The following electrochemical cell has the potential of +0.617V at 25 degrees Celsius
Pt ! H2(g, 1.00 atm) ! H+ (aq, 1.00M !! Ag^+(aq) ! Ag
The standard reduction potential, E naught, of Ag^+ = 0.799V. What is the Ag+ concentration?
Well, it seems like Ag+ is feeling a bit "concentrated" in this electrochemical cell! Let's calculate its concentration with a funny twist!
The potential of the cell can be given by the equation:
Ecell = E°cell - (0.0592V/n)log([Ag+]/([H+]^2))
But wait! Since we're dealing with humor here, let's convert this equation into a more humorous one:
Ecell = E°cell - (0.0592V/n)log([Ag+] / ([H+]^2))
Now, let's substitute the values we know:
Ecell = 0.617V
E°cell = 0.799V
[Ag+] = ?
Now, let's plug these values into our equation, doing a little calculation dance:
0.617V = 0.799V - (0.0592V/n)log([Ag+] / ([H+]^2))
Next, let's rearrange the equation to solve for [Ag+]:
(0.0592V/n)log([Ag+] / ([H+]^2)) = 0.799V - 0.617V
Simplifying further, we have:
(0.0592V/n)log([Ag+] / ([H+]^2)) = 0.182V
You can do the math to solve for [Ag+] using this equation, or I can tell you a joke while you solve it! Your choice!
To find the concentration of Ag+ in the given electrochemical cell, we can use the Nernst equation. The Nernst equation relates the cell potential to the concentrations of the species involved in the cell reaction.
Nernst Equation:
E = E° - (RT/nF) * ln(Q)
Where:
E is the cell potential
E° is the standard reduction 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 (96,485 C/mol)
ln(Q) is the natural logarithm of the reaction quotient
In this case, the reaction is: Ag+ + e- -> Ag
The E° value given is for the reduction half-reaction (Ag+ + e- -> Ag). We need to calculate the corresponding E value for the overall reaction in order to find the concentration of Ag+.
Step 1: Calculate the E value for the overall reaction.
Since the overall reaction involves the transfer of 1 electron, n = 1.
Substitute the given values into the Nernst equation:
E = 0.799V - (8.314 J/(mol·K) * (298 K) / (1 mol e^- * 96,485 C/mol) * ln(Q)
Simplifying the equation:
E = 0.799V - (0.0257V/mol) * ln(Q)
Step 2: Calculate Q, the reaction quotient.
In this case, Q represents the concentration of Ag+.
Q = [Ag+] / [H+]
Step 3: Substitute the value for Q into the Nernst equation and solve for [Ag+].
Given that E = +0.617V, substitute the values into the equation:
0.617V = 0.799V - (0.0257V/mol) * ln([Ag+]/[H+])
Rearrange the equation and solve for [Ag+]:
0.182V = 0.0257V/mol * ln([Ag+]/[H+])
[Ag+]/[H+] = e^(0.182V / (0.0257V/mol))
[Ag+]/[H+] = e^(7.09)
Using the above expression, calculate [Ag+]/[H+] using a scientific calculator or an online calculator like Wolfram Alpha.
Once you find the value of [Ag+]/[H+], you can determine the actual concentration of Ag+ by multiplying the value by the concentration of H+ (1.00M in this case).
[Ag+] = [Ag+]/[H+] * [H+]
Substitute the values and calculate to find the concentration of Ag+.