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L-Serine is an amino acid that often is provided when intravenous feeding solutions are used to maintain the health of a patient. It has a molecular weight of \(105,\) is produced by fermentation and recovered and purified by crystallization at \(10^{\circ} \mathrm{C}\). Yield is enhanced by adding methanol to the system, thereby reducing serine solubility in aqueous solutions. An aqueous serine solution containing 30 wt\% serine and \(70 \%\) water is added along with methanol to a batch crystallizer that is allowed to equilibrate at \(10^{\circ} \mathrm{C}\). The resulting crystals are recovered by filtration; liquid passing through the filter is known as filtrate, and the recovered crystals may be assumed in this problem to be free of adhering filtrate. The crystals contain a mole of water for every mole of serine and are known as a monohydrate. The crystal mass recovered in a particular laboratory run is \(500 \mathrm{g},\) and the filtrate is determined to be \(2.4 \mathrm{wt} \%\) serine, \(48.8 \%\) water, and \(48.8 \%\) methanol. (a) Draw and label a flowchart for the operation and carry out a degree-of- freedom analysis. Determine the ratio of mass of methanol added per unit mass of feed. (b) The laboratory process is to be scaled to produce \(750 \mathrm{kg} / \mathrm{h}\) of product crystals. Determine the required aqueous serine solution rates of aqueous serine solution and methanol.

Step by step solution

01

Understanding the problem and labeling

A diagram should be constructed to represent the system. The system should be divided into three main streams labelled as Feed (F), Product recuperated crystals (P) and Filtrate (E). The quantities provided by the problem should now be inserted in the-block diagram. Methanol (M) is only present in the feed and the effluent. The feed is 30 wt% amino acid (serine), 70 wt% water; the product is serine monohydrate (combination of one molecule of serine with one molecule of water; i.e., it is half serine by moles); the effluent is 2.4 wt% serine, 48.8 wt% water, and 48.8 wt% methanol.

02

Degree-of-freedom Analysis

The degree of freedom for this problem can be determined by the formula DOF = C – E + 2; where C = number of components and E = Equations linking variables in the system. In this case, we have three components (Serine, Water, Methanol). We have 2 independent balance equations (Serine and Water) plus one extra equation that Total feed = Total output. Therefore, DOF = 3 – 3 + 2 = 2. This means two independent variables must be specified or two pieces of information are needed to solve this problem completely.

03

Solving for methanol addition per feed mass.

Write mass balance equations for serine and water, and solve for the methanol requirement M. The general form would be (Mass of serine or water in feed) + (Mass of serine or water in methanol) = (Mass of serine or water in filtrate) + (Mass of serine or water in product). Since there is no methanol in the product and filtrate, its mass balance will be (Mass of methanol in feed) = (Mass of methanol in filtrate). From solving these equations, you can find M/F, the ratio of mass of methanol added per unit feed.

04

Scaling and flow rate calculations.

To determine the flow rate of the aqueous serine solution and methanol for a production target of \(750 \mathrm{kg} / \mathrm{h}\), the results from the laboratory run need to be scaled up. This can be done by finding the mass percentages of product, feed and methanol from the lab run and assuming these ratios will be the same at the larger scale. Use the known target output rate to calculate the mass flow rate of aqueous serine solution and methanol required.

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Key Concepts

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

Amino Acid Crystallization

Amino acid crystallization is an essential process in chemical engineering, especially for producing high-purity L-Serine, an amino acid utilized in intravenous feeding solutions. The crystallization process here involves separating L-Serine from an aqueous mixture by including methanol, which reduces the solubility of serine. Lower solubility means serine can easily crystallize out of the solution when the temperature is reduced. In our example, the process takes place at a low temperature of 10°C. This temperature facilitates the formation of crystals by slowing down molecular movements, permitting serine molecules to arrange themselves into a crystalline structure.

Once the crystals form, they are filtered off from the liquid phase, known as the filtrate. The fascinating aspect of this procedure is that the crystals formed contain water in a 1:1 ratio with serine molecules, classifying them as monohydrates. Understanding the nature of crystals and solubility behavior is paramount in optimizing this purification technique. This allows for maximizing the yield of serine crystals which are crucial for medical and biochemical applications.

Degree-of-Freedom Analysis

In chemical engineering, performing a degree-of-freedom (DOF) analysis is crucial for predicting whether a system can be solved or more data is needed. The DOF analysis uses the equation: \( \text{DOF} = C - E + 2 \), where \( C \) is the number of components and \( E \) is the number of independent equations. This equation tells us how many variables need to be specified to find a solution.

For our amino acid crystallization process, we consider three components: serine, water, and methanol. In the laboratory experiment, the balance includes two independent mass balance equations for serine and water. There’s also a total balance equation that assures the sum of all outputs equals the feed. The result, in this case, is that we have two degrees of freedom, meaning we need two additional pieces of information or specified variables to solve the problem entirely.

Approaching this analysis systematically helps when scaling up processes, such as determining if more methanol or other conditions need altering to refine production.

Mass Balance Equations

Understanding mass balance equations is fundamental because they ensure that mass entering a system equals mass leaving, accounting for any generation or consumption. This principle is the cornerstone of chemical engineering and is particularly useful in crystallization processes where we aim for reliability and precision.

In the L-Serine crystallization exercise, we write mass balance equations for each component. For instance, for serine, the equation would include its initial mass in the feed plus any interaction in the methanol stream equating to the mass in the filtrate and product (crystals). The balance is crucial because it outlines how much methanol should be added to achieve optimal crystallization and recovery.

Similarly, mass balance for water follows the same logic, keeping track of water in the feed, in the formed crystals, and the filtrate. Solving these equations provides insight into the system's dynamics, such as the quantity of methanol required, ensuring no methanol is left in the end product, refining both efficiency and purity in the crystallization process.