The standard reduction potential for Cr3+(aq) is
−0.74 V.
The half-reaction for the reduction of Cr3+(aq) is the following.
Cr3+(aq) + 3 e− → Cr(s)
The standard reduction potential for Ni2+(aq) is
−0.26 V.
The half-reaction for the reduction of Ni2+(aq) is the following.
Ni2+(aq) + 2 e− → Ni(s)
Using this information, calculate E⁰cell for the voltaic cell powered by the following spontaneous redox reaction.
3 Ni2+(aq) + 2 Cr(s) → 2 Cr3+(aq) + 3 Ni(s)
3Ni^2+ + 2e ==> 3Ni(s) Eo red = - -0.26
2Cr(s) ==> 2Cr^3+ + 3e Eo ox = +0.74
.................Eocell = Eo red + Eo ox = -0.26+ 0.74 = ?
To calculate the standard cell potential (E°cell) for the given redox reaction, you need to use the standard reduction potentials of the half-reactions and apply the Nernst equation.
The Nernst equation relates the standard cell potential (E°cell) to the concentrations of reactants and products involved in the redox reaction. The Nernst equation is given by:
Ecell = E°cell - (0.0592/n) * log(Q)
Where:
- Ecell is the cell potential (in volts)
- E°cell is the standard cell potential (in volts)
- n is the number of electrons transferred in the balanced redox equation
- Q is the reaction quotient (ratio of the concentrations of products to reactants, raised to their stoichiometric coefficients)
First, we need to determine the standard cell potential (E°cell) using the standard reduction potentials provided.
Given:
Standard reduction potential for Cr3+(aq) = -0.74 V
Standard reduction potential for Ni2+(aq) = -0.26 V
To obtain the standard cell potential, we need to subtract the reduction potential of the anode from the reduction potential of the cathode. In this case, Cr is the anode and Ni is the cathode.
E°cell = E°cathode - E°anode
E°cell = (-0.26 V) - (-0.74 V)
E°cell = 0.48 V
Now we have the standard cell potential (E°cell), and we can proceed to calculate the cell potential (Ecell) using the Nernst equation.
In the given redox reaction:
3 Ni2+(aq) + 2 Cr(s) → 2 Cr3+(aq) + 3 Ni(s)
The number of electrons transferred is 6 (3 for each Ni2+ ion and 2 for each Cr atom).
Using the Nernst equation:
Ecell = E°cell - (0.0592/n) * log(Q)
Where the reaction quotient Q can be calculated as:
Q = [Cr3+]^2 / [Ni2+]^3
Now substitute the values into the Nernst equation:
Ecell = 0.48 V - (0.0592/6) * log([Cr3+]^2 / [Ni2+]^3)
To proceed, you need the concentrations of Cr3+ and Ni2+ ions. If the concentrations are given, substitute these values into the equation and calculate Ecell.
To calculate the standard cell potential (E⁰cell) for the given redox reaction, you can use the Nernst equation:
E⁰cell = E⁰cathode - E⁰anode
Step 1: Identify the cathode and anode half-reactions.
Cathode half-reaction: 3 Ni2+(aq) + 6 e⁻ → 3 Ni(s)
Anode half-reaction: 2 Cr(s) → 2 Cr3+(aq) + 6 e⁻
Step 2: Determine the standard reduction potentials for the cathode and anode half-reactions.
Given standard reduction potentials:
E⁰(Ni2+(aq)/Ni(s)) = -0.26 V
E⁰(Cr3+(aq)/Cr(s)) = -0.74 V
Step 3: Calculate E⁰cell using the Nernst equation.
E⁰cell = E⁰cathode - E⁰anode
E⁰cell = (-0.26 V) - (-0.74 V)
E⁰cell = 0.48 V
Therefore, the standard cell potential (E⁰cell) for the given redox reaction is 0.48 V.