Question

A typical frostless refrigerator uses 655 kWh of energy per year in the form of electricity. Suppose that all of this electricity is generated at a power plant that burns coal containing 3.3% sulfur by mass and that all of the sulfur is emitted as SO2 when the coal is burned.

If all of the SO2 goes on to react with rainwater to form H2SO4 , what mass of H2SO4 is produced by the annual operation of the refrigerator? (Hint : Assume that the remaining percentage of the coal is carbon and begin by calculating ΔH∘rxn for the combustion of carbon.)

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Answer 1

E = 655 kWh/year

S --> 3.3%

S + O2 --> SO2

H2O + SO2 = H2SO4

find mass of H2SO4 produced

Assume

C + O2 --> CO2 dH = - 393.509 kJ/mol

calculate moles of C required for

basis -- 1 year

so, total energy required:

E = 655 kWh 3.6*10^6 J/ kWh = 2358000000 J required

E = 2358000000/1000 = 2.358*10^6 kJ

then...

n = Total E / E rxn = (2.358*10^6)/(393.509 ) = 5992.23 kmol of C required

mass of C --> 5992.23*12 = 71906.76 kg of C required

since fuel is (100-3.3) carbon

find Sulfur by mass...

71906.76/(1-0.033)*0.033 = 2453.90 kg of Sulfur

change to mol

MW of S = 32 g/mol = 32 kg/kmol

mol of S = 2453.90 kg / 32 kg /mol = 76.684 kmol of S

1 kmol of S --> 1 kmol of SO2

1 kmol fo SO2 --> 1 kmol of H2SO4

then

total mol of H2SO4 = 76.684 kmol

total mass of H2SO4 = 76.684*98 kg/kmol = 7515.032 kg of H2sO$ produced