Final answer:
To calculate the Ecell for a concentration cell with ion charge of 2 and concentrations of 0.008 M and 2.075 M, we use the Nernst equation with n = 2. The standard Ecell is 0 V, and the reaction quotient Q is the ratio of concentrated to dilute ion concentrations. Substituting values into the Nernst equation yields the predicted Ecell.
Step-by-step explanation:
To predict the Ecell using the Nernst equation for a concentration cell where the metal ion has a charge of 2, and the solution concentrations are 0.008 M (dilute solution) and 2.075 M (concentrated solution), we follow these steps:
- Recognize that the number of electrons transferred in the cell reaction (n) is 2.
- Since the standard Ecell for a concentration cell is 0 V, we only need the Nernst equation to calculate the non-standard conditions.
The Nernst equation at 25°C (298 K) for a concentration cell is given by:
E = E° - (RT/nF) × ln(Q)
Where:
- E° is the standard electrode 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
- F is Faraday's constant (96485 C/mol)
- Q is the reaction quotient
For a concentration cell Q is the ratio of the concentrations, hence:
Q = [concentrated]/[dilute] = 2.075/0.008
Plugging these values into the Nernst equation:
E = 0 - (RT/2F) × ln(2.075/0.008)
By calculating the above formula we obtain the predicted Ecell for this concentration cell.