Question

In a Gobar gas plant, gobar gas is formed by bacterial fermentation of animal refuse. It mainly contains methane and its heat of combustion is $-809kJ$ ${mol}^{-1}$ according to the following equation:
${CH}_4+2O_2⟶{CO}_2+2H_{2}O;\Delta H=-809kJ$
How much gobar gas would have to be produced per day for a small village of $50$ families, if it is assumed that each family requires $20,000kJ$ of energy per day? The methane content in gobar gas is $80$% by mass.

Answer 1

Energy consumption of $50$ families per day
$=50\times 20,000kJ=1\times {10}^{6}kJ$
$809kJ$ of energy is obtained by burning methane$=16g$
$=\frac{16}{809}\times {10}^6=1.98\times {10}^{4}g$
$=19.8Kg$
Since, methane content in gobar gas is $80$% by mass, hence, the mass of gobar gas needed
$=\frac{100}{80}\times 19.8=24.75kg$