Many evolutionary biologists have speculated whether or not Earth\'s vast oceans

Question

Many evolutionary biologists have speculated whether or not Earth's vast oceans were in fact the "primordial soup" from which life arose. Assume that the carbon in the biomass on Earth makes up 6 times 10^14 kg. How diluted would this biomass be if it was spread over the Earth's ocean? Assume that the ocean water covers the entire Earth surface, 4 pi R^2, with R = 6 times 10^6m being the Earth's radius, and has a depth of 1 km everywhere. Next, assume that this biomass is instead contained in cells with an average concentration of 10^3 kg/m^3 and that the number ratio of oxygen to carbon is 3. What is then the carbon concentration? In which of the two cases is the carbon concentration higher? How many times? Assume that the reaction speed is proportional to the concentration. What does this imply for the "primordial soup" scenario outlined above?

Explanation / Answer

Ans. I. Volume of the ocean = Surface area of earth x depth

                                                = 4 p R2 x h

                                                = 4 (3.14) (6x 106 m)2 x 103 m                     ; [1 km = 103 m]

                                                = 4.5216 x 1517 m3

Concertation of carbon = Total carbon biomass / volume of ocean

                                    = 6 x 1014 kg / (4.5216 x 1517 m3)

                                    = 1.33 x 10-3 kg/ m3

                                    = 1.33 g/ 1000 L                           ; [1 kg = 1000 g ; 1 m3 = 1000 L]

                                    = 1.33 x 10-3 g/ L

Ans. II. Given,

Concertation of biomass in cell = 103 kg/ m3

            Molar ration is O : C = 3: 1

Sum of molar ration = 3+1 = 4. That is, for every 4 unit biomass (say, 4 kg mass), oxygen constitutes 3 unit and C constitutes 1 unit.

So,

            4 kg biomass has 1 kg Carbon

      Or, 1 kg    -           -     (1/4) kg carbon

     Or, 103 kg -           -     (1/4)x 103 kg carbon

                                                = 250 kg carbon

Now, concentration of C = Mass of carbon / volume specified

                                                = 250 kg / m3

                                                = 2.50 x 102 kg/ m3

Ans. III. Concertation of carbon in ocean = 1.33 x 10-3 kg/ m3

Concertation of carbon in cell = 2.50 x 102 kg/ m3

Relative abundance = [C] in cell / [C] in ocean

                                    = (2.50 x 102 kg/ m3) / (1.33 x 10-3 kg/ m3)

                                    = 1.87 x 105

                                    = 187000

Thus, [C] in cell is 187000 times greater than that of [C] in ocean.

Ans. IV. The extremely dilute concertation of carbon in the “primordial soup” implies that the reaction rate is very slow. Since, a cell has about 1/10th of a million times more concentrated than primordial soup, it could take very long time for the first cell to evolve in ocean.

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