(1)

(2)

Number of moles of iron entering and leaving the furnace

Number of moles of carbon in gas phase + number of moles of carbon in Fe

(3)

By 2 and 3

(4)

Similarly oxygen balance    
 

(5)

Number of moles of oxygen entering

(6)

Where moles of entering through air and  moles of oxygen with  as the case may be

Since all oxygen leaves as

(7)

By 6 and 7.

(8)

depends on incoming iron oxide and outgoing gases, for example

 .

Of the total carbon charged in the blast furnace a fraction reacts with oxygen and this carbon is called active carbon ()and the rest fraction dissolves in iron and this carbon is termed as inactive carbon. In equation 8 () corresponds to the carbon which has reacted with oxygen and exited the furnace; and hence equal to (). With this argument equation 8 modifies to 

(9)

Note that