Anaerobic digestion of solid waste in landfills is a major generator of methane

Question

Anaerobic digestion of solid waste in landfills is a major generator of methane in the atmosphere, which is thought to be a major contributor to climate change as a greenhouse gas. Landfills exist all over the country, and at a wide range of temperatures. We can use manure as a model compound to determine the heat production in a landfill. The equation for anaerobic degradation of manure (neglecting nitrogen content) catalyzed by micro-organisms is as follows: C_7H_11O_4 + 2.25H_2O Implies 3.125CO_2 + 3.875CH_4 Required Data table for calculations Verify the stoichiometry, then calculate the standard enthalpy of degradation of "one mole of manure" at standard conditions. Calculate the reaction enthalpy for methane formation near the top of a landfill on a hot summer day in Houston, Texas (55degree Celsius inside the landfill). Does the reaction generate more or less heat per mole of methane formed than it does in a landfill on a cold winter day in Seneca County, NY (5degree Celsius inside the landfill, though colder outside)? Calculate both reaction enthalpy values per mole of methane formed. Assume that the gases do not dissolve in the liquid.

Explanation / Answer

a) The balanced chemical equation would be,

C7H11O4 + 2.25H2O ---> 3.125CO2 + 3.875CH4

standard enthalpy

dHo = dHo(products) - dHo(reactants)

        = (3.15 x -393.5 + 3.875 x -74.8) - (-208.5 + 2.25 x -285.6)

        = -1529.375 + 851.1

        = -678.275 kJ/mol

b) Cp(rxn) = Cp(products) - Cp(reactants)

                 = [(3.15 x 0.846 + 3.875 x 2.2) - (1.71 + 2.25 x 4.18)] x 55

                 = [11.1899 - 11.1115] x 55

                 = 4.312 kJ/kg.oC

dH at 55 oC = -678.275 + 4.312 = -673.963 x 3.875 = -2611.607 kJ/mol of methane

dH at 5 oC = -678.275 + 0.392 = -677.883 = -2626.8797 kJ/mol of methane

So the amount of heat generated per mole of methane at 5 oC is greater than heat generated at 55 oC.

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