In view of the problem of climate change, renewable sources of energy are being sought. An imaginative proposal is to use rubber (latex), which is a plant hydrocarbon, polyisoprene. Latex represents about 50% of the carbon fixed in photo synthesis by rubber trees! Presumably this material could be cracked and processed in refineries in a fashion analogous to that used for petroleum. Under good conditions, a rubber tree in Brazil can produce 10 kg of usable latex per year, growing at a density of about 250 trees per hectare. The heat of combustion (fuel value) of hydrocarbons is about 644 kJ mol-1 of CH2 or about 46,000 kJ kg-1.
a. What fraction of a year’s solar energy is stored in rubber crop if the incident solar energy is 43 kJ min-1 m2 and the Sun is shining 500 min on the average? [Compare your answer with the value energy stored/solar energy = 0.3 that can be obtained from photosynthesis in the laboratory under optimal conditions.]
b. In 2011 the total fossil fuel consumption in the United States was 24 X 1016 kJ/year. What fraction of the area of the United States (4.74 X 108 hectares) would have to be devoted to growing rubber trees (if they would grow in the climate of the United States, which they will not) to replace our present sources of fossil fuel by latex?
c. In laboratory experiments, it is found that photosynthesis occurs optimally with about 3% CO2in the (artificial) atmosphere. CO, occurs at only 0.03% in the natural atmosphere. Propose a scheme for increasing the energy yield of agricultural crops (not necessarily rubber trees) based on this observation. List some possible additional advantages and disadvantages of your scheme, based on your background in kinetics and thermodynamics.
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