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Hydrogen sulfide has the distinctive unpleasant odor associated with rotten eggs, and it is poisonous. It often must be removed from crude natural gas and is therefore a product of refining natural gas. In such instances, the Claus process provides a means of converting \(\mathrm{H}_{2} \mathrm{S}\) to elemental sulfur. Consider a feed stream to a Claus process that consists of 10.0 mole \(\% \mathrm{H}_{2} \mathrm{S}\) and \(90.0 \% \mathrm{CO}_{2}\). Onethird of the stream is sent to a furnace where the \(\mathrm{H}_{2} \mathrm{S}\) is burned completely with a stoichiometric amount of air fed at 1 atm and \(25^{\circ} \mathrm{C}\). The combustion reaction is $$\mathrm{H}_{2} \mathrm{S}+\frac{3}{2} \mathrm{O}_{2} \rightarrow \mathrm{SO}_{2}+\mathrm{H}_{2} \mathrm{O}$$ The product gases from this reaction are then mixed with the remaining two- thirds of the feed stream and sent to a reactor in which the following reaction goes to completion: $$2 \mathrm{H}_{2} \mathrm{S}+\mathrm{SO}_{2} \rightarrow 3 \mathrm{S}+2 \mathrm{H}_{2} \mathrm{O}$$ The gases leave the reactor at \(10.0 \mathrm{m}^{3} / \mathrm{min}, 320^{\circ} \mathrm{C},\) and \(205 \mathrm{kPa}\) absolute. Assuming ideal-gas behavior, determine the feed rate of air in kmol/min. Provide a single balanced chemical equation reflecting the overall process stoichiometry. How much sulfur is produced in \(\mathrm{kg} / \mathrm{min} ?\)

Step by step solution

01

Identify the Stoichiometry of Individual Reactions

The given chemical reactions are: \[ \mathrm{H}_{2} \mathrm{S} + \frac{3}{2} \mathrm{O}_{2} \rightarrow\mathrm{SO}_{2} + \mathrm{H}_{2} \mathrm{O} \] and \[ 2 \mathrm{H}_{2} \mathrm{S} +\mathrm{SO}_{2} \rightarrow 3 \mathrm{S} + 2\mathrm{H}_{2} \mathrm{O}. \] From these reactions, we can identify that one molecule of H2S reacts with half as many molecules of O2 to form one molecule of SO2 and H2O in the first reaction, and two molecules of H2S react with one molecule of SO2 to form three molecules of S and two molecules of H2O in the second reaction.

02

Determine Feed Rate of Air

If we consider the furnance system, \[ n_{H_2S} = n_{\frac{air}{5}} = 0.1n_{feed} \] \[1-0.1 = 0.9 = n_{CO_2} \] Multiplying by 5 and solving for \( n_{air} \) yields: \[ n_{air} = 5(0.1)n_{feed} - n_{feed} = 0.4n_{feed} \] Since one third of the feed goes through the system, the air feed rate is 0.4/3 mol/min.

03

Determine the Overall Balanced Chemical Equation

Multiplying the first reaction by 3 and adding it to the second reaction gives \[ 3\mathrm{H}_{2} \mathrm{S} + \frac{9}{2} \mathrm{O}_{2} +2 \mathrm{H}_{2} \mathrm{S} +\mathrm{SO}_{2} \rightarrow 3 \mathrm{SO}_{2} + 3 \mathrm{H}_{2} \mathrm{O} + 3 \mathrm{S} + 2\mathrm{H}_{2} \mathrm{O} \] Simplifying this yields \[ 5\mathrm{H}_{2} \mathrm{S} + \frac{9}{2} \mathrm{O}_{2} \rightarrow 3 \mathrm{SO}_{2} + 5 \mathrm{H}_{2} \mathrm{O} + 3 \mathrm{S}, \] which is the overall balanced chemical equation for the process.

04

Determine the Quantity of Sulfur Produced

The second reaction yields 3 moles of sulfur from 2 moles of H2S and 1 mole of SO2. We have one-third of H2S reactant gone through the reaction, so it's 0.1/3 mol/min. The rate of sulfur produced is therefore (3/2) times the rate of H2S reacted, which is (3/2)*(0.1/3) mol/min. Then multiply by the molar mass of sulfur (32.06 kg/kmol) to get the mass of sulfur produced per minute.

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Key Concepts

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

Claus Process

The Claus process is widely utilized in the chemical industry to remove hydrogen sulfide (\( \mathrm{H}_2\mathrm{S} \)) from natural gas and convert it into elemental sulfur. This process is essential because hydrogen sulfide is not only toxic but also has a distinct, foul odor reminiscent of rotten eggs. The transformation of \( \mathrm{H}_2\mathrm{S} \) into sulfur mitigates these hazards and yields a useful byproduct.
The Claus process typically unfolds in two steps:

• First, the \( \mathrm{H}_2\mathrm{S} \) is partially oxidized to \( \mathrm{SO}_2 \) in a furnace, where it reacts with air in a controlled manner. This step involves the combustion of one-third of the \( \mathrm{H}_2\mathrm{S} \) in the presence of a stoichiometric amount of oxygen, following the reaction:

\[\mathrm{H}_2\mathrm{S} + \frac{3}{2} \mathrm{O}_2 \rightarrow \mathrm{SO}_2 + \mathrm{H}_2\mathrm{O}.\]

• In the second step, the remaining \( \mathrm{H}_2\mathrm{S} \) is reacted with the \( \mathrm{SO}_2 \) produced to yield elemental sulfur, represented by the equation:

\[2 \mathrm{H}_2\mathrm{S} + \mathrm{SO}_2 \rightarrow 3 \mathrm{S} + 2 \mathrm{H}_2\mathrm{O}.\]This process is highly effective at removing and converting hydrogen sulfide, with the formation of sulfur offering a commercial advantage.

Ideal Gas Behavior

In chemical engineering, understanding gas behavior is essential, especially in processes such as the Claus process. Ideal gas law offers a simplified correlation between pressure (\( P \)), volume (\( V \)), and temperature (\( T \)), making it easier to predict the behavior of gases in various conditions. This law is expressed by the equation:\[PV = nRT,\]where \( n \) is the number of moles, and \( R \) is the ideal gas constant.
Assuming ideal-gas behavior simplifies calculations in engineering processes. However, it is important to remember this assumption works best at high temperatures and low pressures where gases behave more ideally. This is particularly relevant in the Claus process where gases are mixed and reacted under specific conditions. By treating gases as ideal, engineers can accurately estimate emissions, product yields, and reactant needs. Furthermore, ideal gas behavior aids in determining various parameters, such as the air feed rate in the furnace, which is crucial for ensuring optimal conditions for sulfur recovery.
Despite its simplifications, the ideal gas assumption is a foundational tool in chemical engineering, offering accuracy for most practical purposes and simplifying complex process calculations.

Chemical Engineering Education

Chemical engineering education plays a pivotal role in preparing students to tackle real-world problems like those encountered in the Claus process. Students are equipped with knowledge of chemical thermodynamics, reaction kinetics, and process design to efficiently handle industrial applications.
By engaging with problems that require understanding of stoichiometry and reaction balancing, such as the transformation of \( \mathrm{H}_2\mathrm{S} \) to sulfur, students develop critical thinking skills necessary for designing and optimizing chemical processes. Education in chemical engineering also emphasizes the importance of understanding gas behavior and assumptions like ideal gas behavior, which simplify calculations and aid in process design.
Furthermore, modern chemical engineering education integrates hands-on experiments and simulations. Students gain insights into the operation of refining and purification processes, helping them to appreciate the environmental and economic impacts of their work. With a combination of theoretical knowledge and practical application, chemical engineering students are well-prepared to innovate and contribute to technological advancements.

• Understanding stoichiometry and reaction mechanics is crucial.
• Application of ideal gas laws for process optimization is emphasized.
• Hands-on practice ensures familiarity with real industrial conditions and challenges.

In essence, chemical engineering education is about equipping future engineers with the skills needed to lead advancements in industry and improve efficiency and safety in chemical processes.