Question

The average daily diet of an adult woman is 2.1×103kcal. The molar mass of ATP is 507 g/mole.

Part A) If all the energy in her diet is converted to ATP, how many kg of ATP are synthesized in one day?

Part B) If the average amount of ATP in the body is 250 g, what is the lifetime, in minutes, of ATP?

Answer 1

Ans. Free energy change of ATP hydrolysis = -7.3 kcal/mol-    , i.e. 1 mol ATP produces 7.3 kcal energy upon hydrolysis.

#A. Moles of ATP equivalent to daily diet =

Energy content of daily diet / Free energy change of ATP hydrolysis

= 2.1 x 10³ kcal / (7.3 kcal/mol)

= 287.67 mol

So, there must be the synthesis of 287.67 mol ATP per day to compensate energy equivalent to daily diet.

Now,

            Mass of ATP synthesized per day = Moles of ATP synthesized daily x Molar mass

                                    = 287.67 mol x (507 g/mol)

                                    = 145849.32 g

                                    = 145.85 kg

#B. Given, average amount of ATP in body = 250 g.

To synthesize 145.85 kg ATP per day, the same 250.0 g ATP is recycled again and again per day. The one recycling event is equivalent to one lifecycle. As calculated in part A, 145849.32 g ATP is synthesized in a period of 24 hours.

So,

            Lifetime of ATP = Mass of ATP in body / ATP synthesized per day

                                    = 250 g / (145849.32 g/ 24 hr)

                                    = 7.1421 x 10^-5 hr                                         ; [1 hr = 60 min]

                                    = 0.004285 min

                                    = 4.29 x 10^-3 min

So, ATP in body is recycled every 0.004285 min.

Thus, lifetime of ATP = 0.004285 min