A given species of tree can sequester 2 kg of CO2/year·m^2 of planted area, in growing conditions where average sunlight makes available 100 W/m^2, taking into account the night/day and seasonal cycles, as well as variability in the weather. (a) How much energy is required to convert the CO2 via

Question

A given species of tree can sequester 2 kg of CO[latex]_2[/latex]/year·m[latex]^2[/latex] of planted area, in growing conditions where average sunlight makes available 100 W/m[latex]^2[/latex], taking into account the night/day and seasonal cycles, as well as variability in the weather. (a) How much energy is required to convert the CO[latex]_2[/latex] via photosynthesis into carbon that is sequestered? (b) What percentage of annual available energy is used for this conversion?

Accepted Answer

(a) First calculate the number of molecules of CO[latex]_2[/latex] in 2 kg, using Avogadro’s number, or 6.022 × 10[latex]^{23}[/latex]:

[latex]\frac{6.022 imes 10^{23} ext { molecules } / \mathrm{g} \cdot \mathrm{mol}}{44 \mathrm{~g} / \mathrm{g} \cdot \mathrm{mol} \mathrm{CO}_{2}}\left(1000 \frac{\mathrm{g}}{\mathrm{kg}} ight)(2 \mathrm{~kg})=2.74 imes 10^{25}[/latex]

The energy requirement is then (2.74 × 10[latex]^{25}[/latex])( 9.47 × 10[latex]^{-19}[/latex] J) = 2.59 × 10[latex]^{7}[/latex] J, or 25.9 MJ.

(b) The rate of energy transfer from the sun of 100 W/m[latex]^2[/latex] is equivalent to 100 J arriving each second.

Therefore, the energy available per year is:

[latex]100 \mathrm{~J} / \mathrm{s} imes\left(3600 \frac{\mathrm{s}}{\mathrm{h}} ight)\left(8760 \frac{\mathrm{h}}{ ext { year }} ight)=3.15 imes 10^{9} \mathrm{~J}[/latex]

The amount used in conversion of carbon of 25.9 MJ is therefore 0.822% of the arriving energy.

Discussion Note that some additional energy use in photosynthesis will have taken place to convert CO[latex]_{2}[/latex] to glucose for later use by the tree.

Because of the difficulties in accurately measuring in real time the rate of photosynthesis of trees in their natural habitat, it is difficult to measure exactly what percent of available energy in sunlight is converted to glucose in photosynthesis. Some estimates put the amount at 10 to 11%. Also, because of the relatively small percentage of energy that is actually channeled to sequestration, one fruitful area of research may be the development of trees, plants, and microorganisms that convert CO[latex]_{2}[/latex] more rapidly, and retain more of the carbon that they convert.

Question 7.1: A given species of tree can sequester 2 kg of CO2/year·m^2 o...

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