Calculate the mass of glucose metabolized by a 78.8 kg person in climbing a mountain with an elevation gain of 1570 m. Assume that the work performed in the climb is four times that required to simply lift 78.8 kg by 1570 m.

The mass of glucose metabolized by a 78.8 kg person in climbing a mountain with an elevation gain of 1570 m, is 311.5 grams

Explanation:

Step 1: Data given

Mass of the person = 78.8 kg

elevation = 1570 meters

Molar mass of glucose = 180.16 g/mol

Standard enthalpy of combustion of glucose = - 2805 kJ / mol

Step 2:

W = m*g*h

with m = mass of the person in kg = 78.8 kg

with g = acceleration due to gravity = 9.81 m/s²

with h = height in meters = 1570 meters

W = 78.8 * 9.81 * 1570 = 1213653.96 J = 1.213 * 10^6 J

Step 3: Calculate actual work

Actual work = 4W = 4.85 * 10^6 J = 4.85 * 10³ kJ

Step 4: Calculate moles glucose

Moles glucose = work / standard enthalpy

Moles glucose = 4.85 * 10³ kJ / 2805 kJ/mol = 1.729 moles

Step 5: Calculate mass of glucose

Mass glucose = moles glucose * Molar mass glucose

Mass glucose = 1.729 moles * 180.16 g/mol

Mass glucose = 311.5 grams

The mass of glucose metabolized by a 78.8 kg person in climbing a mountain with an elevation gain of 1570 m, is 311.5 grams