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 50 families per day
`=50xx20,000kJ=1xx10^(6)kJ`
809 kJ of energy is obtained by burning methane=16g
`1xx10^(6)kJ` of energy will be obtained by burning methane
`=(16)/(809)xx10^(6)=1.98xx10^(4)g`
`=19.8kg`
Since, methane content in gobar gas is 80% by mass, hence, the mass of gobar gas needed
`=(100)/(80)xx19.8=24.75kg`