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Liquid methanol is fed to a space heater at a rate of \(12.0 \mathrm{L} / \mathrm{h}\) and burned with excess air. The product gas is analyzed and the following dry-basis mole percentages are determined: \(\mathrm{CH}_{3} \mathrm{OH}=0.45 \%\) \(\mathrm{CO}_{2}=9.03 \%,\) and \(\mathrm{CO}=1.81 \%\) (a) Draw and label a flowchart and verify that the system has zero degrees of freedom. (b) Calculate the fractional conversion of methanol, the percentage excess air fed, and the mole fraction of water in the product gas. (c) Suppose the combustion products are released directly into a room. What potential problems do you see and what remedies can you suggest?

Short Answer

Expert verified
The fractional conversion of methanol, percentage excess air, and the mole fraction of water in the product gas can be calculated using the provided data and applying chemical reaction stoichiometry and balance equations. However, releasing combustion products directly into a room can pose serious health and safety issues and hence, it is recommended to ensure proper safety measures and controls.

Step by step solution

01

Drawing and labelling the flowchart

First, identify the reactants and the products of the combustion reaction. Draw a flowchart where liquid methanol and air are fed into a space heater, and the products (methanol, carbon dioxide, and carbon monoxide) exit from the other end. Since all the reactants and their flow rate along with the products and their corresponding analysis is provided, this system has zero degrees of freedom.
02

Calculate fractional conversion of Methanol

The rate of methanol fed into the system is 12.0 L/h. Let's assume that fully combusted methanol gives only CO2 as the product. Under these conditions, look at the moles of CO2 produced. Since 0.45% of the product is unburned methanol (CH3OH), and 9.03% is CO2, then the remaining 90.52% must be made up of CO and unquantified products, most likely including water. The fractional conversion of methanol is then calculated as the moles of methanol converted (which can be inferred from CO2 produced) divided by the total moles of methanol fed into the system.
03

Calculate the percentage excess air

Calculate the stoichiometric air required for full combustion of methanol and compare it with the actual air supplied. The excess air percentage can be determined by the formula: \(excess\ air\%= \frac{(actual\ air\ supplied - stoichiometric\ air) x 100}{stoichiometric\ air}\)
04

Calculate mole fraction of water

Since water is also a combustion product, determine it based on the balance of the combustion equation. The mole fraction of water in the product gas can be calculated by dividing moles of water by the total moles of products.
05

Potential problems and recommendations

If the combustion products are released directly into a room, they may lead to serious health and safety issues. The presence of carbon monoxide (a poisonous gas), unburned methanol (a flammable substance), and excess heat can pose serious threats. It is highly recommended to ensure proper ventilation, heat insulation, and combustion control measures to mitigate these risks.

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Key Concepts

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

Fractional Conversion
Fractional conversion is a useful measure in chemical engineering and combustion processes. It tells us what proportion of a reactant is transformed into a product during a chemical reaction, such as the combustion of methanol. In the given problem, we know that liquid methanol (CH₃OH) is being fed into a space heater and burned. The analysis of the product gas shows 0.45% unburned methanol and 9.03% carbon dioxide (CO₂). Let's dive deeper:
  • The unburned methanol indicates the amount that hasn't reacted.
  • The COâ‚‚ proportion helps us understand the methanol that successfully underwent combustion.
To calculate the fractional conversion, you divide the moles of methanol converted into the intended products (mostly inferred from COâ‚‚ produced) by the total moles of methanol fed into the system. This provides a clear picture of the efficiency of the reaction.
Understanding fractional conversion is crucial as it helps in optimizing reaction conditions for better energy efficiency and reduced waste in industrial processes.
Excess Air Calculation
During combustion, air is needed to provide the oxygen required for the chemical reaction to proceed. Sometimes, more air than necessary – known as "excess air" – is supplied. This is often a strategy to ensure that all the fuel combusts.How do we calculate this? First, determine the stoichiometric air, which is the amount of air needed for complete combustion of methanol with no unburned fuel. In the problem, you'll compare this to the actual air supplied to find the excess air percentage. The formula goes like:\[excess\ air\% = \frac{(\text{actual air supplied} - \text{stoichiometric air}) \times 100}{\text{stoichiometric air}}\]This concept is important because:
  • Excess air ensures complete combustion, reducing pollutants like CO.
  • Too much excess air, however, can lead to thermal inefficiencies.
Balancing excess air in combustion systems boosts their efficiency and effectiveness – a key goal in both environmental and industrial contexts.
Health and Safety in Combustion
Combustion, while necessary for many industrial and residential heating applications, can also entail significant health and safety risks if not properly managed. Let's consider what happens when combustion products are released into a confined space like a room. The main health concern here is the presence of carbon monoxide (CO), a colorless, tasteless, and odorless gas resulting from incomplete combustion. It's poisonous and can be fatal if inhaled in large quantities. Furthermore:
  • Unburned methanol is a flammable substance and poses a fire risk.
  • Excess heat from combustion can also become a safety issue, potentially causing burns or triggering fires.
To prevent these hazards, it is crucial to ensure proper ventilation in areas where combustion occurs. This will dilute any harmful gases and lower the risk of fire. Implementing controls to maintain an appropriate combustion temperature and efficiency can also significantly reduce safety risks. Awareness and practical precautions go a long way in safeguarding health around combustion systems.

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Most popular questions from this chapter

Water enters a \(2.00-\mathrm{m}^{3}\) tank at a rate of \(6.00 \mathrm{kg} / \mathrm{s}\) and is withdrawn at a rate of \(3.00 \mathrm{kg} / \mathrm{s}\). The tank is initially half full. (a) Is this process continuous, batch, or semibatch? Is it transient or steady state? (b) Write a mass balance for the process (see Example 4.2-1). Identify the terms of the general balance equation (Equation 4.2-1) present in your equation and state the reason for omitting any terms. (c) How long will the tank take to overflow?

Effluents from metal-finishing plants have the potential of discharging undesirable quantities of metals, such as cadmium, nickel, lead, manganese, and chromium, in forms that are detrimental to water and air quality. A local metal-finishing plant has identified a wastewater stream that contains 5.15 wt\% chromium (Cr) and devised the following approach to lowering risk and recovering the valuable metal. The wastewater stream is fed to a treatment unit that removes \(95 \%\) of the chromium in the feed and recycles it to the plant. The residual liquid stream leaving the treatment unit is sent to a waste lagoon. The treatment unit has a maximum capacity of 4500 kg wastewater/h. If wastewater leaves the finishing plant at a rate higher than the capacity of the treatment unit, the excess (anything above \(4500 \mathrm{kg} / \mathrm{h}\) ) bypasses the unit and combines with the residual liquid leaving the unit, and the combined stream goes to the waste lagoon. (a) Without assuming a basis of calculation, draw and label a flowchart of the process. (b) Wastewater leaves the finishing plant at a rate \(\dot{m}_{1}=6000 \mathrm{kg} / \mathrm{h}\). Calculate the flow rate of liquid to the waste lagoon, \(\dot{m}_{6}(\mathrm{kg} / \mathrm{h}),\) and the mass fraction of \(\mathrm{Cr}\) in this liquid, \(x_{6}(\mathrm{kg} \mathrm{Cr} / \mathrm{kg})\) (c) Calculate the flow rate of liquid to the waste lagoon and the mass fraction of Crin this liquid for \(\dot{m}_{1}\) varying from \(1000 \mathrm{kg} / \mathrm{h}\) to \(10,000 \mathrm{kg} / \mathrm{h}\) in \(1000 \mathrm{kg} / \mathrm{h}\) increments. Generate a plot of \(x_{6}\) versus \(\dot{m}_{1}\). (Suggestion: Use a spreadsheet for these calculations.) (d) The company has hired you as a consultant to help them determine whether or not to add capacity to the treatment unit to increase the recovery of chromium. What would you need to know to make this determination? (e) What concerns might need to be addressed regarding the waste lagoon?

A mixture of 75 mole \(\%\) methane and 25 mole \(\%\) hydrogen is burned with \(25 \%\) excess air. Fractional conversions of \(90 \%\) of the methane and \(85 \%\) of the hydrogen are achieved; of the methane that reacts, \(95 \%\) reacts to form \(\mathrm{CO}_{2}\) and the balance reacts to form CO. The hot combustion product gas passes through a boiler in which heat transferred from the gas converts boiler feedwater into steam. (a) Calculate the concentration of \(\mathrm{CO}\) (ppm) in the stack gas. (b) The CO in the stack gas is a pollutant. Its concentration can be decreased by increasing the percent excess air fed to the furnace. Think of at least two costs of doing so. (Hint: The heat released by the combustion goes into heating the combustion products; the higher the combustion product temperature, the more steam is produced.)

Ethanol can be produced commercially by the hydration of ethylene: $$\mathrm{C}_{2} \mathrm{H}_{4}+\mathrm{H}_{2} \mathrm{O} \rightarrow \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}$$ Some of the product is converted to diethyl ether in the side reaction $$2 \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH} \rightarrow\left(\mathrm{C}_{2} \mathrm{H}_{5}\right)_{2} \mathrm{O}+\mathrm{H}_{2} \mathrm{O}$$ The feed to the reactor contains ethylene, steam, and an inert gas. A sample of the reactor effluent gas is analyzed and found to contain 43.3 mole\% ethylene, 2.5\% ethanol, 0.14\% ether, 9.3\% inerts, and the balance water. (a) Take as a basis 100 mol of effluent gas, draw and label a flowchart, and do a degree-of-freedom analysis based on atomic species to prove that the system has zero degrees of freedom. (b) Calculate the molar composition of the reactor feed, the percentage conversion of ethylene, the fractional yield of ethanol, and the selectivity of ethanol production relative to ether production. (c) The percentage conversion of ethylene you calculated should be very low. Why do you think the reactor would be designed to consume so little of the reactant? (Hint: If the reaction mixture remained in the reactor long enough to use up most of the ethylene, what would the main product constituent probably be?) What additional processing steps are likely to take place downstream from the reactor?

The reaction between ethylene and hydrogen bromide to form ethyl bromide is carried out in a continuous reactor. The product stream is analyzed and found to contain 51.7 mole \(\% \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{Br}\) and 17.3\% HBr. The feed to the reactor contains only ethylene and hydrogen bromide. Calculate the fractional conversion of the limiting reactant and the percentage by which the other reactant is in excess. If the molar flow rate of the feed stream is \(165 \mathrm{mol} / \mathrm{s}\), what is the extent of reaction?

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