Cu(s) | Cu2+(0.10M) || H+ (0.20M), MnO4-(0.35M), Mn2+(0.15M) | C(s)
Determine the cell potential.
ii. Is this reaction spontaneous? Prove using ∆G.
iii. The equilibrium constant can also be found from Standard Cell Potentials. Eventually the cell will reach equilibrium.
In layman’s terms we say, “The battery is dead”. This means that ∆G = 0. This also means that Ecell = 0.00V. Substituting this value into the Nernst equation and then changing Q to K, find the equilibrium constant for this reaction.
To determine the cell potential, we can use the Nernst equation:
Ecell = E°cell - (0.0592/n) * log(Q)
First, let's write the balanced equation for the reaction happening in the cell:
Cu(s) + 2H+ (aq) + MnO4- (aq) → Cu2+ (aq) + Mn2+ (aq) + H2O(l)
The cell potential can be calculated by finding the difference between the standard reduction potentials of the half-reactions involved.
The half-reactions are:
1. Cu2+ (aq) + 2e- → Cu(s) (reduction)
2. MnO4- (aq) + 8H+ (aq) + 5e- → Mn2+ (aq) + 4H2O(l) (reduction)
We can lookup the standard reduction potentials (E°) for these half-reactions:
E°(Cu2+/Cu) = +0.34V
E°(MnO4-/Mn2+) = +1.51V
From the given equation, it can be observed that:
For the Cu half-reaction, we have n = 2 (equivalent to the number of electrons transferred).
For the MnO4- half-reaction, we have n = 5.
Now, let's calculate the cell potential:
Ecell = E°cell - (0.0592/n) * log(Q)
For the cell potential (Ecell), we will substitute the values of E°cell, n, and Q.
E°cell = E°(Cu2+/Cu) + E°(MnO4-/Mn2+)
= 0.34V + 1.51V
= 1.85V
We also need to calculate Q, which is the reaction quotient. Q is the ratio of the concentrations of products to reactants, with each concentration raised to the power of its stoichiometric coefficient.
Q = [Cu2+] / [H+]^2 * [Mn2+] / [MnO4-]^5
Substituting the given concentrations:
Q = (0.10M) / (0.20M)^2 * (0.15M) / (0.35M)^5
Calculate Q and substitute the value of E°cell and Q into the Nernst equation to solve for Ecell.
Once you have calculated Ecell, you can move on to the next steps.
To determine the cell potential, we need to use the Nernst equation. The Nernst equation is as follows:
Ecell = E°cell - (0.0592/n) * log(Q),
where Ecell is the cell potential, E°cell is the standard cell potential, n is the number of electrons transferred in the balanced equation, and Q is the reaction quotient.
Given the half-reactions:
Cu(s) → Cu2+(aq) + 2e- (reduction)
MnO4-(aq) + 8H+(aq) + 5e- → Mn2+(aq) + 4H2O(l) (oxidation)
we can see that 5 electrons are transferred in the overall balanced equation when combining these half-reactions.
The standard cell potential (E°cell) can be found using standard reduction potentials. The table of standard reduction potentials shows that the reduction potential for the Cu2+(aq) + 2e- → Cu(s) half-reaction is +0.34V. The reduction potential for the MnO4-(aq) + 8H+(aq) + 5e- → Mn2+(aq) + 4H2O(l) half-reaction is +1.51V.
To calculate the reaction quotient (Q), we need to determine the concentrations of each species in the cell.
For the given half-cell reactions, the concentrations are:
[Cu2+] = 0.10M
[H+] = 0.20M
[MnO4-] = 0.35M
[Mn2+] = 0.15M
Using the Nernst equation:
Ecell = E°cell - (0.0592/n) * log(Q)
We can substitute in the given values:
Ecell = (+1.51V) - (0.0592/5) * log((0.10M)/(0.20M)) * ((0.35M)/(0.15M))5
After calculating this expression, you will determine the cell potential (Ecell).
To determine if the reaction is spontaneous or not, we can use the relationship between Gibbs free energy change (∆G) and the cell potential (Ecell):
∆G = -nF * Ecell
where ∆G is the Gibbs free energy change, n is the number of electrons transferred, and F is the Faraday's constant (96,485 C/mol).
If ∆G is negative, the reaction is spontaneous. If ∆G is positive, the reaction is non-spontaneous. If ∆G is zero, the reaction is at equilibrium.
To find the equilibrium constant (K), we can use the relationship between ∆G and K:
∆G = -RT * ln(K)
where R is the gas constant (8.314 J/(mol·K)) and T is the temperature in Kelvin.
Setting ∆G = 0, we can solve for K:
0 = -RT * ln(K)
ln(K) = 0
K = 1
So, the equilibrium constant for the reaction is 1.
I hope this helps! Let me know if you have any more questions.