nsider the following electochemical cell.
Pt | Cr3+ (2.7010-4 M), Cr2+ (0.500 M) || Pb2+ (0.0710 M) | Pb
Calculate the voltage of the cell, Ecell, including the sign.
To calculate the voltage of the electrochemical cell, Ecell, you need to use the Nernst equation, which relates the concentrations of the reactants and products to the cell potential.
The Nernst equation is as follows:
Ecell = E°cell - (0.0592 V / n) * log(Q)
Where:
- E°cell is the standard cell potential, which is a tabulated value.
- n is the number of electrons transferred in the balanced equation.
- Q is the reaction quotient, which is calculated from the concentrations of the reactants and products.
In this case, we need to determine the Ecell for the given electrochemical cell. Let's break down the given information:
Pt | Cr3+ (2.7010^-4 M), Cr2+ (0.500 M) || Pb2+ (0.0710 M) | Pb
From this cell diagram, we can infer the following balanced equation:
Cr3+ + 3e- → Cr2+
Pb2+ + 2e- → Pb
Since we have two separate half-cells, we need to calculate the cell potential for each half-cell and then subtract them.
For the Cr half-cell, we can use the Nernst equation to calculate the potential (E°Cr = 0 V):
Ecell(Cr) = E°Cr - (0.0592 V / 3) * log(Cr2+ / Cr3+)
Ecell(Cr) = 0 V - (0.0592 V / 3) * log(0.500 M / 2.7010^-4 M)
Similarly, for the Pb half-cell, we can use the Nernst equation to calculate the potential (E°Pb = -0.126 V):
Ecell(Pb) = E°Pb - (0.0592 V / 2) * log(Pb2+ / Pb)
Ecell(Pb) = -0.126 V - (0.0592 V / 2) * log(0.0710 M / 1)
Finally, the overall Ecell can be calculated by subtracting the potential of the anode (Cr) from the potential of the cathode (Pb):
Ecell = Ecell(Pb) - Ecell(Cr)
By substituting the values calculated above, you can determine the voltage of the electrochemical cell, Ecell, including the sign.