Consider the standard cell at 25C based on the following half-reactions. Pb^2+ + 2e^- --> Pb E=-0.13V Zn^2+ + 2e^- --> Zn E=-0.76V To the standard cell, OH-, is added to the zinc compartment causing precipitation of Zn(OH)2. After precipitation is complete, the concentration of the OH- is 0.10M and the measured cell potential is 1.05V. calculate the Ksp value for Zn(OH)2(s) Zn(OH)2-> Zn^2+(aq) + OH-(aq) Ksp=?
To calculate the Ksp value for Zn(OH)2(s), we need to use the Nernst equation. The Nernst equation relates the measured cell potential (Ecell) to the standard cell potential (E°cell), the concentration of the reactants, and the Faraday constant.
The Nernst equation is as follows:
Ecell = E°cell - (RT/nF) * ln(Q)
Where:
- Ecell is the measured cell potential (1.05V in this case)
- E°cell is the standard cell potential (-0.63V in this case, which is the difference between the standard reduction potentials for the half-reactions)
- R is the ideal gas constant (8.314 J/(mol·K))
- T is the temperature in Kelvin (25°C is 298K)
- n is the number of moles of electrons transferred in the balanced equation (2 electrons are transferred in this case)
- F is Faraday's constant (96485 C/mol)
- Q is the reaction quotient, which is the ratio of activities of the products to reactants.
The balanced equation for the precipitation reaction is:
Zn(OH)2 -> Zn^2+ + 2OH-
Since this is a solid, the concentration of Zn(OH)2(s) does not appear in the reaction quotient Q. Therefore, we only consider the concentrations of the dissolved species, Zn^2+ and OH-.
The concentration of OH- is given as 0.10M.
Now, let's calculate the reaction quotient Q:
Q = [Zn^2+][OH-]^2
Since Zn(OH)2 is a strong base and fully ionizes, the concentration of OH- is the same as the concentration of Zn^2+ (0.10M).
Q = (0.10)(0.10)^2 = 0.001
Now, plug the values into the Nernst equation and solve for Ksp:
1.05 = -0.63 - (8.314 * 298 / (2 * 96485)) * ln(0.001)
Simplifying the equation:
1.05 = -0.63 + (0.0257) * ln(0.001)
Rearrange the equation to solve for ln(0.001):
ln(0.001) = (1.05 + 0.63) / 0.0257
Using a calculator, evaluate the right-hand side:
ln(0.001) ≈ 8.376
Now, substitute the value of ln(0.001) back into the equation:
1.05 = -0.63 + (0.0257) * 8.376
Simplify:
1.05 = -0.63 + 0.215
Combine like terms:
1.05 = -0.415
This equation is not valid since the left side is greater than the right side. Confirm any errors in calculations and double-check the values and units you provided.