Question

A 70 kg (154 lb) adult requires a calorie intake of 2,000 kcal (8,360 kJ) of food per day. The food is metabolized and the free energy is used to synthesize ATP for useful work. The efficiency of converting food energy into ATP is 50%.
1) Calculate the mass of ATP used by an adult human in 24h.

(ATP formula weight = 505 g/mol, DG'° = -30.5 kJ/mol)

2) If ATP is present at 5 mM inside cells, and if the intracellular volume corresponds to about 25% of an adult mass, how frequently is an ATP molecule hydrolyzed and rephosphorylated, on average?

Answer 1

1)

Given

ATP formula weight = 505 g/mol

DG'° = -30.5 kJ/mol

The mass of ATP used by an adult human in 24h

Step 1- Calculate the moles of ATP used

Moles of ATP = calorie intake / DG'°

Moles of ATP = 8,360 kJ/30.5 kJ/mol

Moles of ATP = 274.098 moles

The efficiency of converting food energy into ATP is 50%.

So, number of moles of ATP used =274.098 x (50/100) = 137.049 moles

Step 2- Calculate the mass of ATP

We can calculate mass of ATP by multiplying number of moles of ATP used with molar mass of ATP

Mass of ATP used = 137.049 moles x 505 g/mol = 69209 g

Convert g into Kg by dividing with 1000

69209 g = 69209 /1000 = 69.2 Kg

The mass of ATP used by an adult human in 24h would be 69.2 Kg

2. The reaction ATP + H2O <—-> ADP + Pi

ATP concentration is 5mM which is 0.005 moles.

Since, 1 mol of ATP is 505g,

      0.005 moles ATP would be 0.005 x 505 = 2.525g

The intracellular volume corresponds to about 25% of an adult mass,

Intracellular volume = 70 Kg x (25/100) = 17.5 Kg

The concentration of ATP would be = 69.2 Kg/17.5 Kg = 3.95428 Kg

= 3954 g

Turnover = 3954 g/2.525g = 1566 times