Gobar gas obtained by bacterial fermentation of animal refuse contains mainly methane. The heat of combustion of methane to `CO_2` and water (gas) is given by
`CH_4(g) + 2O_2(g) to CO_2(g) + 2H_2O (g) + 809 kJ`.
How much gobar gas would have to be produced per day for a small village community of 100 families, if we assume that each family has to be supplied 20,000 kJ of energy per day to meet all its needs and that the methane content in gobar gas is 80% by weight?

Explanation

To solve the problem, we need to determine how much gobar gas is required to meet the energy needs of a village community of 100 families, given that each family requires 20,000 kJ of energy per day and that the methane content in gobar gas is 80% by weight.

### Step-by-Step Solution:

1. **Calculate Total Energy Requirement:**
Each family requires 20,000 kJ of energy per day. For 100 families:
\[
\text{Total Energy} = 100 \times 20,000 \text{ kJ} = 2,000,000 \text{ kJ} = 2 \times 10^6 \text{ kJ}
...