2.2 A 75kg person doing light work requires about 3000 kcal of food energy per d

Question

2.2 A 75kg person doing light work requires about 3000 kcal of food energy per day, 40% of which is actually used by the body's cells. (The other 60% is lost as heat and in waste products.) Before being used by the cells, effectively all of this energy is stored in ATP, which is then cleaved into ADP and PO2 with the release of 12.5 kcal per mole of ATP. (a) How many moles of ATP are turned over per day in this fashion? What snTcl ipt AT 507 g/mol.) The body actually contains approximately 5 g ATP. Estimate the average recycle time for an ATP molecule. You see that it is much more efficient to reuse ADP rather than to synthesize it de novo (from scratch) (b)

Explanation / Answer

Ans. # Note that only 40% of the total energy consumed per day is actually used up by the cells, the rest 60% being dissipated as heat without availability to cells.

So, Daily energy consumption by cells = 40% of 3000 kcal

                                                = 1200 kcal

#a. Given,      Energy yield of ATP = 12.5 kcal/ mol

Required moles of ATP per day = Daily energy consumption by cells / Energy yield of ATP

                                                = 1200 kcal / (12.5 kcal/ mol)

                                                = 96 mol

So, 96 moles of ATP are consumed per day.

Mass of ATP consumed per day = Moles of ATP usage per day x Molar mass of ATP

                                                = 96 mol x (507 g/ mol)

                                                = 48672 g

#b. Moles of ATP present in body = Mass / Molar mass

                                                = 5.0 g / (507 g/ mol)

                                                = 9.8619 x 10-3 mol

Let the average recycle time = X minute

That is, 9.8619 x 10-3 mol ATP is recycled every X minutes.

So, Rate of ATP recycling = 9.8619 x 10-3 mol ATP / X minute.

Total minutes in a day = 24 hr x (60 min / Hr) = 1440 min

Now,

Total ATP recycles per day = Rate of ATP recycling x No. of minutes per day

                                    = (9.8619 x 10-3 mol ATP / X minute) x 1440 min

                                    = (14.20114 / X) mol ATP

# From #a, total ATP consumed per day = 96 mol

So, total ATP recycled per day must be equal to the total moles of ATP consumed per day.

So,

            (14.20114 / X) mol = 96.0 mol

            Or, X = 14.20114 / 96.0

            Hence, X = 0.1479 min

Hence, ATP recycling time = 0.1479 min = 8.88 seconds

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