f the synthesis of 1.00 mol of ATP from adenosine diphosphate (ADP) requires a ΔG of 37.7 kJ, how many moles of ATP are synthesized per mole of O2?
Oh, when it comes to ATP synthesis, I know how to make energy funny. So, let's dance into the equation.
The synthesis of 1 mole of ATP requires a ΔG of 37.7 kJ. Now, to find how many moles of ATP are synthesized per mole of O2, we need to bring our pal, the oxygen, into the equation.
But guess what? Oxygen is such a party animal, it loves to have two moles to have some true fun. So, we need to multiply... are you ready for this? ... multiply by 2 moles of O2.
So, ta-da! We have 37.7 kJ * 2 moles of O2. And the result, my friend, is the number of moles of ATP synthesized per mole of O2.
But hey, don't take my word for it. Check my math before thanking me for the laughs.
To determine the number of moles of ATP synthesized per mole of O2, we need to use the standard Gibbs free energy change (ΔG°) for the reaction of ATP synthesis, as well as the number of moles of electrons transferred during the reaction.
The balanced reaction for ATP synthesis from ADP and inorganic phosphate (Pi) is:
ADP + Pi + H2O → ATP + H2O
The standard Gibbs free energy change (ΔG°) for this reaction is given as 37.7 kJ/mol.
In cellular respiration, the transfer of electrons occurs from reduced electron carriers to O2, resulting in the formation of water. The balanced reaction for the reduction of O2 is:
1/2 O2 + 2H+ + 2e- → H2O
From the balanced equation, we can see that for each mole of O2 reduced, 4 moles of electrons (4e-) are transferred.
Now, we need to compare the number of moles of electrons transferred in ATP synthesis with the number of moles of electrons transferred in O2 reduction.
The stoichiometry of ATP synthesis does not directly provide information about the number of moles of electrons transferred. However, based on the overall redox reaction in cellular respiration, we know that the reduction of O2 corresponds to the reoxidation of electron carriers, such as NADH and FADH2. Each mole of NADH and FADH2 can transfer a maximum of 2 moles of electrons to the electron transport chain.
Since ATP synthesis is energetically coupled to the electron transport chain, we can assume that 4 moles of electrons are transferred for each mole of ATP synthesized. This assumption is based on the understanding that for each mole of NADH and FADH2, which represent the primary electron donors in cellular respiration, there is an equivalent transfer of 2 moles of electrons to the electron transport chain.
Therefore, based on the assumption that 4 moles of electrons are transferred for each mole of ATP synthesized, the number of moles of ATP synthesized per mole of O2 can be calculated as follows:
Moles of ATP synthesized per mole of O2 = Moles of ATP synthesized per mole of electrons transferred × Moles of electrons transferred per mole of O2
= 1 mol ATP / 4 mol e- × 4 mol e- / 2 mol O2
= 1 mol ATP / 2 mol O2
Therefore, 1.00 mol of ATP is synthesized per 2.00 moles of O2.
To find the number of moles of ATP synthesized per mole of O2, we need to determine the stoichiometry of the reaction between ATP synthesis and O2.
The equation for the synthesis of ATP from ADP and inorganic phosphate (Pi) is:
ADP + Pi + energy → ATP
Since the problem states that the synthesis of 1.00 mol of ATP requires a ΔG of 37.7 kJ, we can equate this to the energy term in the equation:
1.00 mol ATP × ΔG = 37.7 kJ
To convert kJ to J, we multiply by 1000:
1.00 mol ATP × ΔG = 37.7 × 1000 J
Now, we need to determine the energy required per mole of ATP. Since 1 mol of ATP is synthesized from 1 mol of ADP and inorganic phosphate, the energy required per mole of ATP is the same as the ΔG value provided:
ΔG = 37.7 × 1000 J
Next, we need to determine the energy required per mole of O2. The balanced equation for aerobic respiration, where O2 is consumed, is:
C6H12O6 + 6O2 → 6CO2 + 6H2O + energy
From this equation, we see that for every 6 moles of O2 consumed, a certain amount of energy is released.
To determine the energy released per mole of O2, we divide the energy required per mole of ATP by the stoichiometric coefficient of O2:
Energy released per mole of O2 = ΔG / 6
Now, we can calculate the number of moles of ATP synthesized per mole of O2 by dividing the energy required per mole of ATP by the energy released per mole of O2:
Moles of ATP per mole of O2 = Energy required per mole of ATP / Energy released per mole of O2
Substituting the values:
Moles of ATP per mole of O2 = (37.7 × 1000 J) / (ΔG / 6)
We can now calculate the moles of ATP synthesized per mole of O2 using the given ΔG value of 37.7 kJ.