GATE 2019 CE (CE2) – Question 51

Air Pollution and Municipal Solid Wastes · Municipal solid wastes: generation, collection, transportation and management · 2 marks · Numerical answer

Raw municipal solid waste contains 70% decomposable material convertible to methane. Its water content is 35%. Dry decomposable matter has mass percentages C:H:O:N:other = 44:6:43:0.8:6.2. Methane production follows $$\mathrm{C_aH_bO_cN_d}+n\mathrm{H_2O}\to m\mathrm{CH_4}+s\mathrm{CO_2}+d\mathrm{NH_3}.$$ Atomic masses are C = 12, H = 1, O = 16, N = 14. Find methane production (g) per kg raw MSW, to one decimal place.

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Correct answer: 135 to 140

Explanation

Dry decomposable mass in 1 kg raw waste is $1000(0.70)(0.65)=455$ g. Per 100 g dry matter, atom amounts are $a=44/12$, b = 6, $c=43/16$ and $d=0.8/14$ mol. Balancing the reaction gives $$m=\frac a2+\frac b8-\frac c4-\frac{3d}8=1.89003\ \mathrm{mol}.$$ Methane mass is $1.89003(16)(455/100)=$ **137.6 g**. The inert other fraction does not contribute.