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Ethane is chlorinated in a continuous reactor: $$\mathrm{C}_{2} \mathrm{H}_{6}+\mathrm{Cl}_{2} \rightarrow \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{Cl}+\mathrm{HCl}$$ Some of the product monochloroethane is further chlorinated in an undesired side reaction: $$\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{Cl}+\mathrm{Cl}_{2} \rightarrow \mathrm{C}_{2} \mathrm{H}_{4} \mathrm{Cl}_{2}+\mathrm{HCl}$$ (a) Suppose your principal objective is to maximize the selectivity of monochloroethane production relative to dichloroethane production. Would you design the reactor for a high or low conversion of ethane? Explain your answer. (Hint: If the reactor contents remained in the reactor long enough for most of the ethane in the feed to be consumed, what would the main product constituent probably be?) What additional processing steps would almost certainly be carried out to make the process economically sound? (b) Take a basis of \(100 \mathrm{mol} \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{Cl}\) produced. Assume that the feed contains only ethane and chlorine and that all of the chlorine is consumed, and carry out a degree-of-freedom analysis based on atomic species balances. (c) The reactor is designed to yield a \(15 \%\) conversion of ethane and a selectivity of \(14 \mathrm{mol} \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{Cl} / \mathrm{mol}\) \(\mathrm{C}_{2} \mathrm{H}_{4} \mathrm{Cl}_{2},\) with a negligible amount of chlorine in the product gas. Calculate the feed ratio \(\left(\mathrm{mol} \mathrm{Cl}_{2} /\right.\) mol \(\mathrm{C}_{2} \mathrm{H}_{6}\) ) and the fractional yield of monochloroethane. (d) Suppose the reactor is built and started up and the conversion is only \(14 \% .\) Chromatographic analysis shows that there is no \(\mathrm{Cl}_{2}\) in the product but another species with a molecular weight higher than that of dichloroethane is present. Offer a likely explanation for these results.

Step by step solution

01

Analyzing readability for optimum selectivity

Selectivity is a term in chemical engineering that describes the relative rate at which a reactant is consumed in different reaction pathways. In order to optimize the process for the formation of monochloroethane, the reactor would likely be designed for a low conversion of ethane. This is because, in continuous reactors, the reaction time is inversely proportional to the conversion of the limiting reactant. If the ethane is consumed rapidly (high conversion), the contents of the reactor would be composed mostly of products, allowing for the side reaction to occur and produce dichloroethane. An additional processing step to make the method more economically sound might be the implementation of a separation process after the reactor to separate and recycle unreacted ethane.

02

Calculating degree of freedom for atomic species balances

The atomic species balance equations can be written as follows, based on the reactions:For Carbon: \(1*\) (Mol of \(C_2 H_6\)) + 0 = 1* (Mol of \(C_2 H_5 Cl\)) + 2 * (Mol of \(C_2 H_4 Cl_2\)) For Hydrogen: \(6*\) (Mol of \(C_2 H_6\)) = 5* (Mol of \(C_2 H_5 Cl\)) + 4 * (Mol of \(C_2 H_4 Cl_2\)) + 1 * (Mol of HCl) For Chlorine: \(2*\) (Mol of \(Cl_2\)) = 1* (Mol of \(C_2 H_5 Cl\)) + 2 * (Mol of \(C_2 H_4 Cl_2\)) + 1 * (Mol of HCl) In this case, since the basis has been set as 100 mol \(C_2 H_5 Cl\), there are 3 equations (for each element: C,H,Cl) and 4 unknowns (mol \(C_2 H_6\), mol \(Cl_2\), mol \(C_2 H_4 Cl_2\) and mol HCl).

03

Calculate the feed ratio

The feed ratio can be calculated by the stoichiometry of the reactions. Given 15% conversion, we first need to calculate mol of \(C_2 H_{6}\), mol of \(C_2 H_{4} Cl_{2}\) and mol of Cl_{2}\. With the selectivity of 14 mol \(C_{2} H_{5} Cl_{2}\) per mol of \(C_{2} H_{4} Cl_{2}\), we can find that mol \(C_{2} H_{4} Cl_{2} = 100/14\). Consequently, mol \(C_{2} H_{6}\) = mol \(C_{2} H_{5} Cl_{2}\) + mol \(C_{2} H_{4} Cl_{2}\). The result then can be used to calculate the molar of \(Cl_{2}\) = mol \(C_{2} H_{5} Cl_{2}\) + 2*\(C_{2} H_{4} Cl_{2}\). Thus, feed ratio can be calculated by dividing mol \(Cl_{2}\) by mol \(C_{2} H_{6}\).

04

Calculate the fractional yield of monochloroethane

The fractional yield is given by the moles of \(C_2 H_5 Cl\) produced over the moles of ethane reacted. From the stoichiometry of the reaction, for every 1 mol of ethane reacted, 1 mol of monochloroethane is produced. Thus, fractional yield = mol \(C_2 H_5 Cl\)/ mol \(C_2 H_6\).

05

Explanation for the change in reaction conditions

If the conversion is less than expected and there are species with higher molecular weight than expected in the product, there might have been additional side reactions producing heavier compounds. The presence of these heavy species might be the reason for reduced conversion. Additionally, the absence of Cl2 suggests that chlorine has been entirely consumed, possibly in those side reactions resulting in heavier products.

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Key Concepts

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

Selectivity in Reactions

In chemical reaction engineering, selectivity is crucial when it comes to optimizing production processes. Selectivity determines which products are formed by controlling how reactants are distributed among the possible pathways.
Selectivity can be defined as the ratio of desired product formation to the side or undesired product formation. For example, in the chlorination process of ethane, forming monochloroethane while minimizing dichloroethane is the goal.
To achieve high selectivity, you can balance reaction conditions. Usually, limiting the conversion of reactants like ethane can help, as a high conversion often leads to more by-products. By designing for lower conversion, the reactor reduces the chances of ethane being turned into secondary, undesired products. This means less time for side reactions to occur.
In practical applications, additional steps like separation processes may be necessary. This recycles unreacted materials back into the system. Improving selectivity is not just about reactor conditions but also integrating downstream processes that enhance economic viability.

Chlorination Process

Chlorination is a process where chlorine is added to a molecule, often improving or introducing new properties. In the ethane chlorination process, chlorine reacts with ethane to produce monochloroethane and hydrogen chloride as the primary products.
This reaction is sensitive to conditions such as reaction time and chlorine concentration. Adjusting these parameters helps maximize the desired product and minimize unwanted side reactions, such as forming dichloroethane. The key is to stop the reaction at a point where further chlorination, leading to undesirable products, does not predominantly occur.
Various methods can be used to control the chlorination process, including:

• Managing reactant ratios: Carefully controlling the ratio of ethane to chlorine.
• Temperature control: Keeping the reaction at an optimal temperature to favor selective reaction paths.
• Reaction time management: Ensuring the reaction does not proceed beyond desired levels of product formation.

Overall, understanding and manipulating the chlorination process are essential for optimizing outcomes in industrial applications.

Degree of Freedom Analysis

In chemical engineering, degree of freedom analysis is a method used to determine how many variables can be set independently in a system. For reactions, this involves breaking down components and tracking the number of equations versus unknowns.
To conduct a degree of freedom analysis for the ethane chlorination process, start by identifying atomic species involved: carbon (C), hydrogen (H), and chlorine (Cl). Each element provides a balance equation.
For instance, you have three balance equations for the three elements involved. However, there are also four unknowns to solve for: the moles of ethane, chlorine, dichloroethane, and hydrogen chloride. The difference between equations and unknowns dictates your degree of freedom. Here it results in one degree of freedom, meaning you need additional information or assumptions—like conversion rates—to solve the system fully.
This analysis helps you understand the complexity of a chemical process, assisting in designing reactors and optimizing conditions for specific outcomes.

Stoichiometry in Chemical Reactions

Stoichiometry is the quantitative relationship between reactants and products in a chemical reaction. It is foundational for calculating the quantities needed and predicting the yields of a reaction.
In reactions like ethane chlorination, stoichiometry is utilized to balance the chemical equations, ensuring mass conservation according to the law of conservation of mass. It helps in determining the proportional amounts of each substance needed to react completely.
For example, the stoichiometry of the ethane-chlorine system can be represented by the reaction equations. This helps quantify the number of moles of each reactant and product. With a known conversion or selectivity target, stoichiometry can be used to calculate the input amounts and expected output.
When you calculate the feed ratio or fractional yields, stoichiometry provides the framework for those calculations. It tells you how much of a reactant is converted into a particular product, considering all other products formed by side reactions. This is vital for designing efficient industrial chemical processes.