Chapter 13: Problem 134
For the combustion of methane, \(150 \%\) theoretical air is used at \(25^{\circ} \mathrm{C}, 100 \mathrm{kPa}\), and relative humidity of \(70 \%\). Find the composition and dew point of the products.
Short Answer
Expert verified
The products include COâ‚‚, Hâ‚‚O, Oâ‚‚, and Nâ‚‚. Dew point corresponds to the partial pressure of water vapor at 13.08 kPa.
Step by step solution
01
Write the Balanced Chemical Equation
The combustion of methane (CHâ‚„) with air can be represented as follows: \[ \text{CH}_4 + 2(1 + x)(\text{O}_2 + 3.76\text{N}_2) \rightarrow \text{CO}_2 + 2\text{H}_2\text{O} + 2x\text{O}_2 + 7.52(1 + x)\text{N}_2 \]where 1 mole of CHâ‚„ reacts with air containing 21% Oâ‚‚ and 79% Nâ‚‚. Since the air is at 150% of the theoretical requirement, x = 0.5.
02
Determine Theoretical and Excess Air Requirements
The stoichiometric equation for the combustion of methane is:
CH₄ + 2O₂ → CO₂ + 2H₂O.
For stoichiometric combustion, 2 moles of Oâ‚‚ are required per mole of CHâ‚„. With 150% air, we have:
150% air = 2 × 1.5 = 3 moles of O₂ necessary.
03
Calculate Actual Oxygen Needed
Since the theoretical Oâ‚‚ requirement is 2 moles, the actual amount of Oâ‚‚ used will be:
O₂_actual = 2 O₂ × 1.5 = 3 moles.
04
Determine Amounts of Nâ‚‚ in the Air
The air consists of 79% nitrogen (Nâ‚‚), thus for every mole of Oâ‚‚, there are 3.76 moles of Nâ‚‚.
Therefore, with 3 moles of Oâ‚‚ from 150% theoretical air scenario:
N₂ = 3 moles O₂ × 3.76 moles N₂/mole O₂ = 11.28 moles N₂.
05
Calculate Composition of Combustion Products
From the combustion of 1 mole of CHâ‚„, the combustion products are:
- 1 mole of COâ‚‚
- 2 moles of Hâ‚‚O
- 3 - 2 = 1 mole of excess Oâ‚‚
- Excess Nâ‚‚ remains unreacted: 11.28 moles Nâ‚‚.
The overall composition is:
1 mole COâ‚‚, 2 moles Hâ‚‚O, 1 mole Oâ‚‚, and 11.28 moles Nâ‚‚.
06
Determine Partial Pressures and Dew Point
The total number of product moles is 1 + 2 + 1 + 11.28 = 15.28 moles.
Calculate partial pressures using the equation P_i = (n_i / n_total) × P_total = (n_i / 15.28) × 100 kPa.
The partial pressure of Hâ‚‚O = (2/15.28) * 100 kPa = 13.08 kPa.
Using steam tables or dew point tables for 13.08 kPa, find the dew point.
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Stoichiometric Combustion
In stoichiometric combustion, we aim to achieve complete combustion of a fuel with the exact amount of oxygen required. This ensures that all carbon in the fuel is converted to carbon dioxide (COâ‚‚) and all hydrogen is converted to water (Hâ‚‚O). For methane (CHâ‚„), the balanced chemical equation for stoichiometric combustion is expressed as: \[ \text{CH}_4 + 2\text{O}_2 \rightarrow \text{CO}_2 + 2\text{H}_2\text{O} \] This equation shows that 1 mole of CHâ‚„ requires 2 moles of oxygen (Oâ‚‚) to burn completely, producing COâ‚‚ and Hâ‚‚O.
Understanding stoichiometric combustion is crucial because it is the foundation for calculating both excess air and determining the components formed in combustion reactions.
Understanding stoichiometric combustion is crucial because it is the foundation for calculating both excess air and determining the components formed in combustion reactions.
Excess Air Calculation
Excess air is the extra air supplied beyond the stoichiometric requirement for complete combustion. It is given as a percentage over the theoretical air needed. In the exercise, 150% air is provided for methane combustion. This means an additional 50% air beyond what is theoretically required is available.
Here's how it's calculated: If the stoichiometric requirement for O₂ is 2 moles for burning CH₄, then 150% air implies 2 × 1.5 = 3 moles of O₂ are provided. The use of excess air helps ensure complete combustion in practical applications, compensating for inefficiencies and allowing for thorough mixing of air and fuel. It can also impact the composition of the combustion products by introducing more oxygen (O₂) into the system.
Here's how it's calculated: If the stoichiometric requirement for O₂ is 2 moles for burning CH₄, then 150% air implies 2 × 1.5 = 3 moles of O₂ are provided. The use of excess air helps ensure complete combustion in practical applications, compensating for inefficiencies and allowing for thorough mixing of air and fuel. It can also impact the composition of the combustion products by introducing more oxygen (O₂) into the system.
Dew Point Determination
The dew point is the temperature at which water vapor present in the air starts to condense into liquid water. In combustion processes, calculating the dew point of the products helps assess the risk of condensation and potential corrosion in exhaust systems.
In the original problem, the vapor pressure of water produced through combustion was found by calculating the partial pressure, using the ratio of moles of water to the total moles of products. Here, the partial pressure of Hâ‚‚O is 13.08 kPa. By consulting steam tables or dew point charts, this aids in identifying the exact dew point temperature for this pressure level, highlighting the practical aspect of ensuring that the exhaust system remains above the dew point to prevent condensation.
In the original problem, the vapor pressure of water produced through combustion was found by calculating the partial pressure, using the ratio of moles of water to the total moles of products. Here, the partial pressure of Hâ‚‚O is 13.08 kPa. By consulting steam tables or dew point charts, this aids in identifying the exact dew point temperature for this pressure level, highlighting the practical aspect of ensuring that the exhaust system remains above the dew point to prevent condensation.
Chemical Equation Balancing
Balancing chemical equations is like ensuring the 'books' of a reaction are settled; the numbers of each type of atom are the same on both sides of the equation. This is necessary to respect the law of conservation of mass, which implies that mass cannot be created or destroyed in chemical reactions.
For the methane combustion scenario, a balanced equation includes all reactants and products: \[ \text{CH}_4 + 2(1 + x)(\text{O}_2 + 3.76\text{N}_2) \rightarrow \text{CO}_2 + 2\text{H}_2\text{O} + 2x\text{O}_2 + 7.52(1 + x)\text{N}_2 \] Here, \( x \) represents the excess air factor. Balancing is accomplished by ensuring equal numbers of carbon, hydrogen, and oxygen atoms on each side, thus allowing us to compute the actual combustion products and evaluate any excess reactants.
For the methane combustion scenario, a balanced equation includes all reactants and products: \[ \text{CH}_4 + 2(1 + x)(\text{O}_2 + 3.76\text{N}_2) \rightarrow \text{CO}_2 + 2\text{H}_2\text{O} + 2x\text{O}_2 + 7.52(1 + x)\text{N}_2 \] Here, \( x \) represents the excess air factor. Balancing is accomplished by ensuring equal numbers of carbon, hydrogen, and oxygen atoms on each side, thus allowing us to compute the actual combustion products and evaluate any excess reactants.