Use the Nernst equation to calculate the iron (II) concentration for the following
iron/copper electrochemical cell when [Cu2+] = 0.012 M and Ecell = 0.750 V at 35°C.
Cu2+ (aq) + Fe (s) --> Cu (s) + Fe2+ (aq)
I presume you meant 25C and not 35. If you meant 35 then replace the 0.0592 below by (RT/2*F)
Ecell = Eocell -(0.0592/2)log Q
You have Ecell.
Eocell = Eo for Cu^2+ + 2e --> Cu
and add to Eo for Fe(s) ==> Fe^2+ + 2e
That leaves Q. Q in this case is
Q = (Fe^2+)/(Cu^2+)
Substitute and go.
Thank you very much, but the problem indeed says 35 degree C. I was wondering if there is a way to calculate the Fe2+ (aq)?
Yes, if you follow my directions above that will calculate Fe^2+. You have Eocell and Ecell which allows you to calculate Q. Then Q has the definition I gave and that has the concentrations in it. Q = (Fe^2+)/(Cu^2+). You know Q and Cu^2+, solve for Fe^2+.
If you need help in evaluating RT/2F note that I omitted the 2.303 to convert log base e to log base 10.
RT/2*F = (2.303)(8.314*308.15)/(2*96,485) = ?.
Ahhhh, now it's all clear! Thank you!
To use the Nernst equation to calculate the concentration of iron (II) ([Fe2+]) in the electrochemical cell, we need to know the standard cell potential, the temperature, and the concentration of copper (II) ions ([Cu2+]).
Given data:
- [Cu2+] = 0.012 M
- Ecell = 0.750 V
- Temperature (T) = 35°C
The Nernst equation relates the cell potential (Ecell) to the standard cell potential (E°cell), the gas constant (R), the temperature (T), and the concentrations of the species involved in the electrochemical reaction.
The Nernst equation is written as:
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 (K)
- n is the number of moles of electrons transferred in the balanced equation
- F is Faraday's constant (96485 C/mol)
- Q is the reaction quotient
From the given balanced equation:
Cu2+ (aq) + Fe (s) --> Cu (s) + Fe2+ (aq)
We can see that n = 2, as two moles of electrons are transferred in the reaction.
Now, let's calculate Q, the reaction quotient. Since the reaction is at equilibrium, Q equals to the equilibrium constant (K) for this reaction. The equilibrium expression is written as:
K = [Cu] / [Fe2+]
Here, [Cu] is the molarity of copper, which is given as 0.012 M.
To find [Fe2+], we rearrange the equilibrium expression as:
[Fe2+] = [Cu] / K
We need to find the value of K for this equilibrium reaction. The standard cell potential (E°cell) can be related to the equilibrium constant (K) using the equation:
E°cell = (0.0592 V / n) * log10(K)
Rearranging this equation, we get:
K = 10^((n * E°cell) / (0.0592 V))
Substituting the given values:
E°cell = 0.750 V
n = 2
K = 10^((2 * 0.750 V) / (0.0592 V))
Calculate K using the above equation.
Once you have the value for K, substitute it back into the expression for [Fe2+] to find the concentration of iron (II) ion ([Fe2+]) in the electrochemical cell at 35°C.