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Things were going smoothly at the Breaux Bridge Drug Co. pilot plant during the midnight to 8 a.m. shift until Therèse Lagniappe, the reactor operator, let the run instruction sheet get too close to the Coleman stove that was being used to heat water to prepare Lagniappe's bihourly cup of Community Coffee. What followed ended in a total loss of the run sheet, the coffee, and a substantial portion of the novel Lagniappe was writing. Remembering the less than enthusiastic reaction she got the last time she telephoned her supervisor in the middle of the night, Lagniappe decided to rely on her memory of the required flow-rate settings. The two liquids being fed to a stirred-tank reactor were circulostoic acid (CSA: \(M W=75, S G=0.90\) ) and flubitol (FB: \(M W=90, S G=0.75\) ). The product from the system was a popular over-the-counter drug that simultaneously cures high blood pressure and clumsiness. The molar ratio of the two feed streams had to be between 1.05 and 1.10 mol CSA/mol FB to keep the contents of the reactor from forming a solid plug. At the time of the accident, the flow rate of CSA was 45.8 L min. Lagniappe set the flow of flubitol to the value she thought had been in the run sheet: 55.2 L/min. Was she right? If not, how would she have been likely to learn of her mistake? (Note: The reactor was stainless steel, so she could not see the contents.)

Step by step solution

01

Define and understand the parameters

First, it's important to understand the defined parameters. Here, M W refers to the molecular weight of the substances, and S G to the specific gravity. It's also crucial to note that Therèse set the flow of flubitol to 55.2 L/min and the flow rate of CSA is given as 45.8 L/min.

02

Calculate the molar flows

To compute the molar flows, the volumetric flows are converted into molar flows using the specific gravity of each compound (which can be used to obtain mass flow) and the molecular weight. Therèse tries to keep a molar ratio between \(1.05\) and \(1.10\). The formulas used here are: \n\nMolar Flow of CSA, \(F_{CSA}\) = \(\frac{{(FlowRate_{CSA} * S G_{CSA})}}{{M W_{CSA}}}\) \n\nMolar Flow of FB, \(F_{FB}\) = \(\frac{{(FlowRate_{FB} * S G_{FB})}}{{M W_{FB}}}\)

03

Compute the molar ratio

Calculate the molar ratio as follows: \n\nMolar ratio = \(\frac{{F_{CSA}}}{{F_{FB}}}\)

04

Evaluate the result

Compare the calculated molar ratio with the desired range (\(1.05 - 1.10\) per mol of CSA). If the molar ratio is out of this range, it means Therèse's assumed flow rate for FB was incorrect.

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Key Concepts

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

Molecular Weight

Molecular weight, often abbreviated as MW, is a fundamental concept in chemistry that relates to the mass of one mole of a substance. It is usually expressed in grams per mole (g/mol). In practical terms, it gives us a comparative measure of how heavy different molecules are.

Molecular weight is calculated by summing the atomic weights of all the atoms in a molecule. For example, water (H₂O) has a molecular weight of approximately 18 g/mol because it consists of two hydrogen atoms (1 g/mol each) and one oxygen atom (16 g/mol).

In the context of chemical process calculations, knowing the molecular weight is essential for converting between mass and moles, which is necessary when calculating the molar flow rates of different substances in a process.

Specific Gravity

Specific gravity (SG) is a dimensionless number that represents the density of a substance compared to the density of water at a specific temperature, usually 4°C, where water has its maximum density. The specific gravity is defined as the ratio of the density of the substance to the density of water.

For example, a substance with a specific gravity of 2.0 is twice as dense as water. It is useful in various industries because it helps in determining the flow rates and volumes when dealing with liquids, as in the case of the exercise with the stirred-tank reactor.

The specific gravity of circulostoic acid (CSA) is 0.90, meaning it's less dense than water, while the specific gravity of flubitol (FB) is 0.75, indicating it's even less dense. This information, combined with molecular weight, supports the calculations for the molar flow rates of these chemicals.

Molar Flow Rate

The molar flow rate is an expression of the number of moles of a substance passing through a given surface area per unit of time, typically measured in moles per minute (mol/min) or moles per hour (mol/hr).

To calculate the molar flow rate from the volumetric flow rate, you need to know the substance's molecular weight and specific gravity. By multiplying the volumetric flow rate by the specific gravity, you convert volume to mass, which you then divide by the molecular weight to switch from mass flow rate to molar flow rate:
\[\begin{equation}Molar Flow Rate = \frac{Volumetric Flow Rate \times Specific Gravity}{Molecular Weight}\end{equation}\]In a chemical process, the precise control of molar flow rates is vital. Too much or too little of a reactant can lead to inefficient reactions or even safety hazards, such as the potential for chemical plugs mentioned in Therèse Lagniappe's scenario.

Molar Ratio

The molar ratio is a unitless value representing the proportion of one substance relative to another in a chemical reaction. It is calculated as the ratio of the molar flow rates of the reactants.

Correct molar ratios are crucial for ensuring the desired chemical reaction occurs properly. In the case of Therèse Lagniappe, the molar ratio between circulostoic acid (CSA) and flubitol (FB) needs to be between 1.05 and 1.10 mol CSA/mol FB. This precise range guarantees the quality of the final pharmaceutical product.

The molar ratio is determined by:\[\begin{equation}Molar Ratio = \frac{Molar Flow Rate of Substance A}{Molar Flow Rate of Substance B}\end{equation}\]In chemical processing, maintaining the correct molar ratios is crucial, as deviations can affect product yield, purity, and could lead to undesired side reactions or products.

Stirred-Tank Reactor

A stirred-tank reactor is a common type of vessel used in chemical processing that allows for mixing substances to ensure uniformity in temperature, concentration, and reaction rate. These reactors can operate either in a batch or continuous mode.

In a continuously operated stirred-tank reactor, reactants are continuously added, and products are removed to maintain a stable operation. It's essential that the input molar flow rates are controlled accurately to prevent any buildup or depletion of reactants, which could negatively impact the reaction.

Without accurate flow-rate settings, as Therèse Lagniappe experienced in the exercise, reactions within a stirred-tank reactor can become imbalanced, potentially causing the formation of a solid plug or suboptimal product synthesis. The inability to visually monitor the reactor contents adds to the challenge, necessitating a reliable understanding of process calculations.