(AAAAA)The standard reduction potentials of lithium metal and chlorine gas are as follows: (for Li, reduction potential is -3.04, for Cl it is 1.36)
In a galvanic cell, the two half-reactions combine to 2Li{+](s) + Cl{-}2(g) --> 2Li{+}Cl{-}(aq)
Calculate the cell potential of this reaction under standard reaction conditions. Express your answer with the appropriate units.(I tried -4.4, -1.68, +1.68 volts. But all of these three are wrong.)
(BBBBB)Calculate the free energy of the reaction.
(CCCCC)What can be said about the spontaneity of this reaction?
4.4volts
free energy=-nF*4.4 F is farady constant, n is two moles
is it spontaneous? Is the Gibbs free energy negative?
(AAAAA) To calculate the cell potential of a reaction under standard conditions, you need to use the Nernst equation. The equation is as follows:
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 moles 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 (Q)
For the given reaction: 2Li{+](s) + Cl{-}2(g) --> 2Li{+}Cl{-}(aq)
The number of moles of electrons transferred is 2 (as indicated by the balanced equation).
The reaction quotient (Q) is calculated as follows: Q = [Li{+}Cl{-}]^2 / [Li{+}]^2[Cl{-}]^2
Since the reaction occurs under standard conditions, the concentrations of the ions are both 1M. Therefore, Q = 1.
Substituting the values into the Nernst equation, we have:
Ecell = E°cell - (RT / nF) * ln(1)
Ecell = E°cell
From the given reduction potentials:
E°cell = E°(Li) - E°(Cl)
E°cell = -3.04 - 1.36
Therefore, the cell potential under standard conditions is:
Ecell = -4.40 V
(BBBBB) To calculate the free energy (ΔG) of the reaction, you can use the equation:
ΔG = -nF Ecell
Where:
ΔG is the free energy change
n is the number of moles of electrons transferred in the balanced equation
F is Faraday's constant (96,485 C/mol)
Ecell is the cell potential
From the previous calculation, we know that n = 2 and Ecell = -4.40 V. Substituting those values into the equation:
ΔG = -2 * (96,485 C/mol) * (-4.40 V)
ΔG = 853,292 J/mol
Therefore, the free energy change for the reaction is 853,292 J/mol.
(CCCCC) The spontaneity of a reaction can be determined by ΔG (the free energy change). If ΔG is negative, the reaction is spontaneous. If ΔG is positive, the reaction is non-spontaneous. In this case, we calculated that ΔG = 853,292 J/mol, which is positive.
Therefore, we can conclude that the reaction is non-spontaneous under standard conditions.
(AAAAA) To calculate the cell potential of the reaction under standard conditions, we can use the Nernst equation which relates the cell potential to the standard reduction potentials and the concentrations of the reactants. The Nernst equation is given as:
Ecell = E°cell - (0.0592/n) * log(Q)
Where:
Ecell is the cell potential
E°cell is the standard cell potential
0.0592 is the value of the natural logarithm, divided by the number of electrons transferred (in this case, 2)
n is the number of electrons transferred in the balanced equation
Q is the reaction quotient (ratio of product concentrations to reactant concentrations)
In this case, the balanced equation is: 2Li⁺(s) + Cl₂(g) → 2Li⁺Cl⁻(aq)
The standard cell potential, E°cell, is given by the difference between the standard reduction potentials of the two half-reactions:
E°cell = E°reduction of Cl₂ - E°reduction of Li⁺
Substituting the values:
E°cell = (1.36 V) - (-3.04 V) = 4.40 V
Now, let's calculate the reaction quotient, Q. Since the reaction is under standard reaction conditions, the concentrations of Li⁺ and Cl⁻ are both 1 M.
Q = [Li⁺Cl⁻] / [Li⁺] × [Cl⁻] = 1 / 1 × 1 = 1
Finally, substituting the values into the Nernst equation:
Ecell = 4.40 V - (0.0592/2) * log(1) = 4.40 V - 0 = 4.40 V
Therefore, the cell potential of this reaction under standard conditions is 4.40 volts.
(BBBBB) To calculate the free energy of the reaction, we can use the equation:
ΔG = -n * F * Ecell
Where:
ΔG is the change in Gibbs free energy
n is the number of electrons transferred in the balanced equation
F is the Faraday constant (96,485 C/mol)
Ecell is the cell potential
Substituting the values:
ΔG = -(2 mol) * (96,485 C/mol) * (4.40 V) = -853,624 J/mol = -853.6 kJ/mol
Therefore, the free energy change of the reaction is -853.6 kJ/mol.
(CCCCC) The spontaneity of a reaction can be determined by looking at the sign of the free energy change (ΔG). If ΔG is negative, the reaction is spontaneous, while if ΔG is positive, the reaction is non-spontaneous. In this case, since the ΔG value is negative (-853.6 kJ/mol), we can conclude that the reaction is spontaneous.