In order to get maximum calorific output a burner should have an optimum fuel to oxygen ratio which corresponds to three times as much oxygen as is required theorectically for complete combusion of the fuel A burner which has been adjused for methane as fuel (with `x L h^(-1)` of `CH_(4)` and `6x Lh^(-1) of CO_(2))` is to be readjusted for butane `C_(4)H_(10)` in order to get the same calorific output what should be the rate of supply to butane and oxygen? Assume that losses due to incomplete combustion etc are the same for both fuels and that the gases behave ideally Heats of combusion
`CH_(4) =809 kJ mol^(-1),C_(4)H_(10) =2878 kJmol^(-1)` .

Explanation

At same temperature and pressure, equal volumes contain equal moles of gases.

Let `1.0L` of `CH_4` Contain ‘n’ mol
`implies x L "of" CH_(4) "contain" nx mol`
`implies ` Heat evolved in combustion by `x L CH_(4) = 809 nx kJ`
Now, `2878 kJ` energy is evolved from 1 mole `(1/n L) C_(4)H_(10)`
`implies 809 nx kJ` Energy will be evolved from `(809 nx)/(2878n) L "of" C_4H_(10)` of ` = 0.28 x L "of" C_4H_(10)`
Also, the combustion reaction of butane is `C_4 H_(10) + 13/2 O_(2) rarr 4CO_(2) + 5H_2O`
`implies` Rate of supply of oxygen `= 13/2 xx 0.28x xx 3 = 5.4t xL//h`.