A voltaic cell consists of a Pb/Pb2+ half-cell and a Cu/Cu2+ half-cell at 25 C. The initial concentrations of Pb+2 and Cu+2 are 0.0500 M and 1.50 M, respectively.
A. What is the initial cell potential?
B. What is the cell potential when the concentration of Cu+2 has fallen to 0.200 M?
C. What are the concentrations of Pb+2 and Cu+2 when the cell potential falls to 0.35 V?
I answered A and B. For A I got: 0.43 V and for B I got 0.46 V. I cannot figure out part C though. I tried 0.35V=O.47V-((0.0592/2)*log(0.0500+X/1.50-X))but the answer doesn't seem right. I found X to equal 1. When I plug it all back in, it doesn't work though. Is my equation wrong? So confused...
To find the concentrations of Pb+2 and Cu+2 when the cell potential falls to 0.35 V, you need to use the Nernst equation. The Nernst equation relates the cell potential to the concentrations of the species involved in the half-cell reactions.
The general form of the Nernst equation is:
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 electrons transferred in the balanced equation.
- F is the Faraday constant (96485 C/mol).
- Q is the reaction quotient, which is the ratio of product concentrations to reactant concentrations, each raised to the power of their stoichiometric coefficients.
In this case, we can assume that the stoichiometry of the reactions is such that the number of electrons transferred (n) is 2 for both the Pb/Pb2+ and Cu/Cu2+ half-cell reactions.
Let's solve for the concentrations of Pb+2 and Cu+2 when the cell potential falls to 0.35 V:
0.35 V = 0.47 V - [(0.0592 V/2) * log((0.0500 + [Pb+2]) / (1.50 - [Pb+2]))]
Here, [Pb+2] represents the concentration of Pb+2, which we need to determine.
To solve for [Pb+2], we need to rearrange the Nernst equation and solve the equation iteratively. We can start by assuming an initial value for [Pb+2], plug it into the equation, and then refine our estimation by re-plugging the new [Pb+2] value iteratively until we approximate the desired cell potential.
You mentioned that you tried solving the equation and found [Pb+2] to be equal to 1. However, your result did not work when you plugged it back into the equation. This suggests that your initial estimation of [Pb+2] might have been incorrect.
I recommend using a numerical method such as iteration (e.g., the Newton-Raphson method) to solve the equation iteratively. This method involves repeatedly solving the equation with an initial guess and updating the guess until the desired cell potential is obtained.
Here's a general approach to solving this problem numerically:
1. Start with an initial guess for [Pb+2].
2. Plug the initial guess into the Nernst equation.
3. Calculate the resulting cell potential.
4. Compare the resulting cell potential with the desired cell potential (0.35 V).
5. If the resulting cell potential is higher than 0.35 V, decrease the initial guess for [Pb+2]. If it is lower, increase the initial guess.
6. Repeat steps 2-5 until the resulting cell potential is close enough to 0.35 V.