Given these standard reduction potentials at 25 C
1. Cr3+ + e- ===> Cr2+ E1=-0.407 V
2. Cr2+ + 2e- ===> Cr(s) E2=-0.913 V
determine the standard reduction potential at 25C for the half-reaction equation
Cr3+ + 3e- ===> Cr(s)
E=?
When I tried, I got 1.08V and I honesty can't figure out what I did wrong =/
Never mind, it's -.744V I figured it out!
good.
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To determine the standard reduction potential (E) for the half-reaction equation, you can use the given standard reduction potentials for the individual reduction reactions and the Nernst equation.
The Nernst equation relates the standard reduction potential (E), the concentration of reactants/products, the Faraday constant (F), the gas constant (R), and the temperature (T).
The Nernst equation is given by:
E = E° - (RT / nF) * ln(Q)
Where:
E is the standard reduction potential (what we're trying to find)
E° is the standard reduction potential of the reduction half-reaction
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 half-reaction
F is the Faraday constant (96485 C/mol)
Q is the reaction quotient, which is the ratio of concentration of the products to the concentration of the reactants, each raised to their stoichiometric coefficients.
Now, let's go step by step to calculate the standard reduction potential for the given half-reaction:
1. Calculate the reaction quotient (Q):
The half-reaction equation is: Cr3+ + 3e- ===> Cr(s)
Since there are no concentrations given, we'll assume they are all at 1 M. Therefore, Q = [Cr(s)] / [Cr3+]^3 = 1 / [Cr3+]^3
2. Calculate the number of moles of electrons transferred (n):
In the given half-reaction, 3 moles of electrons are transferred.
3. Plug in the values into the Nernst equation:
E = E° - (RT / nF) * ln(Q)
Given values:
E° = ? (what we're trying to find)
R = 8.314 J/(mol*K)
T = 25°C = 298 K
n = 3 (number of moles of electrons transferred)
F = 96485 C/mol
Q = 1 / [Cr3+]^3 (from step 1)
The equation becomes:
E = E° - (8.314 J/(mol*K) * 298 K) / (3 * 96485 C/mol) * ln(1 / [Cr3+]^3)
4. Solve for E:
E = E° - 0.0257 V * ln(1 / [Cr3+]^3)
Now, using the given standard reduction potentials, let's calculate E:
Given potentials:
1. Cr3+ + e- ==> Cr2+ E1 = -0.407 V
2. Cr2+ + 2e- ==> Cr(s) E2 = -0.913 V
By reversing the second reaction, we get:
Cr(s) ==> Cr2+ + 2e- E2(reversed) = +0.913 V
Now we can sum the two reactions to obtain the desired reaction:
Cr3+ + 3e- ==> Cr(s)
The standard reduction potential of the overall reaction is the sum of the individual reactions:
E° = E1 + E2(reversed)
E° = -0.407 V + 0.913 V
E° = 0.506 V
Finally, substituting this value into the Nernst equation calculated earlier:
E = 0.506 V - 0.0257 V * ln(1 / [Cr3+]^3)
By substituting the value of [Cr3+] that you have and calculating this expression, you should obtain the correct standard reduction potential for the given half-reaction.