Question

In: Chemistry

Calculate the mass of glucose metabolized by a 53.6 kg person in climbing a mountain with...

Calculate the mass of glucose metabolized by a 53.6 kg person in climbing a mountain with an elevation gain of 1610 m . Assume that the work performed in the climb is four times that required to simply lift 53.6 kg by 1610 m .

Solutions

Expert Solution

Solution :-

mass of person = 53.6 kg

formula to calculate the work is

W= m*g*h

g= gravity

w= 53.6 kg * 9.80 m per s2 * 1610 m

w =8.457*10^5 J

actual work is 4 times

therefore w total = 8.457*10^5 J * 4 = 3.383*10^6 J

now lets convert joules to kJ .

3.383*10^6 J * 1 kJ / 1000 J = 3383 kJ

so the amount of energy required = 3383 kJ

Now lets calculat the mass of the glucose

standard enthalpy of the combustion of glucose is -2805 kJ per mol

means it gives 2805 kJ energy

now lets calculate the moles of the glucose for the 3383 kJ

3383 kJ * 1 mol / 2805 kJ = 1.206 mol glucose

now lets convert the moles of glucose to its mass

mass = moles * molar mass

mass of glucose = 1.206 mol * 180.16 g per mol

                        = 217 g glucose

Therefore the mass of glucose metabolized = 217 g


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