Cells use the hydrolysis of adenosine triphosphate, abbreviated as ATP, as a source of energy. Symbolically, this reaction can be represented as
ATP(aq) + H2O(l) → ADP(aq) + H2PO4−(aq)
where ADP represents adenosine diphosphate. For this reaction
ΔG° = −30.5 kJ/mol.
(b) If all the free energy from the metabolism of glucose
C6H12O6(s) + 6 O2(g) → 6 CO2(g) + 6 H2O(l)
goes into the production of ATP, how many ATP molecules can be produced for every molecule of glucose?
___________ molecules
To determine how many ATP molecules can be produced for every molecule of glucose, we need to calculate the energy released from the metabolism of glucose and then convert that energy into ATP.
Step 1: Calculate the energy released from the metabolism of glucose using the balanced equation:
C6H12O6(s) + 6 O2(g) → 6 CO2(g) + 6 H2O(l)
According to the equation, the metabolism of one molecule of glucose results in the production of 6 molecules of carbon dioxide and 6 molecules of water. This reaction liberates energy in the form of heat. The standard free energy change (ΔG°) for this reaction can be calculated using ΔG° = ΔG°f(products) - ΔG°f(reactants).
The standard free energy change for the production of 1 mole of CO2 is -394 kJ/mol, and for 1 mole of H2O is -237 kJ/mol. Therefore, the standard free energy change for the production of 6 moles of CO2 and 6 moles of H2O is:
ΔG° = (6 mol CO2)(-394 kJ/mol) + (6 mol H2O)(-237 kJ/mol)
ΔG° = -4068 kJ/mol
Step 2: Convert the energy released into ATP production.
We know that the hydrolysis of ATP releases -30.5 kJ/mol of energy per ATP molecule. So, we can calculate how many ATP molecules can be produced from the energy released in the metabolism of glucose:
(Number of ATP molecules) = (Energy released from glucose metabolism) / (Energy released per ATP molecule)
(Number of ATP molecules) = (-4068 kJ/mol) / (-30.5 kJ/mol)
(Number of ATP molecules) ≈ 133.31
Therefore, approximately 133 ATP molecules can be produced for every molecule of glucose metabolized.
So, the answer is approximately 133 ATP molecules for every molecule of glucose.