Chemistry-Hess’s law

Question

At the end of 2012, global population was about 7.0 billion people. What mass of glucose in kg would be n eeded to provide 1200 Cal/person/day of n ourishment to the global population for one year? Assume that glucose is metabolized entirely to CO2(g) and H2O(l) according to the foll owing thermoch emical equation:

C6H12O6(s)+6O2(g)⟶6CO2(g)+6H2O(l)ΔH∘=−2803kJ

My answer was 8.245x10^11kg but got it wrong.

Answer 1

7x10⁹ ppl x 1.2x10³ kcal/person = 8.4x10¹² kcal/day (assuming you meant Cal and not cal)

8.4x10¹² kcal/day x365 day/yr = 3.1x10¹⁵ kcal/yr

Changing this to joules: 3.1x10¹⁵ kcal/yr x 4.81 kJ/kcal = 1.5x10¹⁶ kJ/yr

1 mol glucose provides 2803 kJ

mol glucose needed = 1.5x10¹⁶ kJ x 1 mol glucose/2803 kJ = 5.4x10¹² moles of glucose

mass glucose needed = 5.4x10¹² mol x 180 g/mol x 1 kg/1000 g = 9.7x10¹¹ 

This answer is very close to what you got. I did a lot of rounding and used only 2 sig figs based on the sig figs in 7.0 billion people.

PS. I don't think this is really an example of Hess' Law, but that's beside the point.