In: Chemistry
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 .
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