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Chapter 3: Problem 30

Coal being used in a power plant at a rate of \(8000 \mathrm{lb}_{\mathrm{m}} / \mathrm{min}\) has the following composition: $$\begin{array}{lc}\hline \text { Component } & \text { Weight } \% \text { (dry basis) } \\ \hline \text { Ash } & 7.2 \\\\\text { Sulfur } & 3.5 \\\\\text { Hydrogen } & 5.0 \\\\\text { Carbon } & 75.2 \\ \text { Nitrogen } & 1.6 \\\\\text { Oxygen } & 7.5 \\\\\hline\end{array}$$ In addition, there are \(4.58 \mathrm{lb}_{\mathrm{m}} \mathrm{H}_{2} \mathrm{O}\) per \(\mathrm{lb}_{\mathrm{m}}\) of coal. Determine the molar flow rate of each element in the coal (including water) other than ash.

Short Answer

Expert verified
The molar flow rates of each element (C, H, O, N, S and H2O) other than ash in the coal are calculated by firstly deriving their mass flow rates and then converting these values into molar flow rates using the respective molar masses. The specific values are determined from the calculations described in the step-by-step solution.

Step by step solution

01

Identify the Provided Data

From the problem, it's given that the overall coal usage is 8000 lbm/min. The composition of the coal by weight (on a dry basis) is also given, as well as the additional 4.58 lbm H2O per lbm of coal.
02

Determine the Mass Flow Rate of Each Elemental Component

The mass flow rate of each element can be calculated by multiplying the total coal usage with the respective weight percent (converted into decimal form). For example, the mass flow rate of carbon (C) is \(8000 lbm/min \times 0.752 (or 75.2 / 100)\). Follow this procedure for each element in the coal.
03

Compute the Molar Flow Rate of Each Element

The molar flow rate of each element is obtained by dividing its mass flow rate by its molar mass. The molar mass of each element is: carbon (C): 12 lbm/lbmol, hydrogen (H): 1 lbm/lbmol, oxygen (O): 16 lbm/lbmol, nitrogen (N): 14 lbm/lbmol, and sulfur (S): 32 lbm/lbmol. Water (H2O) has a molar mass of 18 lbm/lbmol.
04

Include Water in the Calculation

Besides the elements in the coal, water is also present. Calculate the mass flow rate of water by multiplying the total amount of coal with the given ratio (4.58 lbm H2O per lbm of coal). This mass flow rate is then converted into molar flow rate using the molar mass of water.

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Key Concepts

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

Elemental Composition
Elemental composition is a fundamental concept in chemical process analysis, where we dissect a substance into its elemental constituents. In the context of coal, this means understanding the makeup of each element present in the coal. Knowing the composition is crucial for further calculations, such as determining mass and molar flow rates.
The given problem specifies the elemental composition of coal used in a power plant. Each element, on a dry basis, has a percentage weight:
  • Ash: 7.2%
  • Sulfur: 3.5%
  • Hydrogen: 5.0%
  • Carbon: 75.2%
  • Nitrogen: 1.6%
  • Oxygen: 7.5%
Understanding these values helps us calculate how much of each element is present, considering both the coal and the additional water content. This is a critical step before diving into mass and molar flow calculations.
Molar Flow Rate
The molar flow rate tells us how many moles of a chemical species flow through a system over a given time. Understanding molar flow rate is essential in processes where chemical reactions occur. The calculation involves two steps: first, identifying the mass flow rate of an element, and second, converting that to its molar equivalent by dividing the mass by its molar mass.
For instance, in the given problem, if the carbon mass flow rate is determined by the equation \[ \text{Mass Flow Rate of Carbon} = 8000 \text{ lbm/min} \times 0.752 \] we then calculate the molar flow rate using the molar mass of carbon (12 lbm/lbmol):\[ \text{Molar Flow Rate of Carbon} = \frac{\text{Mass Flow Rate of Carbon}}{12 \text{ lbm/lbmol}} \]
We perform a similar calculation for other elements, like sulfur, hydrogen, oxygen, and nitrogen, using their respective molar masses. This method ensures streamlined and systematic conversion from mass to mole units.
Coal Combustion Analysis
Coal combustion analysis involves studying how coal burns, where elemental composition plays a significant role. By understanding the composition, we can predict how efficiently the coal will burn, the heat released, and the emissions generated.
This problem highlights coal's interaction with additional water. Water changes combustion dynamics since it needs energy to evaporate, thus impacting the efficiency.
In combustion analysis, calculating the molar flow rates helps understand the stoichiometry of the combustion reactions. Knowing exact proportions of carbon, hydrogen, and other elements, including additional water, allows engineers to optimize combustion processes, improve efficiency, and reduce pollutants.
For example, precise molar flow rates of hydrogen and carbon allow the calculation of water and carbon dioxide produced during combustion, which is vital in designing emission control systems. Therefore, a meticulous approach to elemental analysis boosts the understanding and optimization of coal combustion.

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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.

In April \(2010,\) the worst oil spill ever recorded occurred when an explosion and fire on the Deepwater Horizon offshore oil-drilling rig left 11 workers dead and began releasing oil into the Gulf of Mexico. One of the attempts to contain the spill involved pumping drilling mud into the well to balance the pressure of escaping oil against a column of fluid (the mud) having a density significantly higher than those of seawater and oil. In the following problems, you may assume that seawater has a specific gravity of 1.03 and that the subsea wellhead was 5053 ft below the surface of the Gulf. (a) Estimate the gauge pressure (psig) in the Gulf at a depth of \(5053 \mathrm{ft}\). (b) Measurements indicate that the pressure inside the wellhead is 4400 psig. Suppose a pipe between the surface of the Gulf and the wellhead is filled with drilling mud and balances that pressure. Estimate the specific gravity of the drilling mud. (c) The drilling mud is a stable slurry of seawater and barite (SG \(=4.37\) ). What is the mass fraction of barite in the slurry? (d) What would you expect to happen if the barite weight fraction were significantly less than that estimated in Part (c)? Explain your reasoning.

The feed to an ammonia synthesis reactor contains 25 mole \(\%\) nitrogen and the balance hydrogen. The flow rate of the stream is \(3000 \mathrm{kg} / \mathrm{h}\). Calculate the rate of flow of nitrogen into the reactor in \(\mathrm{kg} / \mathrm{h}\). (Suggestion: First calculate the average molecular weight of the mixture.)

The reaction \(A \rightarrow B\) is carried out in a laboratory reactor. According to a published article the concentration of A should vary with time as follows: \(C_{\mathrm{A}}=C_{\mathrm{A} 0} \exp (-k t)\) where \(C_{\mathrm{A} 0}\) is the initial concentration of \(\mathrm{A}\) in the reactor and \(k\) is a constant. (a) If \(C_{\mathrm{A}}\) and \(C_{\mathrm{A} 0}\) are in \(\mathrm{Ib}-\) moles \(/ \mathrm{ft}^{3}\) and \(t\) is in minutes, what are the units of \(k ?\) (b) The following data are taken for \(C_{\mathrm{A}}(t):\) $$\begin{array}{cc}\hline t(\min ) & C_{\mathrm{A}}\left(\mathrm{lb}-\mathrm{mole} / \mathrm{ft}^{3}\right) \\\\\hline 0.5 & 1.02 \\\1.0 & 0.84 \\\1.5 & 0.69 \\\2.0 & 0.56 \\\3.0 & 0.38 \\\ 5.0 & 0.17 \\\10.0 & 0.02 \\\\\hline\end{array}$$ Verify the proposed rate law graphically (first determine what plot should yield a straight line), and calculate \(C_{\mathrm{A} 0}\) and \(k\) (c) Convert the formula with the calculated constants included to an expression for the molarity of A in the reaction mixture in terms of \(t\) (seconds). Calculate the molarity at \(t=265 \mathrm{s}\).

In the manufacture of pharmaceuticals, most active pharmaceutical ingredients (APIs) are made in solution and then recovered by separation. Acetaminophen, a pain-killing drug commercially marketed as Tylenol", is synthesized in an aqueous solution and subsequently crystallized. The slurry of crystals is sent to a centrifuge from which two effluent streams emerge: ( 1 ) a wet cake containing 90.0 wt\% solid acetaminophen \((\mathrm{MW}=\) 151 g/mol) and 10.0 wt\% water (plus some acetaminophen and other dissolved substances, which we will neglect), and (2) a highly dilute aqueous solution of acetaminophen that is discharged from the process. The wet cake is fed to a dryer where the water is completely evaporated, leaving the residual acetaminophen solids bone dry. If the evaporated water were condensed, its volumetric flow rate would be \(50.0 \mathrm{Lh}\). Following is a flowchart of the process, which runs 24 h/day, 320 days/yr. A denotes acetaminophen. (a) Calculate the yearly production rate of solid acetaminophen (tonne/yr), using as few dimensional equations as possible. (b) A proposal has been made to subject the liquid solution leaving the centrifuge to further processing to recover more of the dissolved acetaminophen instead of disposing of the solution. On what would the decision depend?
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