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:

a) Verify the stoichiometry, then calculate the standard enthalpy of degradation of “one mole of manure” at standard conditions.

b) Calculate the reaction enthalpy for methane formation near the top of a landfill on a hot summer day in Houston, Texas (55o C 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 (5o C 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) H° = ( × Hf°) (products) - ( × Hf°) (reactants)

= [(3.125 x (-393.5)) + (3.875 x(-74.8))] - [(1 x (-208.5)) + (2.25 x(-285.6))] = - 1519.54 - (- 851.1) = - 668.44 kJ.

b) Since, Cp = a + bT + (C/T2 ) Thus, we have H°T2 - H°T1 = integration over T1 to T2 (CpdT)

= a (T2 - T1 ) +(1/2)(b)( T2 2 - T2 1 ) -(c)[ (1/T2 ) - (1/T1 )] . This is Kirchoff's Law

Using this equation we can calculate the enthalpy change at one temperature from the enthalpy change at another temperature.

where a, b and c are the difference between a, b and c values of the products and the reactants.

These values are not given here.

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