A galvanic cell has an iron electrode in contact with 0.20 M FeSO4 and a copper electrode in contact with a CuSO4 solution. If the measured cell potential at 25 degrees Celcius is 0.61 V , what is the concentration of Cu2+ in the CuSO4 solution?
Use Nernst.
0.61=0.79-(0.0592/2)*log 0.20/x
-0.18=-0.296*log 0.20/x
6.0810811=log 0.20/x
1205260.93387=0.20/x
x=1.6593917083*10^-7
To determine the concentration of Cu2+ in the CuSO4 solution, we need to use the Nernst equation.
The Nernst equation relates the cell potential (Ecell) to the concentrations of the ions involved in the cell reaction:
Ecell = E°cell - (RT/nF) * ln(Q)
Where:
- Ecell is the measured cell potential (0.61 V in this case)
- E°cell is the standard cell potential
- R is the gas constant (8.314 J/(mol·K))
- T is the temperature in Kelvin (25°C = 298 K)
- n is the number of electrons transferred in the cell reaction (depends on the balanced equation)
- F is the Faraday constant (96485 C/mol)
- Q is the reaction quotient, which is equal to the ratio of concentration of products to the concentration of reactants raised to their stoichiometric coefficients
Since we are given the measured cell potential, we can assume it is at standard conditions. Therefore, E°cell is also 0.61 V.
The balanced equation for the overall cell reaction is:
Fe(s) + Cu2+(aq) → Fe2+(aq) + Cu(s)
In this reaction, 2 electrons are transferred. So, n = 2.
We can substitute the values into the Nernst equation and solve for ln(Q):
0.61 V = 0.61 V - ((8.314 J/(mol·K)) * 298 K) / (2 * (96485 C/mol)) * ln(Q)
Simplifying the equation:
0 = - (8.314 J/(mol·K)) * 298 K / (2 * (96485 C/mol)) * ln(Q)
Rearranging and solving for ln(Q):
ln(Q) = 0
Since ln(Q) = 0, this means that Q = 1.
In the reaction, Fe2+ is being formed and Cu2+ is being reduced. From the balanced equation, we can see that one Cu2+ ion is needed to form one Fe2+ ion.
Therefore, the concentration of Cu2+ in the CuSO4 solution is the same as the concentration of Fe2+ in the FeSO4 solution, which is 0.20 M.
To determine the concentration of Cu2+ in the CuSO4 solution, you need to use the Nernst equation. The Nernst equation relates the cell potential (Ecell) to the concentration of the species involved in the redox reaction.
The Nernst equation is given as:
Ecell = Ecell° - (RT/nF) * ln(Q)
Where:
- Ecell is the measured cell potential.
- Ecell° 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 electrons transferred in the redox reaction.
- F is the Faraday constant (96485 C/mol).
- Q is the reaction quotient, which is the concentration of the products raised to their stoichiometric coefficients divided by the concentration of the reactants raised to their stoichiometric coefficients.
In this case, the reaction occurring in the cell is:
Fe(s) + Cu2+(aq) -> Fe2+(aq) + Cu(s)
The number of electrons transferred (n) is 2, as indicated by the balanced equation.
Now, let's calculate the value of Q, which represents the reaction quotient.
Q = [Fe2+]/[Cu2+]
To determine the concentration of Fe2+, we need to use the relation C1V1 = C2V2, where C1 is the initial concentration of FeSO4 (0.20 M) and V1 is the volume of solution used (which is not given). Assuming the volume is 1 L, C2 can be calculated as follows:
0.20 M * V1 = [Fe2+]
Let's assume V1 = 1 L
0.20 M * 1 L = 0.20 mol
So, the concentration of Fe2+ is 0.20 M.
Now, rearrange the Q equation to solve for [Cu2+]:
Q = [Fe2+]/[Cu2+]
0.20/[Cu2+] = Q
Substituting the given values:
0.20/[Cu2+] = e^(-2 * (0.61 - 0)) (since Ecell° is not given, it is assumed to be 0 for simplicity)
We can simplify and solve for [Cu2+]:
0.20/[Cu2+] = e^-1.22
1/[Cu2+] = e^-1.22 * 0.20
1/[Cu2+] = 0.295
Taking the reciprocal of both sides:
[Cu2+] = 1/0.295
Therefore, the concentration of Cu2+ in the CuSO4 solution is approximately 3.39 M.