Cells use the hydrolysis of adenosine triphosphate (aTP) as a source of energy. This reaction can be written as, ATP(aq) + H2O(l) --> ADP(aq) + H2PO4-(aq), wehre ADP represents adenosine diphosphate. For this reaction, Delta Grxn = -30.5KJ/mol. If all the free energy from the metabolism of glucose, C6H12O6(s) + 6O2(g) --> 6CO2(g) + 6H2O(l), goes into the conversion of ADP to ATP, how many ATP molecules can be produced for each mole of glucose?
I solved for DGrxn for the glucose reaction and got -2872KJ/mol. I don't know how to figure out the number of ATP. Please help.
To find out the number of ATP molecules that can be produced for each mole of glucose, we need to use the information provided about the free energy change (ΔGrxn) for the hydrolysis of ATP and the metabolism of glucose.
First, we need to calculate the amount of ATP that can be produced from each mole of glucose by comparing the ΔGrxn values of the two reactions.
The reaction for the hydrolysis of ATP is given as:
ATP(aq) + H2O(l) → ADP(aq) + H2PO4-(aq)
The given ΔGrxn for this reaction is -30.5 KJ/mol.
The reaction for the metabolism of glucose is given as:
C6H12O6(s) + 6O2(g) → 6CO2(g) + 6H2O(l)
The given ΔGrxn for this reaction is -2872 KJ/mol.
Next, we can use the equation of ΔGrxn = ΔG°rxn + RTln(Q) to relate the ΔGrxn to the equilibrium constant (Q) of the reaction.
In this case, we will assume the reactions are at standard conditions (1 atm and 25°C), making ΔG°rxn equal to ΔGrxn.
We can calculate the equilibrium constant (Q) by using the equation:
Q = (P(CO2))^6(P(H2O))^6 / (P(C6H12O6))(P(O2))^6
Since both glucose and oxygen are in the solid and gaseous states, respectively, we assume their partial pressures are 1. The partial pressures of CO2 and H2O can be approximated to 1 as well under normal conditions.
Thus, Q = (1)^6(1)^6 / (1)(1)^6 = 1/1 = 1
Now, let's substitute the values into the equation ΔGrxn = ΔG°rxn + RTln(Q) to solve for ΔG°rxn.
-30.5 KJ/mol = ΔG°rxn + (8.31 J/(mol·K))(298 K)ln(1)
Since ln(1) = 0, the equation simplifies to:
-30.5 KJ/mol = ΔG°rxn
Therefore, the standard Gibbs free energy change (ΔG°rxn) for the hydrolysis of ATP is also -30.5 KJ/mol.
Finally, we can calculate the number of moles of ATP produced from one mole of glucose using the equation:
n(ATP) = -ΔG°rxn(2) / ΔGrxn
n(ATP) = -(-30.5 KJ/mol)(2) / -2872 KJ/mol
n(ATP) ≈ 0.02 mol (approximately)
Therefore, approximately 0.02 moles of ATP can be produced from one mole of glucose.
Since one mole of ATP contains 6.022 x 10^23 molecules, we can multiply 0.02 mol by Avogadro's number to find the approximate number of ATP molecules produced:
Number of ATP molecules ≈ 0.02 mol x (6.022 x 10^23 molecules/mol)
Number of ATP molecules ≈ 1.2044 x 10^22 molecules
Therefore, approximately 1.2044 x 10^22 ATP molecules can be produced from one mole of glucose.