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.