The standard enthalpy change involved in the complete metabolic oxidation of glucose ($ ext{C}_6 e

Question

The standard enthalpy change involved in the complete metabolic oxidation of glucose ($	ext{C}_6	ext{H}_{12}	ext{O}_6$) is $-2880	ext{ kJ mol}^{-1}$. Exactly $25\%$ of this released metabolic energy is harnessed and made available for muscular work. If $100	ext{ kJ}$ of muscular work is required to walk a distance of one kilometer, calculate the maximum distance (in $	ext{km}$) that a person can walk after consuming $120	ext{ g}$ of glucose.

Professor PC Thomas Classes · Answer

The molar mass of glucose ($	ext{C}_6	ext{H}_{12}	ext{O}_6$) is $6(12) + 12(1) + 6(16) = 180	ext{ g mol}^{-1}$. The number of moles of glucose consumed is $n = 120	ext{ g} / 180	ext{ g mol}^{-1} = 2/3	ext{ mol}$. The total metabolic energy released upon oxidation of this quantity of glucose is $E_{	ext{total}} = (2/3	ext{ mol}) 	imes 2880	ext{ kJ mol}^{-1} = 1920	ext{ kJ}$. Since only $25\%$ of this energy can be converted into mechanical muscular work, the useful energy available is $E_{	ext{useful}} = 0.25 	imes 1920	ext{ kJ} = 480	ext{ kJ}$. Given that walking $1	ext{ km}$ requires an expenditure of $100	ext{ kJ}$ of work, the maximum distance that can be covered is $D = E_{	ext{useful}} / 100	ext{ kJ km}^{-1} = 480 / 100 = 4.8	ext{ km}$.