A Cu/Cu^2+concentration cell has a voltage of 0.22v at 25 C. The concentration of Cu^2+ in one of the half cells is 1.5x10^-3 M. What is the concentrate of Cu^2+ in the other half cell?
I think I will have to use Nernst equation, but I am so stuck! please help.
Thank you so much.
To determine the concentration of Cu^2+ in the other half-cell, we can use the Nernst equation. The Nernst equation relates the voltage of an electrochemical cell to the standard cell potential and the concentrations of the species involved.
The Nernst equation is given as:
E = E° - (RT/nF) * ln(Q)
Where:
E: cell potential (voltage)
E°: standard cell potential
R: gas constant (8.314 J/(mol·K))
T: temperature (in Kelvin)
n: number of moles of electrons transferred in the cell reaction
F: Faraday's constant (96485 C/mol)
ln: natural logarithm
Q: reaction quotient
In this case, we have a concentration cell, so the standard cell potential (E°) is zero since both half-cells involve the same redox reaction.
The given information states that the voltage (E) of the cell is 0.22 V at 25°C. To calculate the concentration of Cu^2+ in the other half-cell, we need to rearrange the Nernst equation and solve for the concentration (Q):
Q = e^((E° - E) * (nF/RT))
Since E° is zero, the equation simplifies to:
Q = e^((-E) * (nF/RT))
Now, we can substitute the known values into the equation:
E = 0.22 V (given)
E° = 0 V (standard cell potential for a concentration cell)
R = 8.314 J/(mol·K) (gas constant)
T = 25°C = 298 K (temperature in Kelvin)
n = 2 (the number of electrons involved in the Cu^2+ + 2e^- -> Cu half-reaction)
F = 96485 C/mol (Faraday's constant)
Plugging these values into the equation and solving for Q will give us the concentration of Cu^2+ in the other half-cell:
Q = e^((-0.22) * (2 * 96485 / (8.314 * 298)))
Calculating Q using these values will give us the concentration of Cu^2+ in the other half-cell.