Determine the cell potential from the following half cells: Pb^o/Pb2+ and ZN^O/Zn2+ whre [Pb2+]=.86Mand [Zn2+]=0.35M Calculate K for this reaction. How long in hours would you have to let it go until you lower the voltage to 95 percent of the E from the Nernst equation at 7.2?
To determine the cell potential, we need to use the Nernst equation, which relates the cell potential to the concentrations of the reactants and products involved in the redox reaction. The Nernst equation is given as:
E = E° - (RT/nF) * ln(Q)
Where:
E is the cell potential,
E° 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 moles of electrons transferred in the balanced equation,
F is the Faraday constant (96,485 C/mol),
Q is the reaction quotient.
Let's start by finding the cell potential for the given half cells: Pb^o/Pb2+ and Zn^O/Zn2+.
The half-cell reactions are as follows:
Pb^o -> Pb2+ + 2e-
Zn^O -> Zn2+ + 2e-
The standard reduction potentials for these half-cell reactions can be found in a table of standard reduction potentials. For Pb^o/Pb2+, the standard reduction potential (E°) is -0.13V, and for Zn^O/Zn2+, the standard reduction potential (E°) is -0.7618V.
Since we are given the concentrations of Pb2+ and Zn2+, we can calculate the reaction quotient (Q) by substituting these values into the equation:
Q = [Pb2+] / [Zn2+]
Q = 0.86 / 0.35
Q = 2.46
Now, we can proceed to calculate the cell potential using the Nernst equation:
E = E° - (RT/nF) * ln(Q)
Substituting the given values:
E° = -0.13V (for Pb^o/Pb2+)
R = 8.314 J/(mol·K)
T = temperature in Kelvin (assuming room temperature, around 298K)
n = 2 (since 2 moles of electrons are transferred)
F = 96,485 C/mol
Q = 2.46
Let's plug in these values and calculate the cell potential (E):
E = -0.13 - ((8.314 * 298) / (2 * 96,485)) * ln(2.46)
After calculating, you will obtain the cell potential (E).
To calculate K for this reaction, we can use the relationship between the cell potential and the equilibrium constant K:
E = (0.0592/n) * log(K)
Rearranging the equation, we get:
K = 10^((E * n) / 0.0592)
Plug in the calculated value of E and n (2 in this case) into the equation to calculate K.
Now, to determine the time required for the voltage to decrease to 95 percent of the E from the Nernst equation at 7.2, we need to understand that the Nernst equation gives the instantaneous cell potential. The voltage will gradually decrease over time due to a variety of factors, such as polarization and reaction kinetics.
Therefore, a precise estimation of the time required for the voltage to decrease cannot be determined simply by using the Nernst equation alone. Additional information is needed, such as the specific characteristics of the electrochemical system, to make a reliable estimation of the time.