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Chapter 3: Problem 32

A mixture of methane and air is capable of being ignited only if the mole percent of methane is between 5\% and 15\%. A mixture containing 9.0 mole\% methane in air flowing at a rate of 7.00 \(\times 10^{2} \mathrm{kg} / \mathrm{h}\) is to be diluted with pure air to reduce the methane concentration to the lower flammability limit. Calculate the required flow rate of air in mol/h and the percent by mass of oxygen in the product gas. (Note: Air may be taken to consist of \(\left.21 \text { mole } \% \mathrm{O}_{2} \text { and } 79 \% \mathrm{N}_{2} \text { and to have an average molecular weight of } 29.0 .\right)\)

Short Answer

Expert verified
The required flow rate of air is approximately \( 4403340\, mol/hr \) and the percent by mass of oxygen in the product gas is \( 23.54 \% \).

Step by step solution

01

Calculation of Moles of Methane and Air

First, calculate the original flow rate in moles per hour using the molecular weight of air and given mass flow rate. From there, find the moles of methane and air using the molar percentage of methane. Let \( x \) be the moles of air. \n\n Using the equation: \n\n \( \frac{9.0}{100} = \frac{7.00 脳 10^2 kg/h}{x (29.0 g/mol) 脳 (10^3 g/kg)} \)\n\n solving for \( x \), is found to be \( 2.718 脳 10^6 mol/h \). \nNow find methane and air moles as: \nMethane moles = \( \frac{9}{100} \times 2.718 脳 10^6 = 244620 mol/h \) \nAir moles = \( 2.718 脳 10^6 - 244620 = 2473380 mol/h \).
02

Calculation of Mole Ratio for Desired Methane Concentration

Now we aim to calculate the additional moles of air required to dilute the methane mixture to its lower flammability limit (5%). \n\n This is achieved by setting up the equation based on mole fractions: \n\n \( \frac{methane\,moles}{methane\,moles + Air\,moles + additional\,air\,moles} = 0.05 \) \n\n Inserting the previously calculated values: \n\n \( \frac{244620}{244620 + 2473380 +x} = 0.05 \), \n\n Solving this gives the \( x \) value to be \( 4403340\, mol/hr \). The total air moles now are \( 2573000 \, mol/hr \).
03

Calculation of Oxygen Mass Percentage

Finally, calculate the mass percentage of Oxygen in the product gas. Since the air consists of 21 mole% of Oxygen, moles of Oxygen will be \( 0.21 \times 6879620 \, (total\, moles) = 1444714 \, mol\). The total weight is given by \( (0.21 脳 6879620 脳 32) + (0.79 脳 6879620 脳 28) = 196497680 \, g \), using the molecular weight of \( \mathrm{O}_{2} \,and\, \mathrm{N}_{2} \) respectively. Hence, the mass percentage of oxygen can now be calculated as \n\n \( \frac{1444714 脳 32}{196497680 } 脳 100 \% = 23.54 \% \).

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Key Concepts

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

Flammability Limits
Flammability limits define the concentration range of a flammable gas or vapor in air that can ignite. For a methane-air mixture, this range is between 5% and 15% by volume of methane. Outside of these limits, the mixture is either too lean or too rich to support combustion.

Understanding these limits is crucial for safe industrial operations. For instance, if the methane concentration falls below 5%, the mixture won't ignite. Likewise, if it exceeds 15%, there's also no risk of flammability. This happens because, in a too-rich mixture, insufficient oxygen is available to sustain combustion.
  • The lower flammability limit (LFL) indicates the lowest concentration of a gas that will sustain a flame.
  • The upper flammability limit (UFL) is the highest concentration that allows ignition.
Keeping flammable gas concentrations within these limits can prevent explosion hazards. Engineers use dilution or enrichment techniques to control gas mixtures effectively and safely.
Methane-Air Mixtures
Methane is a primary component of natural gas and is widely used in various industrial processes. When mixed with air, methane creates a combustible bond with oxygen. The process efficiency and safety depend on maintaining specific methane concentrations.

In our example, the ratio of methane to air is initially 9% methane. Since it's within the flammability limits, there's a potential fire hazard. To render the mixture safe, we dilute it with additional air to decrease the methane concentration to 5%, the lower flammability limit, thus making it non-flammable.
  • Methane-air mixes follow simple stoichiometric rules for combustion reactions.
  • Proper ventilation and monitoring help maintain safe concentration levels.
Understanding the behavior of methane in air helps design safer chemical processes and avoid explosive environments.
Oxygen Mass Percentage
Oxygen is a significant component of air, typically comprising about 21% by volume. Calculating its mass percentage in a gas mixture involves considering the mole fraction and molecular weights of the gases involved.

In the methane dilution problem, after adjusting methane to the lower flammability limit, we calculate the Oxygen mass percentage in the new mixture. Here's how:
  • The total moles of the new gas mixture include moles from both the original and added air.
  • Oxygen moles are derived from multiplying the total moles by 0.21 (since air is 21% oxygen).
We then use the molecular weight of oxygen and nitrogen to compute the total weight of the mixture. Finally, by finding the proportion of this weight that is oxygen, we determine its mass percentage. In our case, it's about 23.54%, emphasizing that more air increases the overall oxygen share.

These calculations are vital in ensuring that the products of chemical processes are predictable and safe.

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Most popular questions from this chapter

Certain solid substances, known as hydrated compounds, have well-defined molecular ratios of water to some other species. For example, calcium sulfate dihydrate (commonly known as gypsum, \(\left.\mathrm{CaSO}_{4} \cdot 2 \mathrm{H}_{2} \mathrm{O}\right),\) has 2 moles of water per mole of calcium sulfate; alternatively, it may be said that 1 mole of gypsum consists of 1 mole of calcium sulfate and 2 moles of water. The water in such substances is called water of hydration. (More information about hydrated salts is given in Chapter 6 .) In order to eliminate the discharge of sulfuric acid into the environment, a process has been developed in which the acid is reacted with aragonite \(\left(\mathrm{CaCO}_{3}\right)\) to produce calcium sulfate. The calcium sulfate then comes out of solution in a crystallizer to form a slurry (a suspension of solid particles in a liquid) of solid gypsum particles suspended in an aqueous \(\mathrm{CaSO}_{4}\) solution. The slurry flows from the crystallizer to a filter in which the particles are collected as a filter cake. The filter cake, which is 95.0 wiff solid gypsum and the remainder CaSO_solution, is fed to a dryer in which all water (including the water of hydration in the crystals) is driven off to yield anhydrous (water-free) CaSO \(_{4}\) as product. A flowchart and relevant process data are given below. Solids content of slurry leaving crystallizer: \(0.35 \mathrm{kg} \mathrm{CaSO}_{4} \cdot 2 \mathrm{H}_{2} \mathrm{O} / \mathrm{L}\) slurry \(\mathrm{CaSO}_{4}\) content of slurry liquid: \(0.209 \mathrm{g} \mathrm{CaSO}_{4} / 100 \mathrm{g} \mathrm{H}_{2} \mathrm{O}\) Specific gravities: \(\mathrm{CaSO}_{4} \cdot 2 \mathrm{H}_{2} \mathrm{O}(\mathrm{s}), 2.32 ;\) liquid solutions, 1.05 (a) Briefly explain in your own words the functions of the three units (crystallizer, filter, and dryer). (b) Takea basis of one liter of solution leaving the crystallizer and calculate the mass (kg) and volume (L) of solid gypsum, the mass of \(\mathrm{CaSO}_{4}\) in the gypsum, and the mass of \(\mathrm{CaSO}_{4}\) in the liquid solution. (c) Calculate the percentage recovery of \(\mathrm{CaSO}_{4}-\) that is, the percentage of the total \(\mathrm{CaSO}_{4}\) (precipitated plus dissolved) leaving the crystallizer recovered as solid anhydrous \(\mathrm{CaSO}_{4}\) (d) List five potential negative consequences of discharging \(\mathrm{H}_{2} \mathrm{SO}_{4}\) into the river passing the plant.

As described in Problem 3.16 , a drilling mud is a slurry pumped into oil wells being drilled. The mud has several functions: It floats rock cuttings to the top of the well where they can easily be removed; Iubricates and cools the drill bit; and keeps loose solids and water from leaking into the borchole. A drilling mud is prepared by blending barite (SG \(=4.37\) ) with seawater (SG \(=1.03\) ). The seawater has a dissolved salt content of approximately 3.5 wt\%. You have been asked to determine the specific gravity of the mud and the wt\% barite. You collect a sample of the mud from a blending tank on an oil platform and make the following observations: (i) The mud appears homogeneous, even after standing for 2 days; (ii) the tare mass of the calibrated vessel into which you pour the sample of mud is 118 g: (iii) the volume of the collected sample is \(100 \mathrm{mL}\), and the mass of the collection vessel and sample is \(323 \mathrm{g}\); and (iv) the mass of the vessel and residue remaining after completely evaporating water from the sample is \(254 \mathrm{g}\). (a) Estimate the specific gravity of the mud and the wt\% barite. (b) What is the practical importance of Observation (i)?

The viewing window in a diving suit has an area of roughly \(65 \mathrm{cm}^{2}\). (a) If an attempt were made to maintain the pressure on the inside of the suit at 1 atm, what force (N and Ibt) would the window have to withstand if the diver descended to a depth of 150 m. Take the specific gravity of the water to be 1.05. (b) Repeat the calculation of Part (a) for the deepest Guiness-verified SCUBA dive.

The liquid level in a tank is determined by measuring the pressure at the bottom of the tank. A calibration curve is prepared by filling the tank to several known levels, reading the bottom pressure from a Bourdon gauge, and drawing a plot of level (m) vs. pressure (Pa). (a) Would you expect the calibration curve to be a straight line? Explain your answer. (b) The calibration experiment was done using a liquid with a specific gravity of \(0.900,\) but the tank is used to store a liquid with specific gravity of \(0.800 .\) Will the liquid level determined from the calibration curve be too high, too low, or correct? Explain. (c) If the actual liquid level is 8.0 meters, what value will be read from the calibration curve? If the tank has a height of \(10.0 \mathrm{m},\) what value will be read from the curve when the tank overflows?

since the 1960 s, the Free Expression Tunnel at North Carolina State University has been the University's way to combat graffiti on campus. The tunnel is painted almost daily by various student groups to advertise club meetings, praise athletic accomplishments, and declare undying love. You and your engineering classmates decide to decorate the tunnel with chemical process flowcharts and key equations found in your favorite text, so you purchase a can of spray paint. The label indicates that the can holds nine fluid ounces, which should cover an area of approximately \(25 \mathrm{ft}^{2}\). (a) You measure the tunnel and find that it is roughly 8 feet wide, 12 feet high, and 148 feet long. Based on the stated coverage, how many cans of spray paint would it take to apply one coat to the walls and ceiling of the tunnel? (b) Having just heard a lecture on process safety in your engineering class, you want to take appropriate safety precautions while painting the tunnel. One useful source for this type of information is the Safety Data Sheet (SDS), a document used in industry to provide workers and emergency personnel with procedures for safely handling or working with a specified chemical. Other sources of information about hazardous substances can be found in handbooks, and some countries, including the United States, have laws that require employers to provide their employees with Safety Data Sheets. \(^{6}\) Besides composition information, the SDS contains information such as physical properties (melting point, boiling point, flash point, etc.), other threats to health and safety, recommended protective equipment, and recommended procedures for storage, disposal, first aid, and spill handling. The SDS can typically be found online for most common substances. Search the web for "spray paint SDS" and find a representative SDS for a typical spray paint product. Based on the document you find, what are the top three hazards that you might encounter during your tunnel painting project? Suggest one safety precaution for each listed hazard.
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