A voltaic cell utilizes the following reaction and operates at 298K
3Ce{4+}(aq)+Cr(s)--->3Ce{3+}(aq)+Cr{3+}(aq)
{}=Charge
What is the EMF of this cell under standard conditions?
What is emf of cell when [Ce{4+}]=2.1M, [Ce{3+}]=.13M, and [Cr{3+}]=2.0*10^-2
To find the EMF (Electromotive Force) of the voltaic cell under different conditions, we need to use the Nernst equation.
The Nernst equation relates the EMF of an electrochemical cell to the concentrations of the reactants and products involved in the reaction.
The Nernst equation is given by:
Ecell = E°cell - (RT/nF) * ln(Q)
Where:
- Ecell is the cell potential under non-standard conditions.
- E°cell is the cell potential under standard conditions.
- R is the ideal gas constant (8.314 J/(mol·K)).
- T is the temperature in Kelvin.
- n is the number of electrons transferred in the balanced redox equation.
- F is the Faraday constant (96,485 C/mol).
- Q is the reaction quotient, which is the ratio of the concentrations of the products to the concentrations of the reactants, each raised to their stoichiometric coefficients.
Now let's calculate the EMF under each condition:
1) EMF under standard conditions:
Under standard conditions, the reaction quotient Q is equal to 1, as all the concentrations are 1M. Therefore, the Nernst equation simplifies to:
Ecell = E°cell - (RT/nF) * ln(1)
Ecell = E°cell
So the EMF under standard conditions is equal to the cell potential (E°cell).
2) EMF when [Ce{4+}] = 2.1M, [Ce{3+}] = 0.13M, and [Cr{3+}] = 2.0 * 10^-2M:
Using the given concentrations, we can calculate the value of Q and then use the Nernst equation to find the EMF.
Q = [Ce{3+}]^3 * [Cr{3+}]/[Ce{4+}]^3
Substituting the values:
Q = (0.13)^3 * (2.0 * 10^-2)/(2.1)^3
After calculating Q, we can use the Nernst equation as follows:
Ecell = E°cell - (RT/nF) * ln(Q)
Substituting the given values into the equation, we can compute the EMF of the cell under the given conditions.