1. Walking consumes approximately 100 kcal/mi. In the hydrolysis of ATP (ATP → ADP + Pi), the reaction that drives the muscle contraction, ΔGo’ is -7.3 kcal/mol (-30.5 kJ/mol). Calculate how many grams of ATP must be produced to walk a mile. ATP synthesis is coupled to the oxidation of glucose (ΔGo’ = -686 kcal/mol). How many grams of glucose are actually metabolized to produce this amount of ATP? (Assume that only glucose oxidation is used to generate ATP and that 40% of the energy generated from this process is used to phosphorylate ADP. The gram molecular weight of glucose is 180 g and that of ATP is 507 g.
Okay, I had to think about this question because you supplied ΔGo’, and not ΔG. So you have to solve for ΔG to solve this problem, and you have to use the concentration of ATP, ADP, and Pi in muscle cells, because the concentrations very by cell type. The concentrations of ATP, ADP, and Pi are 5.0, 0.5, and 1.0mM, respectively. ΔGo’ for the formation of ATP is 7.3 cal/mol or 30.5 kJ/mol, the reverse of its hydrolysis. Converting from mM to M, and plugging the values into the equation, ΔG=ΔGo’+RTlnQ, we get
ΔG=30.5 kJ/mol+(2.58 kJ/mol)(9.21)=54.3kJ/mol
Since, 100kcal/mi*(4.2kJ/1kcal)=420kJ/mi
Determine moles of ATP
420kJ/54.3kJ/mol=7.73 moles of ATP
7.73 moles of ATP *( 507 g of ATP/1 mole of ATP)=3.92 X10^3 g of ATP= 3.92 kg of ATP.
I am not sure about the final number, because different references have different values for ATP, ADP, and Pi for muscle cells.
Since 40% of the ATP can not be used because it is being used to phosphorylate ADP, then the number of moles of ATP needed from the oxidation of ATP is equal to the number of ATP required plus an extra 40%.
7.73 moles of ATP + 40%= 10.8 moles of ATP
The production of 10.8 moles of ATP will require 586kJ
Since The complete oxidation of glucose is equal to 686 kcal/mol or 2,881kJ/mole (check these values),
586kJ/2,881kJ/mole=moles of glucose needed, which is 0.203 moles of Glucose.
0.203 moles of Glucose *(180 g of glucose/1 mole of glucose)= 36.6 g of glucose.
Not sure about the answers, because of the values, but I hope this helps.
I totally screwed up on the second part.
7.8 moles of ATP is correct, and you need to take into account how much ATP is lost by the oxidation of glucose, which is 40%.
Depending on what textbooks you use, 1 molecule of glucose will yield 30, 34, or 36 ATP. But lets use 1 molecule yields 36 ATP as our conversion factor, and let's subtract 40% from the 36, which gives us 22 free ATP per molecule of glucose.
We need 7.73 moles of ATP, so
7.73 moles of ATP*(6.02 x 10^23 atoms of ATP/1 mole of ATP)= atoms of ATP
Since 1 atom of glucose=22 ATP
atoms of ATP *( 1glucose/22 ATP)=number of glucose molecules
And since 1 mole glucose=180 g of glucose and 1 mole of glucose =6.02 x 10^23 atoms,
number of glucose molecules*(1 mole of glucose/6.02 x 10^23 atoms)*(180 g of glucose/1 mole glucose)= g of glucose needed for oxidation.
I really do apologize for the mixup on the second part. But remember, check the values that I gave you especially for reference values, since they are not all the same in every textbook.
To calculate the number of grams of ATP required to walk a mile, we need to know the energy consumption per mile and the energy yield per ATP molecule.
Given:
Energy consumption per mile (E) = 100 kcal/mi
The energy yield per ATP molecule (ΔG' ATP hydrolysis) = -7.3 kcal/mol
First, let's convert the energy consumption per mile to energy per mole of ATP:
1 mile = 1.60934 km
1 km = 1000 m
Energy consumption per mile = E = 100 kcal/mi = 100 kcal/1.60934 km ≈ 62.15 kcal
1 kcal ≈ 4.184 kJ
Energy consumption per mile = E ≈ 62.15 kcal ≈ 62.15 kcal * 4.184 kJ/kcal ≈ 259.57 kJ
Next, let's calculate the number of moles of ATP required to walk a mile:
ΔGo' ATP hydrolysis = -7.3 kcal/mol ≈ -30.5 kJ/mol
ΔGo' ATP hydrolysis = -30.5 kJ/mol = -30,500 J/mol = -30,500 J/mol * (1 kJ/1000 J) = -30.5 kJ/mol
Number of moles of ATP required = Energy consumption per mile / ΔGo' ATP hydrolysis
Number of moles of ATP required = 259.57 kJ / -30.5 kJ/mol ≈ -8.50 mol
Since the molar mass of ATP is 507 g/mol, we can calculate the grams of ATP required:
Grams of ATP required = Number of moles of ATP required * Molar mass of ATP
Grams of ATP required = -8.50 mol * 507 g/mol ≈ -4313.50 g
However, it is not physically possible to have a negative mass of ATP, so we can assume that there is an error in the calculations or the given values.
Moving on to the next part:
To calculate the grams of glucose metabolized to produce the calculated amount of ATP, we need to consider the energy yield from glucose oxidation and the energy used for ATP synthesis.
Given:
Energy yield from glucose oxidation (ΔG' glucose oxidation) = -686 kcal/mol
Energy used for ATP synthesis = 40% of the energy generated from glucose oxidation
First, let's calculate the energy used for ATP synthesis:
Energy used for ATP synthesis = 40% * Energy yield from glucose oxidation
Energy used for ATP synthesis = 0.40 * -686 kcal/mol ≈ -274.40 kcal/mol
Next, let's calculate the moles of glucose metabolized:
Molar mass of glucose = 180 g/mol
Moles of glucose metabolized = Energy used for ATP synthesis / ΔG' glucose oxidation
Moles of glucose metabolized = -274.40 kcal/mol / -686 kcal/mol ≈ 0.40 mol
Finally, let's calculate the grams of glucose metabolized:
Grams of glucose metabolized = Moles of glucose metabolized * Molar mass of glucose
Grams of glucose metabolized = 0.40 mol * 180 g/mol ≈ 72 g
Therefore, approximately 72 grams of glucose are metabolized to produce the calculated amount of ATP.
To calculate the number of grams of ATP required to walk a mile, we need to determine the energy expenditure of walking a mile in kcal and then convert it to moles of ATP using the ΔGo' value.
Given that walking consumes approximately 100 kcal/mi, we can use this information to calculate the energy expenditure:
Energy expenditure (kcal) = 100 kcal/mi × 1 mi = 100 kcal
Now, we can convert the energy expenditure to moles of ATP using the ΔGo' value:
ΔGo' = -7.3 kcal/mol
Moles of ATP = Energy expenditure (kcal) / ΔGo'
Moles of ATP = 100 kcal / -7.3 kcal/mol ≈ -13.7 mol
Since moles cannot be negative, we use the absolute value:
Moles of ATP = 13.7 mol
Next, we need to convert moles of ATP to grams of ATP. The gram molecular weight of ATP is 507 g/mol:
Grams of ATP = Moles of ATP × 507 g/mol
Grams of ATP = 13.7 mol × 507 g/mol ≈ 6,942.9 g
Therefore, approximately 6,942.9 grams of ATP must be produced to walk a mile.
To calculate the grams of glucose required to produce this amount of ATP, we need to consider that ATP synthesis is coupled to the oxidation of glucose. The reaction ΔGo' for glucose oxidation is -686 kcal/mol.
Given that 40% of the energy generated from glucose oxidation is used to phosphorylate ADP, we can calculate the actual energy available for ATP synthesis:
Energy available for ATP synthesis = Energy generated from glucose oxidation × 40%
Energy available for ATP synthesis = -686 kcal/mol × 0.40 = -274.4 kcal/mol
Now, we can calculate the moles of ATP that can be synthesized from this available energy:
Moles of ATP = Energy available for ATP synthesis / ΔGo'
Moles of ATP = -274.4 kcal/mol / -7.3 kcal/mol ≈ 37.7 mol
Again, using the absolute value:
Moles of ATP = 37.7 mol
Finally, we can convert moles of ATP to moles of glucose. Since only glucose oxidation is used to generate ATP and the molecular weight of glucose is 180 g/mol:
Grams of glucose = Moles of ATP × 180 g/mol
Grams of glucose = 37.7 mol × 180 g/mol ≈ 6,786 g
Therefore, approximately 6,786 grams of glucose are actually metabolized to produce the amount of ATP required to walk a mile.