The equilibrium constant for the reaction
Sr(s) + Mg2+(aq) <---> Sr2+(aq) +Mg(s) is 3.69 x 10^17 at 25 C. Calculate Ecell for a cell made up of Sr/Sr2+ and Mg/Mg2+ half cells.
To calculate the cell potential (Ecell) for a cell made up of Sr/Sr2+ and Mg/Mg2+ half-cells, we need to determine the standard reduction potentials of each half-cell reaction and use the Nernst equation.
Let's start by writing the half-cell reactions:
1. Sr(s) -> Sr2+(aq) + 2e- (reduction half-cell)
2. Mg2+(aq) + 2e- -> Mg(s) (oxidation half-cell)
The standard reduction potential for the reduction half-cell is given by the equilibrium constant (K) of the reaction:
E°(reduction) = -0.0592 V/n * log(K)
= -0.0592 V/2 * log(3.69 x 10^17)
≈ 0.783 V
To find the potential for the oxidation half-cell, we negate the reduction potential since it's in the reverse direction:
E°(oxidation) = -E°(reduction)
= -0.783 V
Now, let's calculate the cell potential (Ecell) using the Nernst equation:
Ecell = E°(reduction) - E°(oxidation) + (0.0592 V/n) * log(Q)
Where:
- E°(reduction) is the standard reduction potential for the reduction half-cell.
- E°(oxidation) is the standard reduction potential for the oxidation half-cell.
- Q is the reaction quotient, calculated from the concentrations of the reaction species.
Since the cell is at standard conditions (1M concentrations for all species), the reaction quotient (Q) is equal to the equilibrium constant (K):
Q = K = 3.69 x 10^17
Therefore, substituting the values into the Nernst equation:
Ecell = 0.783 V - (-0.783 V) + (0.0592 V/2) * log(3.69 x 10^17)
= 1.566 V + 0.0296 V * log(3.69 x 10^17)
Hence, Ecell for the given cell is approximately equal to 1.566 V + 0.0296 V * log(3.69 x 10^17).
To calculate Ecell for the given cell, we need to use the Nernst equation, which is given by:
Ecell = E°cell - (RT/nF) * ln(Q)
Where:
Ecell is the cell potential
E°cell is the standard cell potential
R is the gas constant (8.314 J/mol·K)
T is the temperature in Kelvin
n is the number of electrons transferred in the balanced equation
F is Faraday's constant (96,485 C/mol)
ln(Q) is the natural logarithm of the reaction quotient
First, let's determine the balanced equation for the cell reaction:
Sr(s) + Mg2+(aq) <---> Sr2+(aq) + Mg(s)
The number of electrons transferred (n) in this equation is 2.
Next, we can calculate the standard cell potential using the table of standard reduction potentials:
E°cell = E°cathode - E°anode
The standard reduction potential for Sr2+/Sr is -2.89 V,
The standard reduction potential for Mg2+/Mg is -2.37 V.
E°cell = (-2.37 V) - (-2.89 V)
E°cell = 0.52 V
Now, let's calculate the reaction quotient (Q) using the equilibrium constant (K):
Q = [Sr2+][Mg]/[Sr][Mg2+]
Since the concentrations of the pure solids (Sr and Mg) are considered as 1, their concentrations are canceled out:
Q = [Sr2+][Mg2+]
We can calculate Q using the given equilibrium constant K:
K = [Sr2+][Mg2+]/[Sr][Mg2+]
Rearranging the equation:
[Sr2+][Mg2+] = K * [Sr]
[Sr2+][Mg2+] = (3.69 x 10^17) * 1
[Sr2+][Mg2+] = 3.69 x 10^17
Now, let's substitute the values into the Nernst equation:
Ecell = E°cell - (RT/nF) * ln(Q)
Ecell = 0.52 V - ((8.314 J/mol·K) * (298 K) / (2 * 96,485 C/mol)) * ln(3.69 x 10^17)
Calculating the Ecell will give you the answer.
RT*lnK = nFEcell
Substitute and solve for Ecell.