A gobar gas plant produces methane and supplies to the families. If a family requires 15000 kJ of energy per day, how many days will the quota of 20 kg will last `(Delta_(c) H of CH_(4) = -1665 kJ mol^(-1)`).

Explanation

To solve the problem, we need to determine how many days a quota of 20 kg of methane (CH₄) will last for a family that requires 15,000 kJ of energy per day. We will use the given enthalpy change of combustion for methane (ΔH = -1665 kJ/mol) to find the total energy produced by 20 kg of methane.

### Step-by-Step Solution:

1. **Calculate the number of moles of methane in 20 kg:**
- The molar mass of methane (CH₄) is calculated as follows:
\[
\text{Molar mass of CH}_4 = 12 \, \text{g/mol (C)} + 4 \times 1 \, \text{g/mol (H)} = 16 \, \text{g/mol}
...