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Chapter 4: Problem 95

A mixture of propane and butane is burned with pure oxygen. The combustion products contain 47.4 mole \(\% \mathrm{H}_{2} \mathrm{O}\). After all the water is removed from the products, the residual gas contains 69.4 mole \(\% \mathrm{CO}_{2}\) and the balance \(\mathrm{O}_{2}\) (a) What is the mole percent of propane in the fuel? (b) It now turns out that the fuel mixture may contain not only propane and butane but also other hydrocarbons. All that is certain is that there is no oxygen in the fuel. Use atomic balances to calculate the elemental molar composition of the fuel from the given combustion product analysis (i.e., what mole percent is \(C\) and what percent is \(\mathrm{H}\) ). Prove that your solution is consistent with the result of Part (a).

Short Answer

Expert verified
The mole percent of propane in the fuel is 57.6%. The mole percent of Carbon and Hydrogen in the fuel is 66.9% and 33.1% respectively.

Step by step solution

01

Write the combustion reactions for propane and butane

For propane: \(C_3H_8 + 5O_2 \rightarrow 3CO_2 + 4H_2O\)\For butane: \(C_4H_{10} + 6.5O_2 \rightarrow 4CO_2 + 5H_2O\)
02

Analyze the mole percentages of the combustion products

From the problem, we know the combustion product contains 47.4 mole% \(H_2O\) and 69.4 mole% \(CO_2\) which makes up 116.8 mole % in total. We know that the remaining mole % is \(O_2\), which is \(100 - 116.8 = 16.2\% O_2\). Assuming total 100 moles of gasses are produced after combustion, there are 47.4 moles of \(H_2O\), 69.4 moles of \(CO_2\), and 16.2 moles of \(O_2\).
03

Calculate the mol percent of Propane in the fuel

From step 1, we can assume the fuel is composed of x% propane and (100 - x)% butane. For \(H_2O\); from propane combustion, x moles contribute 4x moles of \(H_2O\), and from butane combustion (100 - x) moles contribute 5*(100 - x) moles of \(H_2O\). From the equation 4x + 5*(100 - x) = 47.4, we compute x = 57.6%, thus the mole percent of Propane in the fuel is 57.6%.
04

Calculate the atomic balances to find the elemental molar composition

Given that there is no oxygen in the fuel, it can be assumed to be composed of C and H. Since the moles of \(H_2O\) equal to half the number of hydrogen atoms and the moles of \(CO_2\) represent the number of carbon atoms, the component composition of the fuel can be calculated as: Carbon moles % = \(69.4/ (69.4 + 47.4/2)*100 = 66.9 % \) and Hydrogen mole% = \(100 - 66.9 = 33.1 %\). Therefore, the mole percent of C is 66.9 and H is 33.1.
05

Check if the found solution is consistent the part (a) result

Calculating the composition of butane and propane we get: Propane C = (57.6% of propane)*3C = 1.8C and H = (57.6% of propane)*8H = 4.61H, Butane C = (100-57.6)% of butane)*4C = 1.68C and H = (100-57.6)% of butane)*10H = 4.21H. When these values are added, they give a C content of 1.8+1.68 = 3.48 and an H content of 4.61+4.21 = 8.82. Making a direct comparison to the moles of C and H found in Step 4 indicates consistency.

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Key Concepts

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

Combustion Analysis
Combustion analysis is a method used to understand the characteristics and components of a burning process. In our scenario, a mixture of propane and butane, both of which are hydrocarbons, is combusted with pure oxygen. The products of this combustion process are primarily carbon dioxide \( (CO_2) \) and water \( (H_2O) \).
To analyze the results of this chemical reaction, we observe the mole percentages of the combustion products. By knowing the quantities of \( CO_2 \) and \( H_2O \), we can deduce the composition of the original fuel mixture. Essentially, combustion analysis helps us identify and quantify the substances present in the initial fuel based on the gaseous products formed.
In practice, this involves balancing chemical equations, analyzing atomic balances, and interpreting the results. It allows us to reverse engineer the combustion process to understand the fuel composition in terms of the chemical elements such as carbon and hydrogen. This method is widely used in chemical reaction engineering to determine specific details about fuel sources and combustion efficiency.
Mole Percent Calculation
Mole percent calculation is a vital concept in chemical reaction engineering. It allows us to determine the composition of a mixture in terms of the different components present. In this context, we are dealing with a combustion problem where various products are formed.
To find the mole percent of a component in a mixture, you calculate the number of moles of that component, divide it by the total number of moles of all substances involved, and multiply by 100 to get a percentage.
In our example, after combustion, we calculated the mole percentages of \( H_2O \) and \( CO_2 \) from the reaction. By further breaking down the results using the balanced chemical equations, we can obtain the mole percentages of propane and butane in the original fuel. Understanding how mole percent calculations work is crucial for analyzing combustion reactions and other chemical processes.
Hydrocarbon Fuels
Hydrocarbon fuels, such as propane and butane, are organic chemical compounds composed primarily of carbon and hydrogen atoms. These fuels are commonly used because they efficiently release energy when combusted. Propane \( (C_3H_8) \) and butane \( (C_4H_{10}) \) are both part of the alkane family and are gaseous at room temperature.
When these hydrocarbons combust in the presence of oxygen, they produce carbon dioxide \( (CO_2) \) and water \( (H_2O) \) as primary products. In the text, we learned about analyzing these combustion products to infer details about the original fuel mixture.
Hydrocarbon fuels are interestingly diverse, and any variation in their carbon and hydrogen content leads to different fuel types, each with unique combustion properties. Understanding the composition and combustion behavior of hydrocarbons is essential, especially in the context of environmental and engineering applications. This knowledge aids in optimizing fuel designs for better efficiency and less environmental impact.

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Most popular questions from this chapter

The fresh feed to an ammonia production process contains nitrogen and hydrogen in stoichiometric proportion, along with an inert gas (I). The feed is combined with a recycle stream containing the same three species, and the combined stream is fed to a reactor in which a low single-pass conversion of nitrogen is achieved. The reactor effluent flows to a condenser. A liquid stream containing essentially all of the ammonia formed in the reactor and a gas stream containing all the inerts and the unreacted nitrogen and hydrogen leave the condenser. The gas stream is split into two fractions with the same composition: one is removed from the process as a purge stream, and the other is the recycle stream combined with the fresh feed. In every stream containing nitrogen and hydrogen, the two species are in stoichiometric proportion. (a) Let \(x_{10}\) be the mole fraction of inerts in the fresh feed, \(f_{\mathrm{sp}}\) the single-pass conversion of nitrogen (and of hydrogen) in the reactor, and \(y_{p}\) the fraction of the gas leaving the condenser that is purged (mol purged/mol total). Taking a basis of 1 mol fresh feed, draw and fully label a process flowchart, incorporating \(x_{10}, f_{\mathrm{sp}},\) and \(y_{\mathrm{p}}\) in the labeling to the greatest possible extent. Then, assuming that the values of these three variables are given, write a set of equations for the total moles fed to the reactor \(\left(n_{\mathrm{r}}\right),\) moles of ammonia produced \(\left(n_{\mathrm{p}}\right),\) and overall nitrogen conversion \(\left(f_{\mathrm{ov}}\right) .\) Each equation should involve only one unknown variable, which should be circled. (b) Solve the equations of Part (a) for \(x_{10}=0.01, f_{\mathrm{sp}}=0.20,\) and \(y_{\mathrm{p}}=0.10\) (c) Briefly explain in your own words the reasons for including (i) the recycle stream and (ii) the purge stream in the process design. (d) Prepare a spreadsheet to perform the calculations of Part (a) for given values of \(x_{10}, f_{\mathrm{sp}},\) and \(y_{\mathrm{p}} .\) Test it with the values in Part (b). Then in successive rows of the spreadsheet, vary each of the three input variables two or three times, holding the other two constant. The first six columns and first five rows of the spreadsheet should appear as follows:Summarize the effects on ammonia production \(\left(n_{\mathrm{P}}\right)\) and reactor throughput \(\left(n_{\mathrm{r}}\right)\) of changing each of the three input variables.

A paint mixture containing \(25.0 \%\) of a pigment and the balance binders (which help the pigment stick to the surface) and solvents (which ensure that the paint stays in liquid form) sells for 18.00 dollar/kg, and a mixture containing 12.0\% sells for 10.00 dollar /kg. (a) If a paint retailer produces a blend containing \(17.0 \%\) pigment, for how much (S/kg) should it be sold to yield a 10\% profit? (b) Paint manufacturers have begun to market "low VOC" paint as a more environmentally friendly product. What are VOCs? List some ways in which paint products can be altered to lower the VOC content.

Mammalian cells can be cultured for a variety of purposes, including synthesis of vaccines. They must be maintained in growth media containing all of the components required for proper cellular function to ensure their survival and propagation. Traditionally, growth media were prepared by blending a powder, such as Dulbecco's Modified Eagle Medium (DMEM) with sterile deionized water. DMEM contains glucose, buffering agents, proteins, and amino acids. Using a sterile (i.e., bacterial-, fungal-,and yeast-free) growth medium ensures proper cell growth, but sometimes the water (or powder) can become contaminated, requiring the addition of antibiotics to eliminate undesired contaminants. The culture medium is supplemented with fetal bovine serum (FBS) that contains additional growth factors required by the cells. Suppose an aqueous stream (SG = 0.90) contaminated with bacteria is split, with 75\% being fed to a mixing unit to dissolve a powdered mixture of DMEM contaminated with the same bacteria found in the water. The ratio of impure feed water to powder entering the mixer is 4.4:1. The stream leaving the mixer (containing DMEM, water, and bacteria) is combined with the remaining 25\% of the aqueous stream and fed to a filtration unit to remove all of the bacteria that have contaminated the system, a total of \(20.0 \mathrm{kg}\). Once the bacteria have been removed, the sterile medium is combined with FBS and the antibiotic cocktail PSG (Penicillin-Streptomycin-L-Glutamine) in a shaking unit to generate 5000 L of growth medium (SG = 1.2). The final composition of the growth medium is 66.0 wt\% H_O, 11.0\% FBS, 8.0\% PSG, and the balance DMEM. (a) Draw and label the process flowchart. (b) Do a degree-of-freedom analysis around each piece of equipment (mixer, filter, and shaker), the splitter, the mixing point, and the overall system. Based on the analysis, identify which system or piece of equipment should be the starting point for further calculations. (c) Calculate all of the unknown process variables. (d) Determine a value for (i) the mass ratio of sterile growth medium product to feed water and (ii) the mass ratio of bacteria in the water to bacteria in the powder. (e) Suggest two reasons why the bacteria should be removed from the system.

A liquid mixture of acetone and water contains 35 mole\% acetone. The mixture is to be partially evaporated to produce a vapor that is 75 mole \(\%\) acetone and leave a residual liquid that is 18.7 mole \(\%\) (a) Suppose the process is to be carried out continuously and at steady state with a feed rate of 10.0 kmol/h. Let \(\dot{n}_{\mathrm{v}}\) and \(\dot{n}_{1}\) be the flow rates of the vapor and liquid product streams, respectively. Draw and label a process flowchart, then write and solve balances on total moles and on acetone to determine the values of \(\dot{n}_{\mathrm{v}}\) and \(\dot{n}_{\mathrm{l}}\). For each balance, state which terms in the general balance equation (accumulation \(=\)input \(+\)generation \(-\)output\(-\)consumption ) can be discarded and why. (See Example 4.2-2.) (b) Now suppose the process is to be carried out in a closed container that initially contains 10.0 kmol of the liquid mixture. Let \(n_{\mathrm{v}}\) and \(n_{1}\) be the moles of final vapor and liquid phases, respectively. Draw and label a process flowchart, then write and solve integral balances on total moles and on acetone. For each balance, state which terms of the general balance equation can be discarded and why. (c) Returning to the continuous process, suppose the vaporization unit is built and started and the product stream flow rates and compositions are measured. The measured acetone content of the vapor stream is 75 mole \(\%\) acetone, and the product stream flow rates have the values calculated in Part (a). However, the liquid product stream is found to contain 22.3 mole \(\%\) acetone. It is possible that there is an error in the measured composition of the liquid stream, but give at least five other reasons for the discrepancy. [Think about assumptions made in obtaining the solution of Part (a).]

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.)
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