A cylinder of indane gas contains 11.2 kg of butane.A normal family requires 25000 kJ energy per day for cooking.How long will the cylinder of gas last if the efficiency of combustion is 80%? (Heat of combustion of butane is 2658 kJ `mol^(-1)`).

Explanation

To solve the problem step by step, we will follow these calculations:

### Step 1: Calculate the molar mass of butane (C₄H₁₀)
- The molecular formula of butane is C₄H₁₀.
- Molar mass = (4 × atomic mass of C) + (10 × atomic mass of H)
- Atomic mass of C = 12 g/mol, atomic mass of H = 1 g/mol
- Molar mass of butane = (4 × 12) + (10 × 1) = 48 + 10 = 58 g/mol

**Hint:** Remember to use the correct atomic masses for each element when calculating molar mass.

### Step 2: Convert the mass of butane to grams
- Given mass of butane = 11.2 kg
- Convert kg to grams: 11.2 kg = 11.2 × 1000 g = 11200 g

**Hint:** Always convert units to the same system before performing calculations.

### Step 3: Calculate the number of moles of butane
- Number of moles = mass (g) / molar mass (g/mol)
- Number of moles of butane = 11200 g / 58 g/mol = 193.1 mol

**Hint:** The number of moles tells you how many times the reaction can occur based on the amount of substance you have.

### Step 4: Calculate the total heat produced from the combustion of butane
- Heat of combustion of butane = 2658 kJ/mol
- Total heat produced = number of moles × heat of combustion
- Total heat produced = 193.1 mol × 2658 kJ/mol = 513,268.58 kJ

**Hint:** Multiplying the number of moles by the heat of combustion gives you the total energy released.

### Step 5: Adjust for the efficiency of combustion
- Given efficiency = 80%
- Effective heat produced = total heat produced × efficiency
- Effective heat produced = 513,268.58 kJ × 0.80 = 410,614.86 kJ

**Hint:** Efficiency reduces the total energy available, so always account for it in your calculations.

### Step 6: Calculate the daily energy requirement
- Daily energy requirement = 25,000 kJ/day

**Hint:** Knowing the daily requirement helps determine how long the energy source will last.

### Step 7: Calculate the number of days the cylinder will last
- Number of days = effective heat produced / daily energy requirement
- Number of days = 410,614.86 kJ / 25,000 kJ/day = 16.4246 days

**Hint:** Dividing the total available energy by the daily requirement gives you the duration the energy will last.

### Final Answer
The cylinder of gas will last approximately **16.4 days**.

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