Question

Use the following data to determine the maximum rate at which a standard man can climb a mountain: Blood contains 16.0 wt% hemoglobin (with molecular weight 65,000 g/mol). Each hemoglobin molecule can carry four oxygen molecules. The heart pumps 101 cm³/s blood of density 1.06 g/cm³. Each oxygen molecule can oxidize one sugar unit (the chemical formula per sugar unit is CH₂O, which is an organic alcohol group) to CO₂ and H₂O; the oxidation of 1 g sugar yields about 17 kJ of energy, of which 25% can be used to do muscle work. (Assume the climber has a mass of 66 kg.)

Answer 1

we need to calculate: the maximum rate at which a standard man can climb a mountain:

% of hemoglobin: 16 wt% hemoglobin (with molecular weight 65,000 g/mol).

amount of blood pumped = 101 cm³/s

Density = 1.06 g/cm³

amount of blood in grams pumped = 101 cm³/s X 1.06 g/cm³ = 107.06 g / s

The amount of hemoglobin in 100 gram blood = 16 g

So amount of hemoglobin in 107.06 grams of blood = 0.16 X 107.06 grams = 17.1296 grams

Number of moles of hemoglobin in 17.1296 grams = Mass / Molecular weight = 17.1296 / 65000 = 2.63 X 10^-4 moles

Number of molecules of hemoglobin in 2.63 X 10^-4 moles = 6.023 X 10^23 X 2.63 X 10^-4 molecules = 1.587 X 10^20

Each hemoglobin molecule can carry four oxygen molecules.

Number of oxygen molecules carried by hemoglobin = 4 X 1.587 X 10^20 = 6.35 X 10^20 molecules

Each oxygen molecule can oxidize one sugar unit (the chemical formula per sugar unit is CH₂O, which is an organic alcohol group) to CO₂ and H₂O;

so number of molecules of sugar can be oxidized = 6.35 X 10^20 molecules

Molecular Mass of one sugar unit = 12+ 2 + 16 = 30g / mole

Mass of sugar oxidized = 6.35 X 10^20 X 30 / 6.023 X 10^23 = 0.0316 grams

Amount of energy released by 0.0316 grams of sugar = 17 X 0.0332 KJ = 0.5376 KJ/ s

the energy which can be utilized 25% therefore energy released = 0.25 x 0.5376 KJ / s = 0.1344 KJ /s = 134.4 J /s

Energy required to climb with 0.01m/ second = Mass X height X acceleration due to gravity = mgh

Energy = 66 X 0.01 X 9.8 = 6.468 Joules / s

From 134.4 JJ energy height climbed = 134.4 J / 6.468 = 20.78 meters / second