For a certain respiration, the free energy is -83 kJ/mol. The proton gradient consists of PH change = 1 and -0.12 Volts.
I'm supposed to figure out how many protons could be pumped per two electrons transferred. How would I go about figuring this out?
To determine how many protons could be pumped per two electrons transferred, you need to consider the stoichiometry of the reaction and the relationship between the free energy change and the number of protons pumped.
First, you need to know the redox reaction involved in the respiration process. Let's assume it is the transfer of two electrons from molecule A to molecule B. So, the reaction can be represented as:
A + 2e^- -> B
Next, you need to determine the stoichiometry of proton pumping per two electrons transferred. This information is usually provided in the context of the respiration process you are studying. Let's assume that for every two electrons transferred from molecule A to molecule B, four protons are pumped across the membrane. Therefore, the stoichiometry can be represented as:
2e^- + 4H^+outside -> 2H^+inside
Now, let's calculate the proton-motive force (PMF) generated by the proton gradient. The PMF consists of two components: the pH difference and the electrical potential difference (membrane voltage). To simplify the calculation, let's assume that the pH change is 1 unit and the voltage change is -0.12 Volts.
The pH component of the PMF can be calculated using the Nernst equation:
∆pH = 2.303 × RT/F × ∆pH_unit
Where:
R = the gas constant (8.314 J/(mol·K))
T = the absolute temperature in Kelvin
F = the Faraday constant (96485 C/mol)
∆pH_unit = pH_change
Now let's substitute the values given:
∆pH = 2.303 × (8.314 J/(mol·K)) × (298 K) / (96485 C/mol) × 1
∆pH ≈ 0.0609 V (Volts)
Now let's calculate the electrical potential component of the PMF:
∆V = voltage_change = -0.12 V
To determine the overall PMF, we add the pH component and the electrical potential component:
PMF = ∆pH + ∆V
PMF ≈ 0.0609 V + (-0.12 V)
PMF ≈ -0.0591 V
Finally, to calculate the number of protons pumped per two electrons transferred, we use the relationship between PMF and the free energy changes involved in pumping protons:
∆G = -n × F × ∆p
Where:
∆G = free energy change
n = number of protons pumped per electron transferred
F = Faraday constant
∆p = electrical potential component of PMF
Rearranging the equation:
n = -∆G / (F × ∆p)
Now let's substitute the values (assuming the given free energy change of -83 kJ/mol):
n = -(-83 kJ/mol) / (96485 C/mol × -0.0591 V)
n ≈ 1.44 protons
Therefore, approximately 1.44 protons would be pumped per two electrons transferred in this respiration process.