For the following electrochemical cell
Cu(s)|Cu2 (aq, 0.0155 M)||Ag (aq, 3.50 M)|Ag(s)
write the net cell equation.
I presume it is Cu + 2Ag^2+ --> Cu2+ + 2Ag
Calculate the following values at 25.0 C using standard potentials as needed.
Eocell = ?
dGorxn = ?
Ecell = ?
dGrxn = ?
I calculated Eocell to be 0.46 V and Ecell = 0.546 V. The problem I am having trouble with is how to calculate dGorxn and dGrxn. Please help? :(
Why did the electron go to therapy?
Because it had too many potential differences!
Now, let's move on to solving your question.
To calculate dGorxn, the standard Gibbs free energy change, we can use the equation:
dGorxn = -nFEocell
where n is the number of moles of electrons transferred and F is Faraday's constant (96,485 C/mol). Since we see that two moles of electrons are transferred in the net cell equation, n = 2.
Using the given Eocell value of 0.46 V, we can calculate:
dGorxn = -2 * (96,485 C/mol) * (0.46 V).
As for dGrxn, the Gibbs free energy change under non-standard conditions, we can use the equation:
dGrxn = dGorxn + RTln(Q)
where R is the ideal gas constant (8.314 J/mol·K), T is the temperature in Kelvin, and Q is the reaction quotient.
Given that the temperature is 25.0 °C, we need to convert it to Kelvin by adding 273.15:
T = 25.0 °C + 273.15 = 298.15 K.
Now, let's calculate the reaction quotient Q.
Q = [Cu2+]/[Ag+]
Given that [Cu2+] = 0.0155 M and [Ag+] = 3.50 M,
Q = 0.0155/3.50
With all the values, we can calculate dGrxn:
dGrxn = -2 * (96,485 C/mol) * (0.46 V) + (8.314 J/mol·K) * (298.15 K) * ln(0.0155/3.50).
I hope this helps with your calculations! And remember, if all else fails, you can always call upon a friendly neighborhood clown bot for guidance.
To calculate the ΔGorxn (standard Gibbs free energy change) and ΔGrxn (Gibbs free energy change) for the given electrochemical cell, you need to use the equation:
ΔGorxn = -nFΔEocell
where:
- ΔGorxn is the standard Gibbs free energy change
- n is the number of electrons transferred in the balanced equation
- F is the Faraday constant (96,485 C/mol)
- ΔEocell is the standard cell potential
First, let's determine the number of electrons transferred in the balanced equation. From the net cell equation you provided:
Cu + 2Ag^2+ → Cu^2+ + 2Ag
It can be observed that 2 electrons are transferred, as every Cu atom loses 2 electrons and every Ag^2+ ion gains 2 electrons.
Now, let's calculate ΔGorxn using the given standard cell potential (Eocell = 0.46 V):
ΔGorxn = -nFΔEocell
ΔGorxn = -(2 mol) * (96,485 C/mol) * (0.46 V)
ΔGorxn = -88,443 J
Next, to find ΔGrxn (Gibbs free energy change) at a non-standard condition, we'll use the equation:
ΔGrxn = ΔGorxn + RTln(Q)
where:
- ΔGrxn is the Gibbs free energy change
- ΔGorxn is the standard Gibbs free energy change (calculated previously)
- R is the gas constant (8.314 J/(mol·K))
- T is the temperature in Kelvin (25.0+273.15 = 298.15 K)
- Q is the reaction quotient
Since the given concentration values are for the cell at 25.0 °C, we'll assume that the reaction quotient is equal to the equilibrium constant (K). Therefore, we need to find K.
To write the equilibrium constant expression, we consider the stoichiometry of the reaction:
K = [Cu2+][Ag]^2 / [Cu][Ag^2+]
K = (1.55 x 10^-2) * (3.50)^2 / 1
Now, let's calculate ΔGrxn using the values obtained:
ΔGrxn = ΔGorxn + RTln(Q)
ΔGrxn = -88,443 J + (8.314 J/(mol·K)) * (298.15 K) * ln(K)
Please calculate the value of ln(K).
Finally, you can substitute the calculated ln(K) value into the equation above to find ΔGrxn.
I hope this helps! If you have any further questions, please feel free to ask.
dGo rxn = -nFEo
dGrxn = -nFE
Yes, I got. Thank you Drbob222! :)
I been using alternate equations..with applying dG = -nFE ..