One kilogram of high-grade coal produces about 2.8 x 10 4 kJ of energy when it i

Question

One kilogram of high-grade coal produces about 2.8 x 104 kJ of energy when it is burned. Fission of one mole of U-235 releases 1.9 x 1010 kJ. Calculate the number of kg of coal needed to produce the same amount of energy as the fission of 1 kg of U-235 (235.05g/mol). = 2.88*10^6

How many kilograms of sulfur dioxide (a major source of acid rain) are produced from the burning of the coal in above question, if the coal is 0.90% by mass sulfur?

Remember to use the relation between the mass of S in coal and the mass of SO2.

Explanation / Answer

1Kg U-235 = 1000 g

U 235 moles = mass/ molar mass = 1000 g/ 235.05 g/mol = 4.2544

Energy released = moles of U235 x energy released by 1mol U235

                     = 4.2544 x 1.9x10^10 KJ = 8.0834 x 10^10 KJ

1 Kg coal gives 2.8 x 10^ 4 KJ

hence to get 8.083 x 10^10 KJ   coal required = ( 8.0834x10^10) / ( 2.8x10^4) = 2.887 x 10^6 kg

cola is 0.9 % of S   , hence S mass = ( 0.9/100) x coal mass = ( 0.9/100) x 2.887x10^6 =25983 kg

S in grams = 25983000 g

S moles = mass of S / molar mass of S = 25983000 /32.065 = 810322.8

1S gives 1SO2 on oxidation , hence SO2 moles = 810322.8

SO2 mass = moles x molar mass of SO2 = 810322.8 x 64.066 = 51914139 g = 51914 kg

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