A student places a zinc electrode in a 0.80 M Zn2+(aq) solution which is connected by an
electrolyte to a 1.30 M Ag+(aq) solution containing a silver electrode. (Note that the solution
concentrations are not standard). Determine the initial voltage of the cell at 298 K. Show your
work. The Nernst equation will help you answer this question.
To determine the initial voltage of the cell, we can use the Nernst equation. The Nernst equation relates the cell potential (Ecell) to the standard cell potential (E°cell), the concentration of species in the half-cells, and the gas constant (R) and temperature (T). The Nernst equation is:
Ecell = E°cell - (RT/nF) * ln(Q)
Where:
Ecell is the cell potential
E°cell 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 transferred in the balanced half-reaction
F is the Faraday constant (96485 C/mol)
ln(Q) is the natural logarithm of the reaction quotient (Q)
In this case, the balanced half-reactions are:
Zn(s) -> Zn2+(aq) + 2e-
Ag+(aq) + e- -> Ag(s)
Since zinc is oxidized and silver is reduced, we can assign n = 2.
The standard cell potential (E°cell) can be found by looking up the reduction potentials for the half-reactions. Using a reference, the standard reduction potentials for the given half-reactions are:
Zn2+(aq) + 2e- -> Zn(s) E° = -0.76 V
Ag+(aq) + e- -> Ag(s) E° = +0.80 V
To calculate Q, we need to determine the concentrations of each species involved. Given that the zinc electrode is placed in a 0.80 M Zn2+ solution and the silver electrode is placed in a 1.30 M Ag+ solution, the concentrations of Zn2+ and Ag+ are 0.80 M and 1.30 M, respectively.
Using the Nernst equation, we can calculate the initial voltage (Ecell):
Ecell = E°cell - (RT/nF) * ln(Q)
Substituting the values:
Ecell = (0.80 V) - [(8.314 J/mol·K) * (298 K) / (2 * 96485 C/mol)] * ln(0.80/1.30)
Calculating this equation will give you the initial voltage of the cell at 298 K.