In a gobar gas plant, gobar gas in obtained by bacterial fermentation of animal refuse. The main combustible gas present in the gobar is found to be methane `( 80%` by weight) whose heat of combustion is 809`kJ mol^(-1))` . How much gobar gas would have to produced per day for a village of 100 families, if the average consumption of a family is 20,000kJ per day to meet all its energy requirements .

Explanation

Total energy requirements for 100 families per day `= 20,000 xx 100kJ = 2 xx 10^(6) kJ`
Methane `(CH_(4))` undergoes combustion as follows `:`
`CH_(4)(g) rarr 2O_(2)(g) rarr CO_(2)(g) + 2H_(2)O(l), Delta H = - 809 kJ mol^(-1)`
For 809 kJ of energy , `CH_(4)`required`=16g` ( Molar mass of `CH_(4) = 16 g mol^(-1))`
For ` 2 xx 10^(6)` kJ mol energy, `CH_(4)` required `(16)/(809) xx 2 xx 10^(6)g = 39.56kg`
As gobar gas contains `80%` by weight of methane , therefore gobar gas required `=(100)/(80) xx 39.56 kg`
`= 49.45kg`