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Ethanol can be produced commercially by the hydration of ethylene: $$\mathrm{C}_{2} \mathrm{H}_{4}+\mathrm{H}_{2} \mathrm{O} \rightarrow \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}$$ Some of the product is converted to diethyl ether in the side reaction $$2 \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH} \rightarrow\left(\mathrm{C}_{2} \mathrm{H}_{5}\right)_{2} \mathrm{O}+\mathrm{H}_{2} \mathrm{O}$$ The feed to the reactor contains ethylene, steam, and an inert gas. A sample of the reactor effluent gas is analyzed and found to contain 43.3 mole\% ethylene, 2.5\% ethanol, 0.14\% ether, 9.3\% inerts, and the balance water. (a) Take as a basis 100 mol of effluent gas, draw and label a flowchart, and do a degree-of-freedom analysis based on atomic species to prove that the system has zero degrees of freedom. (b) Calculate the molar composition of the reactor feed, the percentage conversion of ethylene, the fractional yield of ethanol, and the selectivity of ethanol production relative to ether production. (c) The percentage conversion of ethylene you calculated should be very low. Why do you think the reactor would be designed to consume so little of the reactant? (Hint: If the reaction mixture remained in the reactor long enough to use up most of the ethylene, what would the main product constituent probably be?) What additional processing steps are likely to take place downstream from the reactor?

Step by step solution

01

Basis selection and identification of unknowns

Set the basis to be 100 mol of effluent gas. Now, list down all the unknown quantities: the moles of components in the reactor feed, the moles of components in the reactor outlet, the percentage conversion of ethylene, the fractional yield of ethanol and selectivity of ethanol production.

02

Atomic balance

Apply the law of mass conservation to each of the atomic species (Carbon, Hydrogen and Oxygen) involved in the reactions. You have three equations here since for each atomic species, the number of atoms entering the reactor should equate the number of atoms leaving the reactor.

03

Calculating the balance

Next, calculate the balance for each of the atomic species using the information given in the problem. This gives you three more equations which can be solved to find the molar composition of the reactor feed.

04

Percentage Conversion

Percentage conversion of ethylene can be calculated as follows: Percentage Conversion = [(Initial moles - final moles) / Initial moles] * 100 . Use the values from step 3 to get the result.

05

Calculating the fractional yield and selectivity

Fractional yield of ethanol can now be determined by the ratio of moles of ethanol formed to the moles of ethylene reacted. The selectivity of ethanol production relative to ether production can be determined by the ratio of moles of ethanol formed to the moles of ether formed.

06

Reasoning for low conversion

Lastly, the reason for low conversion is that a high percentage of ethylene conversion would lead to a higher percentage of ether in the product (according to the second reaction). Hence to maximize ethanol production, the reactor is designed to have lower ethylene conversion. Post-reactor, the product stream would likely be separated and purified via distillation and perhaps the unreacted ethylene might be recycled back to the reactor.

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Key Concepts

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

Molar Composition

Molar composition refers to the proportion of each component in a mixture, expressed in moles. In chemical reaction engineering, understanding the molar composition is crucial, as it helps determine the proportions of reactants and products involved in reactions.
In the context of the given problem, the effluent from the reactor is analyzed, revealing the molar percentages of components like ethylene, ethanol, ether, inerts, and water. This analysis provides insights into the chemical behavior within the reactor, guiding further calculations and reactor design improvements.
When performing these calculations, the assumption is often made that sample size is representative of the entire system. Molar composition helps inform decisions regarding the efficiency of the reaction and the need for additional steps in the processing line.

Percentage Conversion

Percentage conversion is a critical concept in chemical engineering, providing a quantitative measure of how much of a reactant has been transformed into desired products. For ethylene, the percentage conversion is calculated by comparing the initial moles to the moles remaining post-reaction.
The formula used is: \[ \text{Percentage Conversion} = \left(\frac{\text{Initial moles} - \text{Final moles}}{\text{Initial moles}}\right) \times 100 \]
A low percentage conversion in the given scenario indicates that not much ethylene is being consumed to form the products. This can seem inefficient, but it's often strategically planned.
The low conversion of ethylene prevents excessive formation of unwanted by-products like diethyl ether, which can emerge in higher concentrations if the reactant remains longer in the reactor.

Fractional Yield

Fractional yield is a term used to describe the efficiency of obtaining a desired product from the reactants. It is especially useful when side reactions, as seen in the problem, can produce undesired products.
The fractional yield of ethanol, the primary product of interest, is determined by the ratio of moles of ethanol formed to the moles of ethylene reacted. The formula used is: \[ \text{Fractional Yield} = \frac{\text{Moles of Ethanol Formed}}{\text{Moles of Ethylene Reacted}} \]
This ratio provides a way to assess the effectiveness of the ethylene hydration process. A higher fractional yield signifies a more efficient conversion to the target product, which is crucial for optimizing resource usage and minimizing waste.

Reactor Design

Reactor design plays a critical role in determining the outcome of chemical processes. It involves selecting appropriate conditions (such as temperature, pressure, and residence time) that optimize the yield of desired products while minimizing by-products.
In the given exercise, the reactor is designed to achieve low ethylene conversion to limit the unwanted formation of diethyl ether, favoring ethanol production. This decision is often influenced by downstream processing requirements.
Once the reaction is complete, additional steps such as distillation are likely employed to separate and purify the mixture. Efficient reactor design not only improves economic feasibility but also enhances safety and environmental compliance in industrial operations.