Final answer:
To calculate the cell potential using the Nernst equation at 298 K for the given cell, one must use the concentrations of Ag+ and Ni2+ ions, with the known variables of the Nernst equation, to find Q. Then, using E^0 from Appendix E and plugging all values into the equation, E is calculated.
Step-by-step explanation:
Calculating Cell Potentials Using the Nernst Equation
To calculate the cell potential of the galvanic cell involving silver and nickel at 298 K (25°C), we can apply the Nernst equation. The Nernst equation, which accounts for the effects of concentration on cell potential, is given by:
E = E^0 - (RT/nF) * ln(Q)
Where:
- E is the cell potential under non-standard conditions
- E^0 is the standard cell potential
- R is the universal 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 the reaction:
2 Ag+(aq) (0.50 M) + Ni(s) ⇒ 2Ag(s) + Ni2+(aq) (0.20 M),
we see that silver ion is being reduced while nickel solid is being oxidized. The standard cell potential can be found in Appendix E of the textbook. With a value for E^0 and the concentrations of Ag+ and Ni2+, we can calculate Q and plug all values into the Nernst equation to find E.
The reaction quotient Q for the cell reaction is:
Q = [Ni2+]2 / [Ag+]2 = (0.20)2 / (0.50)2
Assuming that the standard cell potential is already calculated or given, E can be determined using the Nernst equation, accounting for the change in free-energy under non-standard conditions (-nFE).