In order to get maximum calorific output a burner should have an optimum fuel to oxygen ratio which corresponds to 3 times as much oxygen as required theoretically for complete combustion of fuel. A burner which has been adjusted for methane as fuel (with x litre/hour of `CH_(4)` and 6x litre/hour of `O_(2)`) is to be readjusted for butane `C_(4)H_(10)`. In order to get some calorific output, what should be the rate of supply of butane and oxygen? Assume that losses due to incomplete combustion etc., are the same for both fuels and that gases behave ideally. Heals of combustion, `CH_(4) =-809 kJ//"mol", C_(4)H_(10) = -2878` kJ/mol.

Explanation

To solve the problem, we need to determine the rate of supply of butane (C₄H₁₀) and oxygen (O₂) for a burner that has been adjusted for methane (CH₄) combustion. We will follow these steps:

### Step 1: Write and Balance the Combustion Reactions

1. **For Methane (CH₄)**:
The balanced reaction for the combustion of methane is:
\[
\text{CH}_4 + 2\text{O}_2 \rightarrow \text{CO}_2 + 2\text{H}_2\text{O}
...