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

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