it tells you the voltage that the cell can produce. If the value is positive, the cell can do work spontaneously. If it's negative, the cell reaction is non-spontaneous under standard conditions.

What is the standard cell potential?

The standard cell potential, also known as the standard electromotive force (emf), is a measure of the voltage or electrical potential difference between two half-cells in an electrochemical cell when operating under standard conditions. These standard conditions include all solutes at a concentration of 1 M, a pressure of 1 atmosphere for any gases involved, and a temperature of 25°C (298 K).

The standard cell potential is determined by the intrinsic properties of the materials involved in the half-reactions, and it gives an indication of the cell's ability to produce an electric current when no external current is present. It is calculated by taking the difference between the standard reduction potentials of the cathode and the anode:

$E^{°}{\mathrm{cell}}_{}=E^{°}{\mathrm{cathode}}_{}-E^{°}{\mathrm{anode}}_{}$

A positive standard cell potential indicates a spontaneous reaction, while a negative value suggests a non-spontaneous reaction under standard conditions. Standard cell potentials are tabulated for many reactions and can be used to predict the direction of electron flow and the feasibility of chemical processes.

What happens to the standard cell potential of a battery when the temperature increases?

The standard cell potential, also known as the electromotive force (EMF) of a battery, is influenced by temperature changes. As temperature increases, the standard cell potential can either increase or decrease depending on the nature of the chemical reactions within the battery.

For most batteries, the reactions are exothermic, meaning they release heat. According to the Nernst equation, which relates the cell potential to temperature, an increase in temperature will typically cause the cell potential to decrease for exothermic reactions. This is because the increased thermal energy tends to make the products of the chemical reaction more thermodynamically favored, thus reducing the voltage the battery can produce.

However, if the battery operates based on an endothermic reaction, which absorbs heat, an increase in temperature could lead to an increase in cell potential. This is less common in practical batteries but can occur in certain types of electrochemical cells.

It's important to note that extreme temperatures can damage the battery, reduce its lifespan, or affect its performance in other ways, regardless of the effect on cell potential.