Claculate the voltage of the following cell at 25 Degress Celcius.
2Ag (aq) (0.010M) + Cu(s) -> Cu^2(aq)(0.1M) +2Ag(s)
E Ag = EoAg -(0.0592/1)*log(1/0.01) = ?
E Cu = EoCu -(0.0592/2)*log(1/0.1) = ? then change the sign.
Add the two final values for Ecell.
To calculate the voltage of the cell, we can use the Nernst equation, which relates the cell potential to the concentrations of the species involved in the reaction. The Nernst equation is as follows:
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 equation
- f is the Faraday constant (96,485 C/mol)
- ln(Q) is the natural logarithm of the reaction quotient Q
First, we need to determine the standard cell potential (E°cell) for the given reaction. You can find the standard cell potential values in a standard reduction potentials table.
The half-reactions involved in this cell are:
Cu^2+(aq) + 2e- -> Cu(s) E° = +0.34 V (reduction half-reaction)
Ag+(aq) + e- -> Ag(s) E° = +0.80 V (reduction half-reaction)
Since Cu^2+ has the lower reduction potential, it will be the reduction half-reaction. We need to flip the Cu^2+ reduction reaction and multiply it by 2 to balance the equation, giving:
Cu(s) -> Cu^2+(aq) + 2e- E° = -0.34 V
Now we can calculate the standard cell potential (E°cell) using the standard reduction potentials of the half-reactions:
E°cell = E°reduction - E°oxidation
E°cell = (+0.80 V) - (-0.34 V)
E°cell = +1.14 V
Next, let's calculate the reaction quotient Q. The reaction quotient can be calculated using the concentrations of the species involved. In this case, Q is given by:
Q = [Cu^2+(aq)] / [Ag+(aq)]^2
Given the concentrations: [Cu^2+(aq)] = 0.1 M and [Ag+(aq)] = 0.010 M, we can plug these values into the equation to find Q:
Q = (0.1) / (0.010)^2
Q = 100
Now we have all the necessary values to calculate the cell potential (Ecell) at the given temperature (25 degrees Celsius = 298 Kelvin). Using the Nernst equation:
Ecell = E°cell - (RT / nf) * ln(Q)
Ecell = 1.14 V - ((8.314 J/(mol·K)) * (298 K) / (2 * (96,485 C/mol)) * ln(100)
Ecell = 1.14 V - (0.0257 V) * ln(100)
Ecell = 1.14 V - (0.0257 V) * 4.605
Ecell = 1.14 V - 0.1181 V
Ecell ≈ 1.022 V
Therefore, the voltage of the given cell at 25 degrees Celsius is approximately 1.022 volts.