How did the change in concentration of the copper ions affect the cell potential? Is this change in agreement (qualitatively) with that which would be predicted by LeChatelier's Principle? explain.
My crystal ball is a little fuzzy tonight. What did you do? What was the initial concentration? What was the new concentration? What was the other electrode? Tell us what you did?
To understand the effect of the change in concentration of copper ions on the cell potential, we need to consider the Nernst equation. The Nernst equation relates the cell potential to the concentrations of the reactants and products involved in the electrochemical reaction.
The Nernst equation for a half-cell reaction can be written as follows:
E = E° - (RT/nF) * ln(Q)
Where:
- E is the cell potential under non-standard conditions
- E° is the standard cell potential
- R is the gas constant (8.314 J/(mol·K))
- T is the temperature in Kelvin
- n is the number of moles of electrons exchanged in the reaction
- F is Faraday's constant (96,485 C/mol)
- Q is the reaction quotient, calculated using the concentrations of the reactants and products
In this case, we are interested in the change in concentration of copper ions. By increasing or decreasing the concentration of copper ions, the value of Q in the Nernst equation will change.
According to Le Chatelier's principle, when a system at equilibrium is subjected to a stress, the system will adjust to minimize the effect of the stress and restore equilibrium. The stress in this case can be the change in concentration.
If the concentration of copper ions increases, the reaction quotient Q increases in the Nernst equation. As the natural logarithm of Q is a positive value, this leads to a decrease in the cell potential (E) compared to its standard potential (E°).
Conversely, if the concentration of copper ions decreases, Q decreases in the Nernst equation, leading to an increase in the cell potential compared to its standard potential.
Therefore, the change in concentration of copper ions affects the cell potential in accordance with Le Chatelier's principle. When concentration is increased, the cell potential decreases, and when concentration is decreased, the cell potential increases.
To understand how the change in concentration of copper ions affects cell potential, we need to consider the Nernst equation. The Nernst equation relates the cell potential (E cell) of an electrochemical cell to the concentrations of the reactants.
The Nernst equation is as follows:
E cell = E° cell - (RT/nF) * ln(Q)
Where:
- E° cell is the standard cell potential
- R is the gas constant (8.314 J/K·mol)
- T is the temperature in Kelvin
- n is the number of moles of electrons transferred in the balanced chemical equation of the reaction
- F is the Faraday constant (96,485 C/mol)
- Q is the reaction quotient, which is the ratio of the concentrations of the products to the concentrations of the reactants raised to their stoichiometric coefficients.
When the concentration of copper ions changes, it affects the value of Q in the Nernst equation. As Q changes, the natural logarithm term ln(Q) also changes, consequently affecting the overall value of E cell.
According to LeChatelier's Principle, when a system at equilibrium is subjected to a stress, it will shift to counteract the stress and restore equilibrium. In the case of an electrochemical cell, a change in concentration is a stress to the system.
If the concentration of copper ions increases, Q will increase. The Nernst equation tells us that an increase in Q (ln(Q)) will result in a decrease in E cell. Therefore, the cell potential will decrease as the concentration of copper ions increases.
Conversely, if the concentration of copper ions decreases, Q will decrease, and according to the Nernst equation, the cell potential will increase.
So, the change in concentration of copper ions does indeed affect the cell potential, and this change is in qualitative agreement with LeChatelier's Principle. The cell potential will shift in the direction that counters the stress applied to the system, in this case, a change in concentration.