C102B
Problem of the Week (ANSWERS)
20–24 January, 2003
Global Energy Use
The world’s energy consumption is so large that it is often measured in exajoules (EJ; 1 EJ = 1 x 1018
J). For example, a few rough figures related to energy use are the following:
Annual U.S. energy consumption
Annual world energy consumption
Estimated world oil resources
Estimated word coal resources
“Doubling time” for world energy consumption
90 EJ/year
410 EJ/year
10,000 EJ
> 300,000 EJ
< 20 years
(Note that for describing world oil and coal resources, the even larger zettajoule (1021 J) would be appropriate.)
1. Write a balanced equation for the combustion of octane, C8H18 (mw = 114.2 g mol–1), an important component of gasoline.
2 C8H18 + 25 O2 Æ 16 CO2 + 18 H2O
2. Using the following heats of formation, calculate the enthalpy of combustion of octane in kJ
mol-1. DHf (C8H18) = –249.9 kJ mol-1; DHf (CO2) = –393.5 kJ mol-1; DHf (H2O) = –285.8 kJ mol-1.
[16(–393.5) + 18(–285.8)] – [2(–249.9) + 25(0)] = –10,940 kJ (total), or –5470 kJ mol–1
3. Given that the density of gasoline is approximately 2.80 kg/gallon, calculate the annual energy
consumption for an automobile, if 10,000 miles are driven per year, and gasoline mileage is 20 miles
per gallon.
(10,000 miles/20 miles/gallon)(2.80 kg/gal) = 1400 kg octane (gasoline) /yr
(1400 kg/yr)(1000 g/1 kg)(1 mol/114.2 g)(5470 kJ/mol) = 6.71 x 107 kJ/yr
4. Estimate the number of years that the world’s oil reserves could power a fleet of a billion such
vehicles, neglecting other major uses such as power plants and aviation fuel.
(6.71 x 107 kJ/yr)(1 x 109 cars) = 6.71 x 1016 kJ/yr = 6.71 x 1019 J/yr = 67.1 EJ/yr
10,000 EJ/67.1 EJ/yr = 149 years
5. Could combustion contribute directly to global warming? If the annual world energy consumption were all due to combustion and directed towards warming the oceans (cs = 4.18 J K-1 g-1 for
water, oceanic volume ~1.4 x 109 km3, density of water ~1 kg/L), what would the yearly temperature rise be?
ocean volume = 1.4 x 109 km3 x (103 m/1 km)3 x (103 L/m3) = 1.4 x 1021 L
ocean mass = (1.4 x 1021 L)(1 kg/L)(1000 g/1 kg) = 1.4 x 1024 g
DT = q/mcs;
(410 x 1018 J/yr)/(1.4 x 1024 g)(4.18 J K-1 g-1 )
= 7 x 10–5 deg (not a significant difference)
6. Could combustion activity significantly affect atmospheric CO2 levels? At present, about 98% of
world energy consumption is from combustion. Estimate annual CO2 evolution in a rough way (e.g.,
assume all combustion is from octane) and compare with the present atmospheric CO2 content of
about 370 ppm, which is roughly 6.6 x 1016 moles.
0.98(410 x 1018 J) = 402 x 1018 J/yr = 402 x 1015 kJ/yr from combustion
402 x 1015 kJ /(5470 kJ mol–1) = 7.35 x 1013 mol octane; every mole of octane burned generates 8 moles of CO2; hence 8 x (7.35 x 1013 mol) = 5.9 x 1014 moles/yr; this is 0.9% of
the total CO2 content. Over time, this addition rate would become significant (within 20
years, the rate of addition would double, to 1.2 x 1015 mol/yr.)