[Assume that hydrolysis of ATP yields 12 kcal per mole. 1 watt = 1 joule/sec, 1 calorie = 4.18 joules, Avogadro's number = $6.023 \times 10^{23}$]
Human Body ATP Power Calculation
This problem requires calculating the total power utilized by the human body based on the given number of cells, ATP turnover rate per cell, and energy released per ATP molecule.
Calculation Steps
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Calculate total ATP molecules utilized per minute:
Total ATP turnover per minute is the product of the number of cells and the ATP turnover rate per cell.
Total ATP/min = Number of cells $\times$ ATP rate per cell
Total ATP/min = $(5 \times 10^{13} \text{ cells}) \times (10^9 \text{ ATP/cell/min})$
Total ATP/min = $5 \times 10^{22}$ ATP/min
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Convert total ATP molecules to moles per minute:
Using Avogadro's number, we convert the number of ATP molecules to moles.
Total moles ATP/min = $\frac{\text{Total ATP/min}}{\text{Avogadro's number}}$
Total moles ATP/min = $\frac{5 \times 10^{22} \text{ ATP/min}}{6.023 \times 10^{23} \text{ ATP/mole}}$
Total moles ATP/min $\approx 0.08299$ moles/min
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Calculate total energy released in kcal per minute:
The total energy is the moles of ATP utilized multiplied by the energy yield per mole.
Energy (kcal/min) = Total moles ATP/min $\times$ Energy yield per mole
Energy (kcal/min) = $(0.08299 \text{ moles/min}) \times (12 \text{ kcal/mole})$
Energy (kcal/min) $\approx 0.9959$ kcal/min
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Convert energy from kcal to joules per minute:
We use the conversion factor 1 kcal = 1000 cal and 1 cal = 4.18 J.
Energy (J/min) = Energy (kcal/min) $\times 1000 \times 4.18$
Energy (J/min) = $(0.9959 \text{ kcal/min}) \times 1000 \times 4.18$
Energy (J/min) $\approx 4162.8$ J/min
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Convert energy per minute to power in watts (joules per second):
Power is energy per unit time. 1 watt = 1 joule/sec.
Power (watts) = $\frac{\text{Energy (J/min)}}{60 \text{ sec/min}}$
Power (watts) = $\frac{4162.8 \text{ J/min}}{60 \text{ sec/min}}$
Power (watts) $\approx 69.38$ J/sec
The calculated power utilization is approximately 69.38 watts, rounded to two decimal places. This value falls within the expected range.
Important Questions from Bioenergetics ATP Hydrolysis
- Glucose and hexanoic acid, each having six carbon atoms can undergo complete biological oxidation. In terms of net ATP generation, which of the following statements is CORRECT?
- Four groups of metabolites are given below. Choose the group in which all the compounds contain at least one bond whose ${\Delta}G'^{\circ}$ of hydrolysis is $\leq$ -7.0 kcal/mole.
- Which one of the following statements is NOT correct?
- Which of the following is TRUE about Kreb's cycle?
- The movement of protons through the $F_0F_1$-ATPase during mitochondrial respiration is required for ________
