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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

How many of the following are found in 15.0 kmol of xylene \(\left(\mathrm{C}_{8} \mathrm{H}_{10}\right) ?\) (a) \(\mathrm{kg} \mathrm{C}_{8} \mathrm{H}_{10}\); (b) mol \(\mathrm{C}_{8} \mathrm{H}_{10}\); (c) lb-mole \(\mathrm{C}_{8} \mathrm{H}_{10} ;\) (d) mol (g-atom) \(\mathrm{C} ;\) (e) mol \(\mathrm{H} ;\) (f) \(\mathrm{g} \mathrm{C} ;\) (g) \(\mathrm{g} \mathrm{H} ;\) (h) molecules of \(\mathrm{C}_{8} \mathrm{H}_{10}\).

A mixture of methanol (methyl alcohol) and water contains \(60.0 \%\) water by mass. (a) Assuming volume additivity of the components, estimate the specific gravity of the mixture at \(20^{\circ} \mathrm{C} .\) What volume (in liters) of this mixture is required to provide 150 mol of methanol? (b) Repeat Part (a) with the additional information that the specific gravity of the mixture at \(20^{\circ} \mathrm{C}\) is 0.9345 (making it unnecessary to assume volume additivity). What percentage error results from the volume- additivity assumption?

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 chemical reactor shown below has a cover that is held in place by a series of bolts. The cover is made of stainless steel ( \(\mathrm{SG}=8.0\) ), is 3 inches thick, has a diameter of 24 inches, and covers and seals an opening 20 inches in diameter. During turnaround, when the reactor is taken out of service for cleaning and repair, the cover was removed by an operator who thought the reactor had been depressurized using a standard venting procedure. However, the pressure gauge had been damaged in an earlier process upset (the reactor pressure had exceeded the upper limit of the gauge), and instead of being depressurized completely, the vessel was under a gauge pressure of 30 psi. (a) What force ( \(\left(\mathrm{b}_{\mathrm{f}}\right)\) were the bolts exerting on the cover before they were removed? (Hint: Don't forget that a pressure is exerted on the top of the cover by the atmosphere.) What happened when the last bolt was removed by the operator? Justify your prediction by estimating the initial acceleration of the cover upon removal of the last bolt. (b) Propose an alteration in the turnaround procedure to prevent recurrence of an incident of this kind.

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 \(t=265 \mathrm{s}\).
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