Combustion of Coal in a boiler

[raniero]

A quantity of coal used in a boiler had the following analysis: 82% C; 5% H; 6% O; 2% N; 5% ash. The dry flue gas analysis showed 14% CO2 and some oxygen. Calculate the oxygen content of the dry flue gas.

I have first written the formula for combustion including the variables for balancing the equation:

Considering 1kg of coal:

0.82/12 C + 0.05 H + 0.06/1 O + 0.02/14 N + x(0.233/32 O₂ + 0.767/28N₂) → B(0.14 CO₂ + a O₂ + (0.86-a) N₂)+ b H₂O

When balancing the equation this yields:

Carbon Balance: B = 0.4881

Hydrogen Balance: 0.05 = 2b → b =0.025

The problem I am encountering arises in the oxygen balancing:

Oxygen balance: 0.06/16 + x(0.233/32)2 = (0.14)2B + 2aB + b

The book's answer states: 0.06/16 + x(0.233/32) = (0.14)B + aB + b/2

How come the book's answer doesn't add double the amount of substance (kmol) as I did for Oxygen molecules?
Other answers from the book compensate by multiplying by two when molecules such as O₂ are present. Another disagreement I have with the solution is the 'b' divided by 2.

Thanks in advance

 

[Achy47]

for any help.

I am unable to comment on the specific answer provided by the book without further context or information. However, I can offer some general explanations for the differences in the answer.

Firstly, it is important to note that balancing chemical equations involves both mass and moles. In your calculation, you have correctly accounted for the mass of oxygen in the dry flue gas, but it is possible that the book's answer accounts for the moles of oxygen instead. This could explain the difference in the oxygen balancing equation.

Additionally, the book's answer may have divided the 'b' term by 2 in order to account for the fact that there are two oxygen atoms in each water molecule. This is a common practice in balancing equations, as it ensures that the number of atoms on each side of the equation is equal.

Overall, it is important to carefully consider the units and variables used in the equations, as well as the context of the problem, in order to arrive at the correct answer. If you are still unsure, it may be helpful to consult with a colleague or professor for further clarification.