Question

13.10 A sample of dried feedlot manure is being tested for use as a fuel. The mass analysis of the sample is \(42.7 \%\) carbon, \(5.5 \%\) hydrogen \(\left(\mathrm{H}_{2}\right), 31.3 \%\) oxygen \(\left(\mathrm{O}_{2}\right), 2.4 \%\) nitrogen \(\left(\mathrm{N}_{2}\right)\), \(0.3 \%\) sulfur, and \(17.8 \%\) noncombustible ash. The sample is burned completely with \(120 \%\) of theoretical air. Determine (a) the balanced reaction equation. (b) the air-fuel ratio on a mass basis.

Short answer

Balanced combustion equation and air-fuel ratio calculation based on the 120% excess air assumption.

Step-by-step solution

Write the combustion equation

Start by writing the general combustion equation for a hydrocarbon with the given mass percentages. We assume 1 kg of dried feedlot manure as the basis. The equation for complete combustion will look like this:

Convert mass percentages to mass in kg

Convert the percentages to masses by assuming 1 kg of feedstock:

Convert masses to moles

Next, convert the masses of each element to moles.

Sum the moles of air required theoretically

Calculate the total moles of air required for complete combustion on theoretical basis.

Implement 120% excess air

Adjust for 120% excess air by multiplying the moles of air by 1.2.

Write the balanced reaction equation

Include the adjusted moles of O2 in the balanced combustion equation. The balanced reaction equation is: Combustion equation including all elements along with 120% excess air.

Calculate the mass basis air-fuel ratio

Finally, calculate the air-fuel ratio by using the balanced equation and mass basis.

Key concepts

Introduction to Mass Analysis in Combustion Reactions

Mass analysis is a crucial step when dealing with combustion reactions. It involves determining the mass fractions of different components in a fuel. This is particularly important for understanding the energy potential and combustion characteristics of the fuel. In our problem, the dried feedlot manure was analyzed, and its mass composition was found to be: 42.7% carbon, 5.5% hydrogen, 31.3% oxygen, 2.4% nitrogen, 0.3% sulfur, and 17.8% noncombustible ash.
By assuming a basis of 1 kg of dried feedlot manure, we can convert these percentages into masses. For instance, 42.7% of carbon in 1 kg becomes 0.427 kg of carbon.
Converting mass percentages to actual masses enables us to further work with moles, which simplifies the computation of the combustion process and air requirements.

Understanding Theoretical Air Requirement

Theoretical air is the precise amount of oxygen needed for complete combustion of a given amount of fuel. It ensures that all the combustible elements in the fuel react fully with oxygen.
For our dried feedlot manure sample, we need to calculate the moles of oxygen required to combust each of the fuel's components: carbon, hydrogen, sulfur, and others.
The concept of theoretical air is foundational because it helps in determining how much oxygen (and therefore air) is necessary for complete combustion. This is also crucial in the design and optimization of combustion systems to ensure efficiency.

• Example: To combust 1 mole of carbon, 1 mole of oxygen is needed. For hydrogen, 0.5 moles of O2 per mole of H2.
• The total moles of oxygen needed are summed up to calculate the total air required theoretically.

Creating the Balanced Reaction Equation

A balanced reaction equation accounts for all atoms of reactants converting to products, ensuring mass conservation. For combustion reactions, this means accurately representing the conversion of fuel and oxygen to products like CO2, H2O, SO2, etc.
Starting from the masses and converting these to moles, we can structure the balanced combustion equation systematically. By including all the components like carbon, hydrogen, oxygen, sulfur, and adjusting for the air added, we get a complete picture of the combustion process.
In our problem, once the theoretical oxygen requirements were multiplied by 1.2 to account for 120% theoretical air, the balanced equation was formed incorporating the requisite excess oxygen. This follows the combustion principle that excess air helps ensure complete combustion of all fuel components.

Calculating the Air-Fuel Ratio

The air-fuel ratio (AFR) is a critical parameter in combustion reactions. It describes the amount of air needed per unit mass of fuel. The AFR ensures the correct proportioning of air to fuel, impacting combustion efficiency and emissions.
To determine the AFR on a mass basis, we use the balanced reaction equation from our previous step. The mass of air required includes oxygen as well as nitrogen (since air is roughly 21% O2 and 79% N2 by volume).

• First, calculate the mass of oxygen from the balanced equation.
• Then, convert this to the total air mass by considering the air composition (multiply the mass of O2 by about 4.76).

The final step involves dividing the total air mass by the mass of fuel to get the air-fuel ratio. For our example, this ratio provides insight into how much air is needed to completely combust 1 kg of dried feedlot manure, ensuring efficient and clean combustion.