The metabolism of glucose, C 6 H 12 O 6 , yields carbon dioxide, C O 2 ( g ) , a
ID: 824673 • Letter: T
Question
The metabolism of glucose, C6H12O6, yields carbon dioxide, CO2(g), and water, H2O(l), as products. Energy released in this metabolic process is converted to useful work, w, with about 76.0% efficiency. Use the data below to answer questions about the metabolism of glucose.
Calculate the mass of glucose metabolized by a 76.3kg person in climbing a mountain with an elevation gain of 1590m . Assume that the work performed in the climb is four times that required to simply lift 76.3kg by 1590m .
Substance ?H?f(kJ/mol) CO2(g) ?393.5 C6H12O6(s) ?1273.3 H2O(l) ?285.8 O2(g) 0
Explanation / Answer
The /H values are heats of formation.
In summary, you are to find:
C6H12O6 + 6O2 ===> 6CO2 + 6H2O /H = ?
You need C6H12O6 on the left and C, H2, and O2 on the right, so write the heat of formation of C6H12O6 backwards and reverse the sign:
C6H12O6 ===> 6C+ 6H2 + 3O2 /H = -1273.3 kJ/mol
You need 6CO2on the right, so multiply the heat of formation of CO2 by 6:
6C + 6O2 ===> 6CO2 /H = 6 x -393.5 = -2373 kJ/mole
You need 6H2O on the right, so multiply the heat of formation of H2O by 6:
6H2 + 3O2 ===> 6H2O /H = 6 x -285.8 = -1714.8 kJ/mole
Next, add up all of the new equations, cancel C's, H2's, and O2's on each side, and add up the /H's.:
C6H12O6 + 6O2 ===> 6CO2 + 6H2O /H = -1273.3 -2373 - 1714.8 = -5361.1 kJ/mole
Now assume 72.0% efficiency in converting energy to useful work. Let energy be called E. Let work be called W. Let glucose be called G.
-5361kJE/mole x 72kJW/100kJE = -3860kJW/mole
Atomic weights: C=12, H=1, O=16, C6H12O6=180
-3860kJW/mole x 1molG/180gG = 21 kJ/g glucose
Next, you are to calculate the work carried out by a 61.4 kg person (not 61.4g!) ascending by 1790 m. That would be 61.4 x 1790 = 109,906 m-kg. But you are supposed to multiply that by 4, which is 439,624 m-kg. So you are to finish the problem by calculating how many kJ is 439,624 m-kg, and multiplying that by 1gGlucose/21kJ to find the mass of glucose called for.
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