To calculate the mass of the anode electrode in a concentration cell, we need to use the Nernst equation to relate the cell potential to the concentrations of species involved. The Nernst equation is given by:
E = E° - (RT/nF) * ln(Q)
Where:
- E is the cell potential (0.01231V in this case)
- E° is the standard cell potential (-0.761V in this case)
- R is the gas constant (8.314 J/mol K)
- T is the temperature in Kelvin (303K in this case)
- n is the number of electrons transferred in the balanced half-reaction (2 in this case)
- F is Faraday's constant (96485 C/mol)
- Q is the reaction quotient, which is determined by the concentrations of species involved
First, let's calculate the reaction quotient Q using the concentrations of the Zn(2+) ions:
For the anode half-cell:
[Zn(2+)]anode = 0.101 M
For the cathode half-cell:
[Zn(2+)]cathode = 0.427 M
Since the anode is losing Zn(2+) ions and the cathode is gaining Zn(2+) ions, the reaction quotient Q can be calculated as:
Q = [Zn(2+)]cathode / [Zn(2+)]anode
Q = 0.427 M / 0.101 M
Q = 4.227
Now, we can substitute the values into the Nernst equation:
0.01231V = -0.761V - (8.314 J/mol K / (2 * 96485 C/mol)) * ln(4.227)
Solving this equation will give us the value of ln(4.227), and then we can calculate the mass of the anode electrode.
Please note that in order to calculate the actual mass of the anode electrode, we need to know the molar mass of Zn. Assuming it is 65.38 g/mol, we can proceed with the calculation:
Let's define the mass of the anode electrode as "x".
x / (65.38 g/mol) = (100.0 g) / (0.101 mol/L)
Solving this equation for x will give us the mass of the anode electrode.
Please perform these calculations using a calculator or software capable of handling natural logarithms (ln) to get the final answer.