One in 4 600 water molecules contains a deuterium atom.If all the deuterium could be extracted from 1 m³ of water and then reacted,how much energy could be obtained? (Each D-D fusion liberates 3.65 MeV of energy,1 MeV = 1.6 × 10^-13 J,ρ_{water =} 10³kg/m³,one mole of water has a mass of 18 g,and N_A = 6.02 × 10²³) A)4.2E+12 J B)1.3E+25 J C)3.5E+11 J D)2.1E+12 J E)6.9E+14 J

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Quizplus · Accepted Answer

First, calculate the number of water molecules in 1 m³ of water. The mass of 1 m³ of water is 1000 kg, and since one mole of water has a mass of 18 g (0.018 kg), the number of moles in 1000 kg is 1000 / 0.018. The number of water molecules is then this value multiplied by Avogadro's number (6.02 × 10²³). So, the total number of water molecules is (1000 / 0.018) * 6.02 × 10²³. Since one in 4,600 water molecules contains a deuterium atom, the number of deuterium atoms (and thus D-D pairs since each reaction requires two deuterium atoms) is this total divided by 4,600. The energy per D-D fusion is 3.65 MeV, or 3.65 * 1.6 × 10⁻¹³ J. The total energy is then the number of D-D pairs times the energy per reaction. Following through with the calculations leads to the correct answer, which is approximately 2.1E+12 J.

One in 4 600 Water Molecules Contains a Deuterium Atom