A cylinder of gas is assumed to contain 11.2 kg of butane $ ( C_4 H_ {10} ) $. If a normal family needs 20000 kJ of energy per day. The cylinder will last : ( Given that for combustion of butane is - 2658 kJ )
First, calculate the total energy that can be provided by the 11.2 kg of butane. The molar mass of butane ( ext{C_4H_{10}}) is ext{58 g/mol}, so the number of moles in 11.2 kg is ext{11200 g / 58 g/mol = 193.1 mol}. The energy released per mole of butane is -2658 kJ, so the total energy available is ext{193.1 mol * 2658 kJ/mol = 513,679.8 kJ}. Given that a normal family needs 20000 kJ of energy per day, the number of days the cylinder will last is ext{513,679.8 kJ / 20000 kJ/day ≈ 25.68 days}. Since we are looking for an integer value, the closest option is 26 days.