Warning: foreach() argument must be of type array|object, bool given in /var/www/html/web/app/themes/studypress-core-theme/template-parts/header/mobile-offcanvas.php on line 20

\(13.49\) Liquid methanol \(\left(\mathrm{CH}_{3} \mathrm{OH}\right)\) at \(25^{\circ} \mathrm{C}, 1\) atm enters an insulated reactor operating at steady state and burns completely with air entering at \(100^{\circ} \mathrm{C}, 1 \mathrm{~atm}\). If the combustion products exit at \(1256^{\circ} \mathrm{C}\), determine the percent excess air used. Neglect kinetic and potential energy effects.

Short Answer

Expert verified
The combustion uses 200% excess air.

Step by step solution

01

- Write Balanced Chemical Equation

The balanced chemical equation for the complete combustion of methanol \(\text{CH}_3\text{OH} + \frac{3}{2}\text{O}_2 \rightarrow \text{CO}_2 + 2\text{H}_2\text{O} \) Each mole of methanol reacts with 1.5 moles of oxygen.
02

- Determine Theoretical Air Required

Using the balanced equation, each mole of methanol requires 1.5 moles of oxygen. Air is composed of about 21% oxygen by volume; thus, the moles of air required theoretically per mole of methanol is: \(\frac{1.5}{0.21} = 7.14 \text{ moles of air per mole of methanol} \)
03

- Use Given Conditions To Find Actual Air

Using the given conditions, we must first determine enthalpy change using standard enthalpy values. These values are usually found in thermodynamic tables. Use: Enthalpy of reactants and products meeting at standard reference states and the exit temperature of products being significantly higher.
04

- Calculate Mass and Energy Balances

Perform energy balances to find the actual air. This includes: \(Q-\text{ΔH}=0\) with \(Q= nCpΔT\) for actual air based on actual conditions. Using provided tables, calculate heat added to products from reactants.
05

- Calculate Actual Air-to-Fuel Ratio

Using the determined enthalpies from previous steps and applying air-to-fuel ratio principles. If specific heat capacities \(C_p\text{s}\) are available, calculate energy required and provided by air. Analytical calculation can involve iterating actual air assumption until solving \(Q-\text{ΔH}=0\).
06

- Determine Excess Air Percentage

Compare the actual air-to-fuel ratio to the theoretical air requirement determined in Step 2. This can be expressed as: \(\text{Excess Air} [\text{%}] = \frac{\text{Actual Air} - \text{Theoretical Air}}{\text{Theoretical Air}} \times 100\).
07

- Conclusion

Summarize the excess air value once energy balances offset correctly.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with Vaia!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Thermodynamics
Thermodynamics is the science of energy transfer and transformation. It deals with how energy moves and changes form. In a combustion process, thermodynamics helps us understand how fuel converts into heat and work.

Key principles include:
  • First Law of Thermodynamics: This is the law of energy conservation. It states that energy cannot be created or destroyed, only transformed from one form to another.
  • Second Law of Thermodynamics: This law states that energy processes have a preferred direction towards increasing entropy. This means energy will naturally disperse and spread out if not contained.

In combustion, understanding these principles helps us calculate the energy released from fuel and how it's transferred to the surroundings. For example, in our exercise, knowing the enthalpy changes for methanol combustion allows us to find out how much energy is released and how much air is needed for complete combustion.
Combustion Reaction
A combustion reaction is a chemical process where a substance reacts with oxygen, releasing heat and forming combustion products like carbon dioxide and water. In thermodynamics, we often focus on the energy changes during this reaction.

For methanol \(\text{CH}_3\text{OH}\), the balanced combustion equation is:

\(\text{CH}_3\text{OH} + \frac{3}{2}\text{O}_2 \rightarrow \text{CO}_2 + 2\text{H}_2\text{O}\)

This equation tells us that for every mole of methanol burned, 1.5 moles of oxygen are needed. The products are carbon dioxide and water.

By balancing the equation, we ensure mass conservation, meaning the amount of each element before and after combustion remains the same. This balance is crucial for calculating the air needed for combustion and determining excess air.

The combustion process can be complete or incomplete. In complete combustion, all fuel is converted to \(\text{CO}_2\) and \(\text{H}_2\text{O}\). Incomplete combustion can create byproducts like carbon monoxide, indicating not all fuel was burned due to insufficient oxygen.
Energy Balance
Energy balance involves accounting for all energy entering and leaving a system. It's essential for understanding how much energy is converted during a process.

In our problem, the energy balance of the combustion process can be represented by:

\(Q - \text{ΔH} = 0\)

Here, \(Q\) is the heat added or removed from the system, and \(ΔH\) is the change in enthalpy of the reactants and products.

We often use standard enthalpy values from thermodynamic tables to find \(ΔH\). For methanol combustion, the standard enthalpy change reflects the energy released when methanol burns completely.
  • Step 1: Identify the reactants and products.
  • Step 2: Use standard enthalpies to determine the energy change.
  • Step 3: Apply the first law of thermodynamics to balance the energy in and out.

By calculating the energy released (enthalpy change) and observing the energy required for the products to exit at a specific temperature, we can estimate the actual air needed and determine the excess air percentage.
Air-to-Fuel Ratio
The air-to-fuel ratio (AFR) is a critical concept in combustion. It measures the amount of air needed to completely combust a given amount of fuel.

The theoretical air-to-fuel ratio is calculated based on stoichiometry - the precise amount of air needed for complete combustion, derived from the balanced chemical equation. In our case, this is calculated as:

\( \frac{1.5 \text{ moles of } \text{O}_2}{0.21 \text{ (fraction of } \text{O}_2 \text{ in air)}} = 7.14 \text{ moles of air per mole of methanol} \)

This tells us that ideally, 7.14 moles of air are needed per mole of methanol for complete combustion. However, in real scenarios, we often use excess air.

Excess air is the additional air supplied beyond the theoretical requirement, ensuring complete combustion and minimizing pollutants like carbon monoxide.

To find the actual air-to-fuel ratio, we measure the actual air used and compare it to the theoretical ratio:
  • \( \text{Excess Air} [\text{%}] = \frac{\text{Actual Air} - \text{Theoretical Air}}{\text{Theoretical Air}} \times 100 \)

Using the energy balance, if more heat is observed or the products are expected to have higher energy, it implies excess air usage. Balancing actual measurements with theoretical predictions helps optimize combustion processes efficiently.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

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.

13.43 For a natural gas with a molar analysis of \(86.5 \% \mathrm{CH}_{4}, 8 \%\) \(\mathrm{C}_{2} \mathrm{H}_{6}, 2 \% \mathrm{C}_{3} \mathrm{H}_{8}, 3.5 \% \mathrm{~N}_{2}\), determine the lower heating value, in \(\mathrm{kJ}\) per \(\mathrm{kmol}\) of fuel and in \(\mathrm{kJ}\) per \(\mathrm{kg}\) of fuel, at \(25^{\circ} \mathrm{C}, 1 \mathrm{~atm}\).

13.1D The term acid rain is frequently used today. Define what is meant by the term. Discuss the origin and consequences of acid rain. Also discuss options for its control.

13.8D Fuel or chemical leaks and spills can have catastrophic ramifications; thus the hazards associated with such events must be well understood. Prepare a memorandum for one of the following: (a) Experience with interstate pipelines shows that propane leaks are usually much more hazardous than leaks of natural gas or liquids such as gasoline. Why is this so? (b) The most important parameter in determining the accidental rate of release from a fuel or chemical storage vessel is generally the size of the opening. Roughly how much faster would such a substance be released from a \(1-\mathrm{cm}\) hole than. from a 1 -mm hole? What are the implications of this?

13\. Why is combustion inherently an irreversible process?

See all solutions

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free