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 following equation:
`CH_(4) +2O_(2) rarr CO_(2)+2H_(2)O , DeltaH =- 809 kJ`
How much gobar gas would have to be produced per day for a small village of `50` families, it it is assumed that each family requires `20000 kJ` of enegry per day? The methane content in gobar gas is `80%` by mass.

Explanation

Energy consumption of one family per day = 20,000kJ
Total number of families = 100
Energy consumption of 100 familes per day = `100xx20,000 = 2 xx 10^(6)` kJ.
The consumption of methane present in gobar gas may be written as : `CH_(4)(g) + 2O_(2)(g) to CO_(2)(g) + 2H_(2)O(g) + 809 kJ`
According to the equation, 890 kJ of energy is evolved from methane = 6g
`2 xx 10^(6)` kJ of energy will be evolved from methane = `(16)/(809) xx 2 xx 10^(6)g`
`= -3.96 xx 10^(4)g = 39.6 kg`
Since methane content of gobar fas is 80% by weight, therefore, Weight of gobar gas needed = `(39.6 xx 100)/(80) = 49.5 kg`