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Chapter 4: Problem 96

A fuel oil is analyzed and found to contain 85.0 wt\% carbon, \(12.0 \%\) elemental hydrogen (H), \(1.7 \%\) sulfur, and the remainder noncombustible matter. The oil is burned with \(20.0 \%\) excess air, based on complete combustion of the carbon to \(\mathrm{CO}_{2}\), the hydrogen to \(\mathrm{H}_{2} \mathrm{O}\), and the sulfur to \(\mathrm{SO}_{2}\). The oil is burned completely, but \(8 \%\) of the carbon forms CO. Calculate the molar composition of the stack gas.

Short Answer

Expert verified
To calculate the molar composition of the stack gas, determine the number of moles of each gaseous product (including Nitrogen) and then divide by the total moles of gases. The result is the molar fraction of each gas which can be represented as a percentage of complete composition.

Step by step solution

01

Determine the mass of the air required

The oil is burned with 20% excess air based on complete combustion. Thus, by stoichiometric consideration, one mol C needs 1 mol O2, 1 mol H2 needs 0.5 mol O2 and 1 mol of S needs 1 mol of O2. Since oil contains 85.0 wt% of carbon (C), 12.0 wt% of hydrogen (H2) and 1.7 wt% of Sulphur (S), hence (85*C + 12*H2*0.5 + 1.7*S)*1.2 = mass of the air required per 100kg fuel (due to 20% excess, hence multiplied by 1.2)
02

Calculate the elements formed after combustion

Now we will determine the moles of each compound. To do this, we need to remember that 8% of the carbon forms CO, while the rest forms CO2. The remaining components form as follows: H2 forms H2O and S forms SO2. Using the data provided and the stoichiometric ratios identified in the first step, we can determine the quantity of each substance formed.
03

Calculate the molar composition of stack gas

Based on the analysis so far, determine the actual number of moles each compound contributed to the stack gas. This includes those from the fuel (in Step 2) and air. Divide individual mol count by the total mol count to find out the molar composition of the stack gas. Multiply each fraction by 100 to get the percentage.

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Key Concepts

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

Stoichiometric Calculations
Understanding stoichiometric calculations is essential in the field of chemistry, especially when dealing with reactions like combustion. In essence, stoichiometry involves the quantitative relationship between the reactants and products in a chemical reaction.

For a combustion process, this means calculating the precise amount of oxygen required to burn a given fuel completely. In our example, stoichiometric calculations allow us to determine the amount of oxygen needed for the carbon, hydrogen, and sulfur present in the fuel oil to combust fully, forming carbon dioxide (CO2), water (H2O), and sulfur dioxide (SO2), respectively.

Excess Air in Combustion
Excess air in combustion is a key concept to ensure complete burning of fuel and to avoid the production of undesirable products like carbon monoxide. It refers to the amount of air that is provided in the combustion process over and above the stoichiometric requirement. This is often done to compensate for imperfect mixing and ensure that all fuel has access to enough oxygen for complete combustion.

In our scenario, 20% excess air is used, implying that the air supplied is 20% more than what is theoretically needed for complete combustion. While excess air is beneficial to a point, too much can lower combustion temperatures and lead to inefficiencies. Understanding and controlling the correct amount of excess air can significantly affect the performance and emissions of a combustion system.

Furthermore, the presence of excess air affects the molar composition of the resulting stack gases. Since not all the additional oxygen reacts, it becomes part of the stack gas, which must be accounted for when calculating the molar composition. In the exercise, we accommodate the excess air by multiplying the stoichiometric air requirement by 1.2 (representing the 20% excess).
Molar Composition of Gases
The molar composition of gases represents the fraction of each gas present in a mixture. When calculating the molar composition of stack gases in a combustion process, it is important to consider both the gases produced by the combustion of the fuel and the excess air and its constituents.

As per our exercise, after combustion, we have a mixture of different gases in the stack, including CO2, CO, H2O, SO2, excess O2, and nitrogen from the air (which remains unreacted in the combustion process). To calculate the molar composition, we identify the number of moles of each of these gases, sum them up to find the total number of moles, and then calculate the mole fraction of each gas. The mole fraction is then multiplied by 100 to convert it to a percentage.

The presence of 8% CO (carbon monoxide) highlights incomplete combustion, affecting the final composition of the stack gases. The molar composition helps in assessing the efficiency and environmental impact of the combustion process. For industry professionals, maintaining an optimal molar composition of stack gases is crucial for meeting environmental regulations and ensuring the efficient operation of combustion systems.

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Most popular questions from this chapter

A gas contains 75.0 wt\% methane, \(10.0 \%\) ethane, \(5.0 \%\) ethylene, and the balance water. (a) Calculate the molar composition of this gas on both a wet and a dry basis and the ratio (mol \(\mathrm{H}_{2} \mathrm{O} /\) mol dry gas). (b) If \(100 \mathrm{kg} / \mathrm{h}\) of this fuel is to be burned with \(30 \%\) excess air, what is the required air feed rate (kmol/ h)? How would the answer change if the combustion were only \(75 \%\) complete?

Methanol is produced by reacting carbon monoxide and hydrogen. A fresh feed stream containing \(\mathrm{CO}\) and \(\mathrm{H}_{2}\) joins a recycle stream and the combined stream is fed to a reactor. The reactor outlet stream flows at a rate of \(350 \mathrm{mol} / \mathrm{min}\) and contains \(10.6 \mathrm{wt} \% \mathrm{H}_{2}, 64.0 \mathrm{wt} \% \mathrm{CO},\) and \(25.4 \mathrm{wt} \% \mathrm{CH}_{3} \mathrm{OH} .\) (Notice that those are percentages by mass, not mole percents.) This stream enters a cooler in which most of the methanol is condensed. The liquid methanol condensate is withdrawn as a product, and the gas stream leaving the condenser- -which contains \(\mathrm{CO}, \mathrm{H}_{2},\) and \(0.40 \mathrm{mole} \%\) uncondensed \(\mathrm{CH}_{3} \mathrm{OH}\) vapor \(-\mathrm{is}\) the recycle stream that combines with the fresh feed. (a) Without doing any calculations, prove that you have enough information to determine (i) the molar flow rates of CO and \(\mathrm{H}_{2}\) in the fresh feed, (ii) the production rate of liquid methanol, and (iii) the single-pass and overall conversions of carbon monoxide. Then perform the calculations. (b) After several months of operation, the flow rate of liquid methanol leaving the condenser begins to decrease. List at least three possible explanations of this behavior and state how you might check the validity of each one. (What would you measure and what would you expect to find if the explanation is valid?)

Two streams flow into a 500 -gallon tank. The first stream is 10.0 wt\% ethanol and \(90.0 \%\) hexane (the mixture density, \(\rho_{1},\) is \(0.68 \mathrm{g} / \mathrm{cm}^{3}\) ) and the second is \(90.0 \mathrm{wt} \%\) ethanol, \(10.0 \%\) hexane \(\left(\rho_{2}=0.78 \mathrm{g} / \mathrm{cm}^{3}\right) .\) After the tank has been filled, which takes 22 \(\mathrm{min}\), an analysis of its contents determines that the mixture is 60.0 wt\% ethanol, \(40.0 \%\) hexane. You wish to estimate the density of the final mixture and the mass and volumetric flow rates of the two feed streams. (a) Draw and label a flowchart of the mixing process and do the degree-of- freedom analysis. (b) Perform the calculations and state what you assumed.

A liquid mixture contains \(60.0 \mathrm{wt} \%\) ethanol \((\mathrm{E}), 5.0 \mathrm{wt} \%\) of a dissolved solute \((\mathrm{S}),\) and the balance water. A stream of this mixture is fed to a continuous distillation column operating at steady state. Product streams emerge at the top and bottom of the column. The column design calls for the product streams to have equal mass flow rates and for the top stream to contain 90.0 wt\% ethanol and no S. (a) Assume a basis of calculation, draw and fully label a process flowchart, do the degree-of-freedom analysis, and verify that all unknown stream flows and compositions can be calculated. (Don't do any calculations yet.) (b) Calculate (i) the mass fraction of \(S\) in the bottom stream and (ii) the fraction of the ethanol in the feed that leaves in the bottom product stream (i.e., \(\mathrm{kg} \mathrm{E}\) in bottom stream/kg \(\mathrm{E}\) in feed) if the process operates as designed. (c) An analyzer is available to determine the composition of ethanol-water mixtures. The calibration curve for the analyzer is a straight line on a plot on logarithmic axes of mass fraction of ethanol, \(x\) (kg E/kg mixture), versus analyzer reading, \(R\). The line passes through the points \((R=15, x=\) 0.100) and \((R=38, x=0.400)\). Derive an expression for \(x\) as a function of \(R(x=\cdots\) ) based on the calibration, and use it to determine the value of \(R\) that should be obtained if the top product stream from the distillation column is analyzed. (d) Suppose a sample of the top stream is taken and analyzed and the reading obtained is not the one calculated in Part (c). Assume that the calculation in Part (c) is correct and that the plant operator followed the correct procedure in doing the analysis. Give five significantly different possible causes for the deviation between \(R_{\text {measured and }} R_{\text {prediced }}\), including several assumptions made when writing the balances of Part (c). For each one, suggest something that the operator could do to check whether it is in fact the problem.

Gas streams containing hydrogen and nitrogen in different proportions are produced on request by blending gases from two feed tanks: Tank A (hydrogen mole fraction \(=x_{\mathrm{A}}\) ) and Tank \(\mathrm{B}\) (hydrogen mole fraction \(=x_{\mathrm{B}}\) ). The requests specify the desired hydrogen mole fraction, \(x_{\mathrm{p}}\), and mass flow rate of the product stream, \(\dot{m}_{\mathrm{P}}(\mathrm{kg} / \mathrm{h})\) (a) Suppose the feed tank compositions are \(x_{\mathrm{A}}=0.10 \mathrm{mol} \mathrm{H}_{2} / \mathrm{mol}\) and \(x_{\mathrm{B}}=0.50 \mathrm{mol} \mathrm{H}_{2} / \mathrm{mol},\) and the desired blend-stream mole fraction and mass flow rate are \(x_{\mathrm{P}}=0.20 \mathrm{mol} \mathrm{H}_{2} / \mathrm{mol}\) and \(\dot{m}_{\mathrm{P}}=100 \mathrm{kg} / \mathrm{h} .\) Draw and label a flowchart and calculate the required molar flow rates of the feed mixtures, \(\dot{n}_{\mathrm{A}}(\mathrm{kmol} / \mathrm{h})\) and \(\dot{n}_{\mathrm{B}}(\mathrm{kmol} / \mathrm{h})\) (b) Derive a series of formulas for \(\dot{n}_{\mathrm{A}}\) and \(\dot{n}_{\mathrm{B}}\) in terms of \(x_{\mathrm{A}}, x_{\mathrm{B}}, x_{\mathrm{P}},\) and \(\dot{m}_{\mathrm{P}} .\) Test them using the values in Part (a). (c) Write a spreadsheet that has column headings \(x_{\mathrm{A}}, x_{\mathrm{B}}, x_{\mathrm{P}}, \dot{m}_{\mathrm{P}}, \dot{n}_{\mathrm{A}},\) and \(\dot{n}_{\mathrm{B}}\). The spreadsheet should calculate entries in the last two columns corresponding to data in the first four. In the first six data rows of the spreadsheet, do the calculations for \(x_{\mathrm{A}}=0.10, x_{\mathrm{B}}=0.50,\) and \(x_{\mathrm{P}}=\) \(0.10,0.20,0.30,0.40,0.50,\) and \(0.60,\) all for \(\dot{m}_{\mathrm{P}}=100 \mathrm{kg} / \mathrm{h} .\) Then in the next six rows repeat the calculations for the same values of \(x_{\mathrm{A}}, x_{\mathrm{B}},\) and \(x_{\mathrm{p}}\) for \(\dot{m}_{\mathrm{p}}=250 \mathrm{kg} / \mathrm{h} .\) Explain any of your results that appear strange or impossible. (d) Enter the formulas of Part (b) into an equation-solving program. Run the program to determine \(\dot{n}_{\mathrm{A}}\) and \(\dot{n}_{\mathrm{B}}\) for the 12 sets of input variable values given in Part (c) and explain any physically impossible results.
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