Some bacteria get their energy from reduction of CO2 to CH4 by H2.
1. How many electrons are required to reduce CO2 to CH4?
2. Calculate the G for formation of methane based on the two standard reduction potential of -0.171V for reduction of CO2 to CH4 and -0.414V for reduction of H+ to H2.
1. The reduction of CO2 to CH4 involves the addition of four hydrogen atoms. Each hydrogen atom contributes one electron during the reduction reaction. Therefore, four electrons are required to reduce one molecule of CO2 to one molecule of CH4.
2. To calculate the standard Gibbs free energy change (ΔG°) for the formation of methane (CH4), we can use the Nernst equation:
ΔG° = -nFΔE°
Where:
ΔG° is the standard Gibbs free energy change
n is the number of electrons transferred in the reaction
F is the Faraday constant (96,485 C/mol)
ΔE° is the difference in standard reduction potentials between the reactants and products.
In this case:
n = 4 (as mentioned above)
F = 96,485 C/mol
ΔE° = -0.171V (reduction of CO2 to CH4) - (-0.414V) (reduction of H+ to H2).
Substituting these values into the equation, we can calculate ΔG°:
ΔG° = -4 * 96,485 C/mol * (0.414V - 0.171V)
Solving the above equation will give us the value of ΔG° for the formation of methane based on the given standard reduction potentials.
To answer these questions, we need to understand the concepts of electron transfer and reduction potentials.
1. How many electrons are required to reduce CO2 to CH4?
In the reduction process, carbon dioxide (CO2) is converted to methane (CH4). To determine the number of electrons involved, we need to look at the balanced half-reactions. The reduction of CO2 in this case can be represented as follows:
CO2 + 8H+ + 8e- -> CH4 + 2H2O
From the balanced reaction, we can see that 8 electrons (8e-) are required to reduce one molecule of CO2 to CH4.
2. Calculate the ΔG for the formation of methane using the two standard reduction potentials.
The standard reduction potential (E°) is a measure of the tendency of a species to accept electrons and undergo reduction. The ΔG (Gibbs free energy change) can be calculated using the equation:
ΔG = -nFΔE°
Where:
ΔG is the Gibbs free energy change
n is the number of electrons transferred in the reaction
F is Faraday's constant (F = 96,485 C/mol)
ΔE° is the difference in standard reduction potentials
Given the reduction potentials:
E°(CO2 to CH4) = -0.171V
E°(H+ to H2) = -0.414V
We need to consider the reduction potentials in their reduction form (flipping the sign):
E°(CO2 to CH4) = -(-0.171V) = 0.171V
E°(H+ to H2) = -(-0.414V) = 0.414V
Since the reaction involves the reduction of CO2 and H+, we can sum the two reduction potentials:
ΔE° = E°(CO2 to CH4) + E°(H+ to H2)
= 0.171V + 0.414V
= 0.585V
We already know from the previous question that n (number of electrons transferred) is 8, as it takes 8 electrons to convert one molecule of CO2 to CH4.
Now we can substitute the values into the ΔG equation:
ΔG = -nFΔE°
= -(8)(96,485 C/mol)(0.585V)
= -449,431 C/mol
The result is approximately -449,431 Coulombs per mole, which represents the Gibbs free energy change for the formation of methane (CH4) based on the given standard reduction potentials.