Sample Problem 2: Yield of Na₂CO₃·10H₂O Crystals

This page focuses on a problem involving the crystallization of sodium carbonate decahydrate $Na₂CO₃·10H₂O$ from a cooling process. The problem demonstrates how to calculate theoretical yield and actual yield of crystals when a solution of Na₂CO₃ is cooled and partially evaporated.

The solution method follows a systematic approach, starting with the given information about the initial solution composition and conditions. It then applies mass balance principles to determine the masses of liquid, vapor, and crystal phases. The problem introduces the concept of partial evaporation during cooling, which adds complexity to the calculation.

Definition: Theoretical yield - The maximum amount of product that can be produced based on the limiting reagent in a chemical reaction or process.

Example: The problem calculates the yield of Na₂CO₃·10H₂O crystals when 5000 kg of a 12.5% Na₂CO₃ solution is cooled and 5% of the water evaporates.

The solution demonstrates how to calculate yield percentage in production by comparing the amount of Na₂CO₃ in the crystals to the initial amount in the feed solution. This approach is essential for understanding the efficiency of industrial crystallization processes.

Highlight: The problem illustrates the importance of considering both anhydrous and hydrated forms of the compound when calculating yields in crystallization processes.

Sample Problem 3: MgSO₄·7H₂O Crystal Yield and Heat Balance

This page presents a more complex problem involving the crystallization of magnesium sulfate heptahydrate $MgSO₄·7H₂O$ with an added heat balance component. The problem demonstrates the integration of mass and energy balances in crystallization calculations.

The solution process begins with the given data, including the initial solution composition, temperatures, and thermodynamic properties. It then applies both mass and heat balance equations to determine the yield of crystals and the heat removed during the process.

Vocabulary: Heat capacity - The amount of heat required to raise the temperature of a substance by one degree Celsius.

Example: The problem calculates the yield of MgSO₄·7H₂O crystals when 2000 kg of a 30% MgSO₄ solution is cooled from 330 K to 293 K.

The solution demonstrates how to calculate theoretical yield from limiting reagent by considering the solubility of MgSO₄ at different temperatures. It also shows how to incorporate heat capacity and heat of crystallization data into the calculations.

Highlight: This problem emphasizes the importance of considering both mass and energy balances in crystallization processes, which is crucial for industrial applications.

The final step involves calculating the heat removed during the crystallization process, which is essential for designing cooling systems in industrial crystallizers.

Sample Problem 4: Na₂SO₄·10H₂O Crystallization with Heat Balance

This page presents a comprehensive problem involving the crystallization of sodium sulfate decahydrate $Na₂SO₄·10H₂O$, also known as Glauber's salt. The problem combines aspects of mass balance, heat balance, and partial evaporation in a cooling crystallization process.

The solution approach begins by listing the given data, which includes initial solution composition, temperatures, heat capacities, and equipment details. It then applies mass and energy balance principles to determine the yield of hydrated crystals and the heat removed during the process.

Vocabulary: Latent heat of vaporization - The amount of energy required to convert a liquid into a gas at constant temperature.

Example: The problem calculates the yield of Na₂SO₄·10H₂O crystals when a solution containing 500 kg of Na₂SO₄ and 2500 kg of water is cooled from 333 K to 283 K in a steel vessel.

The solution demonstrates how to find actual yield by considering the solubility of Na₂SO₄ at different temperatures and accounting for water loss through evaporation. It also shows how to incorporate the heat capacity of the solution, crystals, and the steel vessel into the heat balance calculations.

Highlight: This problem illustrates the complexity of real-world crystallization processes by including factors such as partial evaporation and heat transfer to the crystallization vessel.

The final steps involve calculating the mass of crystals formed and the heat removed during the process, which are crucial for designing and optimizing industrial crystallization operations.

Continuation of Sample Problem 4 and Summary

This page concludes the solution to the Na₂SO₄·10H₂O crystallization problem, focusing on the final calculations for the heat balance. It demonstrates the application of the energy balance equation to determine the total heat removed during the crystallization process.

The solution shows how to account for various heat contributions, including the sensible heat of the solution, the latent heat of crystallization, and the heat absorbed by the steel vessel. This comprehensive approach is essential for accurately modeling industrial crystallization processes.

Example: The final heat balance equation includes terms for the heat removed from the solution, the heat of crystallization released, and the heat absorbed by the steel vessel.

Highlight: The detailed heat balance calculation emphasizes the importance of considering all energy transfers in crystallization processes, which is crucial for process design and optimization.

The page concludes the series of sample problems, which collectively provide a thorough exploration of crystallization process steps and calculations. These problems cover a range of scenarios, from simple yield calculations to complex heat and mass balances, offering valuable insights into the practical applications of crystallization in chemical engineering and industrial processes.

Definition: Crystallization - A separation and purification technique that produces solid crystals from a solution by manipulating solubility conditions, typically through cooling or evaporation.

These sample problems serve as excellent resources for students and professionals learning about solubility and crystallization calculation examples, providing step-by-step solutions that can be applied to a wide range of crystallization scenarios in both academic and industrial settings.

Sample Problem 1: Calculating Yield of MgSO₄·7H₂O

This page presents a detailed solution for calculating the yield of magnesium sulfate heptahydrate $MgSO₄·7H₂O$ crystals from a cooling crystallization process. The problem involves determining the amount of crystals formed when a saturated solution of MgSO₄ is cooled from 353 K to 303 K.

The solution process begins with listing the given data, including the initial mass of the feed solution, temperatures, and solubility values. It then applies mass balance equations to calculate the masses of the liquid, vapor, and crystal phases. The crystallization process steps are clearly outlined, demonstrating how to use solubility data and mass balances to determine the yield.

Vocabulary: Solubility - The amount of a substance that can dissolve in a given amount of solvent at a specific temperature.

Example: The problem uses a specific case where 1000 kg of a saturated MgSO₄ solution is cooled, resulting in crystal formation.

Highlight: The solution emphasizes the importance of considering both the overall mass balance $OMB$ and the component mass balance $CMB$ in crystallization calculations.

The final step involves calculating the percentage yield of MgSO₄·7H₂O crystals, which is a crucial aspect of how to calculate percentage yield from mass in crystallization processes.