Question

13.9 A coal sample has a mass analysis of \(80.4 \%\) carbon, \(3.9 \%\) hydrogen \(\left(\mathrm{H}_{2}\right), 5.0 \%\) oxygen \(\left(\mathrm{O}_{2}\right), 1.1 \%\) nitrogen \(\left(\mathrm{N}_{2}\right), 1.1 \%\) sulfur, and the rest is noncombustible ash. For complete combustion with \(120 \%\) of the theoretical amount of air, determine the air-fuel ratio on a mass basis.

Short answer

The air-fuel ratio is obtained by evaluating the combustible components, calculating the required air for combustion, and adjusting for 120% theoretical air.

Step-by-step solution

- Determine the combustible fraction of the coal

Sum the percentages of the combustible elements: carbon, hydrogen, oxygen, nitrogen, and sulfur.

- Determine the noncombustible ash

Calculate the noncombustible ash percentage by subtracting the sum of the combustible elements from 100%.

- Calculate the theoretical air required for complete combustion

Use the combustion reaction stoichiometry to find the amount of air needed for the combustion of 1 kg of coal.

- Adjust for the given 120% of theoretical air

Multiply the theoretical air requirement by 1.2 to account for the 120% of the theoretical air.

- Calculate the air-fuel ratio

Divide the total mass of air (from Step 4) by the mass of the coal (1 kg) to obtain the air-fuel ratio.

Key concepts

Air-Fuel Ratio

The air-fuel ratio (AFR) is a critical concept in combustion calculations. It refers to the ratio of the mass of air required for burning a unit mass of fuel. In simpler terms, it tells us how much air is needed to burn the fuel completely. It's crucial to understand that different fuels require different amounts of air for efficient combustion. The calculation often starts with determining the mass of the combustible elements in the fuel. From there, you assess the theoretical air needed for complete combustion (stoichiometric air), and then adjust it for practical scenarios where excess air is supplied.

In our exercise, we calculate the theoretical air and then increase it by 20% to ensure complete combustion. This gives us the total air required. Finally, the air-fuel ratio is derived by dividing this total air mass by the mass of the fuel.

Stoichiometry

Stoichiometry plays a key role in combustion calculations. It deals with the quantitative relationships between reactants and products in a chemical reaction. When it comes to combustion of coal, stoichiometry helps us determine the exact amount of oxygen (from air) needed to react with the fuel's elements, mainly carbon, hydrogen, and sulfur.

By applying stoichiometric principles, we establish balanced chemical equations that show the ideal proportions of reactants. For example, carbon reacts with oxygen to produce carbon dioxide as shown in the equation:

This analysis ensures that we achieve complete combustion without leftover fuel or oxygen. In practical applications, we use stoichiometry to calculate the theoretical air needed, which is then adjusted for actual conditions.

Complete Combustion

Complete combustion occurs when a fuel burns in the presence of ample oxygen, ensuring all combustible elements react fully. This process yields products like carbon dioxide (CO₂) and water (H₂O), with no leftover fuel or partially oxidized elements.

In our example, we assume complete combustion by providing 120% of the theoretical air. This excess air ensures that every bit of the fuel reacts efficiently. Without sufficient oxygen, we would have incomplete combustion, leading to soot or carbon monoxide (CO) formation, which are both undesirable.

Complete combustion is essential for maximizing energy output and minimizing pollutants. In our calculation, we account for all the contained elements like carbon, hydrogen, and sulfur to form CO₂, H₂O, and SO₂ respectively, ensuring full oxidization of the coal components.

Mass Analysis

Mass analysis involves studying the percentages of different elements within the fuel. In this case, a coal sample is broken down into its core components: carbon, hydrogen, oxygen, nitrogen, sulfur, and ash. This elemental breakdown is crucial for accurate combustion calculations.

By understanding the mass percentages, we determine the total combustible and noncombustible parts of the sample. For example, if the coal contains 80.4% carbon, it shows a significant amount of material that will engage in combustion. The noncombustible ash, derived from subtracting the sum of combustible elements from 100%, doesn't participate in the combustion process but remains as residue.

This detailed analysis helps us accurately predict the amount of air needed for burning, ensuring our calculations for the air-fuel ratio are precise and based on the true composition of the fuel.