Question

The following question is offered in anticipation of our chapters on metabolism: Assuming that the average weight of an adult is 154 lbs, how many molecules arrive each second at a mitochondrion of an average active person? Assume that oxygen consumption is 49 mL per minute per kilogram of body weight, adults have about 1 × 1012 cells, and there are 800. mitochondria per cell. Assume that one pound equals 0.454 kg, and that oxygen gas occupies 22.4 L per mol. Report your answer to the nearest ones.

Answer 1

As average weight of an adult is = 154 lbs

or, = 154x0.454

= 69.9 kg

oxygen consumption on average = 49 mL/min/kg

for an adult oxygen consumption per second comes out to be = 49x69.9x60 mL/sec

= 205553.04 mL/sec

= 205.55 L/sec

Now, this oxygen gets divided into all the mitocondrion present in the body. i.e.

total number of mitocondrion= 1x10¹²x800

= 800x10¹²

Hence amount of oxygen arriving in each mitocondrion is = 205.55/(800x10¹²) = 2.56x10^-13 L/sec

as each mole contains 22.4 L , hence number of moles arriving in each mitocondrion is = [2.56x10^-13/22.4]

= 1.14x10^-14 mol/sec

as each mole contains avogadro number of molecules/atoms. i.e 6.023x10²³

Hence number of molecules arriving each mitocondrion per second = 1.14x10^-14x6.023x10²³ = 6.86x10⁹ molecules

Note: The number of cells for adults should be 1x10¹² instead of 1x1012. The answer is calculated taking 1x10¹².

Hence number of molecules came out to be nearly 7 billion.