# Energy and Greenhouse Gas (GHG) Calculations

How much Chemistry and Biology do you need to understand to estimate energy and greenhouse gas production? Very little.

The only chemical reactions that matter are as follows. I will treat the chemical composition of complex organic molecules in a very approximate manner. For example any long chain hydrocarbon (oil, gasoline, kerosene etc.) is essentially CH2 repeated n times. Likewise, carbohydrates (sugars, wood, pasta etc.) are CH2O repeated n times. Saturated fats, edible oils, and alcohols lie somewhere between the two. The amount of energy released by burning these compounds (either in a fire or in your stomach) depends almost entirely on the ratio of hydrogen and oxygen to carbon. The more hydrogen (oxygen) the more (less) energy:

$\textnormal{CH}_4 : 55 \textnormal{ MJ/kg} \nonumber$
$\textnormal{CH}_2 : \textnormal{42 to 45 MJ/kg for oil and gasoline, down to 38 MJ/kg for edible oils} \nonumber$
$\textnormal{CH}_2 \textnormal{O} : 16 \textnormal{ MJ/kg} \nonumber$

Plant life

Plants take sunlight, atmospheric carbon dioxide and water, and via photosynthesis produce carbohydrates and oxygen (Eqn.1)[1]Andrews, J. and Jelley, N. Basic biochemistry from an energy viewpoint. In: Energy Science – Principles, Technologies and Impacts. New York: Oxford University Press, 2007, Chapter 7..

CO2 + H2O + sunlight → CH2O + O2 $\tag{1}$

The efficiency of this process can be defined in several different ways, but if we take it to be the available energy from the carbohydrate divided by the total amount of energy incident on that piece of land averaged over the land (insolation, ‘sunfall’) throughout the year on the land used the grow it, the measured value is a tiny 0.5%.

Animal life

Animals eat carbohydrates and “burn” them to generate the mechanical energy required to breathe and move around (Eqn.2).

CH2O + O2 → CO2 + H2O + 16 MJ per kg of carbohydrate $\tag{2}$

In addition, plants do this at night and, of course, also when they burn. However, in general a living plant is a net generator of oxygen.

Anaerobic digestion

If, after death, plant and animal matter decays in the absence of oxygen, the following reaction takes place (Eqn.3).

2CH2O → CO2 + CH4 $\tag{3}$

This is important in two ways. The methane (CH4) produced is, molecule for molecule, more than 20 times more potent as a greenhouse gas (GHG) than CO2. On the other hand, if captured from say, a landfill site, the methane can be burned. The thermal yield (see problem below) is 92% of what one would have got from burning the original carbohydrates (which may be too damp to be burnable directly) and the combustions products are less of a GHG problem than the methane.

Human life

Humans do what animals do, of course. But this only generates about 100W of power per person (see problem below), which is not nearly enough to keep us in the manner to which we have become accustomed. The average Canadian needs 13 kW to stay comfortable, and this, for the most part, requires a serious amount of oil (approximately CH2), that burns as per Eqn.4.

2CH2 + 3O2 → 2CO2 + 2H2O $\tag{4}$

How to do energy and GHG calculations?

All calculations involving energy and GHG production can be done using simple mass ratios. The masses of oxygen, carbon and hydrogen atoms have the ratios 16:12:1. (Using these simple ratios is equivalent to invoking the chemists’ concept of moles, without actually doing so).

Q. How come two carbohydrate molecules (worth 16 MJ/kg) decay spontaneously into one methane molecule (worth 55 MJ/kg)?

A. The “per kg” bit is all important. Two carbohydrate molecules have a combined molecular mass of 60 (2 times 12+2+16), and one methane has a molecular mass of 16. Hence 60 kg of carbohydrates (worth 60 kg × 16 MJ/kg = 960 MJ) yields 16 kg of methane (worth 16 kg × 55 MJ/kg = 880 MJ).

Hence anaerobic digestion is exothermic, producing 960-880 = 80 MJ per 60 kg of carbohydrate, i.e. 1.3 MJ/kg.

More importantly for the issue of burning waste, 880/960 = 0.92, so 92% of the available energy in the carbohydrate ends up as available in the methane. Hence it is often more productive and easier to use the methane as fuel (it is a gas and can be piped to distant sites) than to dry out the original waste and burn it.

Q. Humans need 2000 food calories (kcal) per day to survive healthily. How does this compare to the statement above that we each generate 100 W?

A. A food calorie is 4.2 kJ, so 2000 kcal = 8.4 MJ. Each day has 60 s/min × 60 min/hr × 24 hr/day = 86 400 s. Dividing one by the other gives 8.4 × 106 J / 86 400 s = 97 W.

Q. One website says that human activity puts 10 billion tonnes (Gt) of carbon into the atmosphere each year. Another says we contribute 37 Gt[2] CO$_2$ Emissions in Reached an All-Time High in 2018, https://www.scientificamerican.com/article/co2-emissions-reached-an-all-time-high-in-2018/ [2019-10-15]. of carbon dioxide per year. Who is right?

A. Carbon has a atomic mass of 12, and CO2 has a molecular mass of 12 + 2 × 16 = 44. Hence 12 kg of carbon is contained in 44 kg of CO2. Likewise 10 Gt of carbon is contained in 10 × 44/12 $\approx$ 37 Gt of CO2.

Q. Canadians need 13 kW per capita for their lifestyle. If this all came from burning oil, what would our annual per capita output of CO2 be?

A. Burning oil is essentially CH2 + 3/2 O2 → CO2 + H2O. Using molecular masses we can see that 14 kg of oil produces 44 kg of CO2 . We also know that 1 kg of oil burns to produce 45 MJ (to take a ballpark figure). Hence 14 kg will produce 630 MJ and 44 kg of CO2.

A power consumption of 13 kW for one year requires (13 000 W)(3.15 × 107 s) = 4 × 1011 J or 4 × 105 MJ. The mass of oil required to produce this is (4 × 105 MJ)/(45 MJ/kg) = 8 900 kg or 8.9 tonnes, which burns to (44/14)(8.9 tonnes) = 28 tonnes of CO2.

In fact Canadians “only” produce 16 tonnes of CO2 per year*, because much of our power comes from greener sources than fossil fuels, namely hydro-electric dams and nuclear reactors[3] List of countries by CO$_2$ emissions, https://en.wikipedia.org/wiki/List_of_countries_by_carbon_dioxide_emissions [2019-10-15]..

* plus the equivalent of 6 tonnes CO2 per year in the form of other GHGs.

Updated (CEW) 2019-10-15

Footnotes   [ + ]

 1 ↑ Andrews, J. and Jelley, N. Basic biochemistry from an energy viewpoint. In: Energy Science – Principles, Technologies and Impacts. New York: Oxford University Press, 2007, Chapter 7. 2 ↑ CO$_2$ Emissions in Reached an All-Time High in 2018, https://www.scientificamerican.com/article/co2-emissions-reached-an-all-time-high-in-2018/ [2019-10-15]. 3 ↑ List of countries by CO$_2$ emissions, https://en.wikipedia.org/wiki/List_of_countries_by_carbon_dioxide_emissions [2019-10-15].