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 `-899kJ mol^(-1)` according to followinf 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

Enegry consumption of `50` families per day
`= 50 xx 20000 kJ = 1 xx 10^(6)kJ`
`809 kJ` of enegry is obtained by buring methane `= 16 g`
`1 xx 10^(6) kJ` of energy will be obtained by buring methane
` = (16)/(809)xx10^(6) = 1.98 xx 10^(4) g = 19.8 kg`
Since methane content in golar gas is `80%` by mass, hence, the mass of gobar has needed
`= (100)/(80) xx 19.8 = 24.75 kg`