Determine the cell potential for Mg(s) + 2 Ag⁺(aq) → Mg²⁺(aq) + 2 Ag(s) where [Ag⁺] = 0.30 M and [Mg²⁺] = 0.020 M using the following standard reduction potentials. Mg²⁺(aq) + 2e⁻ → Mg(s) E° = -2.37 V and Ag⁺(aq) + e⁻ → Ag(s) E° =+0.80 V.
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To determine the cell potential for the given reaction, you can use the Nernst equation. The Nernst equation relates the cell potential (Ecell) to the standard cell potential (E°cell), concentration of the reactants, and the reaction quotient (Q). The Nernst equation is given by:
Ecell = E°cell - (0.0592/n) * log(Q)
Where:
Ecell = cell potential
E°cell = standard cell potential
n = number of electrons transferred in the balanced equation
Q = reaction quotient
First, let's write the balanced equation for the reaction:
Mg(s) + 2 Ag⁺(aq) → Mg²⁺(aq) + 2 Ag(s)
The number of electrons transferred in this reaction is 2 (based on the coefficient of Ag⁺).
Next, let's calculate the value of the reaction quotient (Q) by substituting the concentrations of the reactants into the equation:
Q = [Mg²⁺] * [Ag(s)]² / [Ag⁺]²
= (0.020 M) * (1)^2 / (0.30 M)²
= (0.020 M) / (0.09 M²)
= 0.222 M / M²
Now, plug the values into the Nernst equation to calculate the cell potential:
Ecell = E°cell - (0.0592/2) * log(Q)
= (-2.37 V) - (0.0296) * log(0.222)
Calculating the logarithm:
log(0.222) ≈ -0.653
Substitute the value back into the equation:
Ecell ≈ -2.37 V - (0.0296) * (-0.653)
≈ -2.37 V + 0.0193 V
≈ -2.3507 V
Therefore, the cell potential for the given reaction is approximately -2.3507 V.
To determine the cell potential for the given reaction, we can use the Nernst equation, which relates the cell potential to the standard reduction potentials and the concentrations of the species involved. The Nernst equation is given by:
Ecell = E°cell - (RT / nF) * ln(Q)
where:
Ecell = cell potential
E°cell = standard cell potential
R = gas constant (8.314 J/(mol*K))
T = temperature in Kelvin
n = number of electrons transferred in the balanced equation
F = Faraday's constant (96,485 C/mol)
ln = natural logarithm
Q = reaction quotient (ratio of concentrations of products to reactants)
Let's calculate the cell potential step by step:
1. Determine the overall balanced equation:
Mg(s) + 2 Ag⁺(aq) → Mg²⁺(aq) + 2 Ag(s)
2. Identify the number of electrons transferred in the balanced equation. In this case, it is 2.
3. Calculate the reaction quotient, Q:
Q = [Mg²⁺] / ([Ag⁺]²)
= 0.020 M / (0.30 M)²
= 0.020 M / 0.09 M
= 0.222
4. Now, substituting the given values into the Nernst equation:
Ecell = E°cell - (RT / nF) * ln(Q)
= (0.80 V) - (8.314 J/(mol*K) * T / (2 * 96,485 C/mol) * ln(0.222)
Remember to convert the temperature to Kelvin before calculation.
By plugging in the appropriate values for R, T, n, F and Q, you can calculate the cell potential for the given reaction.