Question

In a textile mill, a double-effect evaporator system concentrates weak liquor containing \(4 \%\) (by mass) caustic soda to produce a lye containing \(25 \%\) solids (by mass). What is the weight of water evaporated per \(100 \mathrm{~g}\) feed in the evaporator? (a) \(125.0 \mathrm{~g}\) (b) \(50.0 \mathrm{~g}\) (c) \(84.0 \mathrm{~g}\) (d) \(16.0 \mathrm{~g}\)

Short answer

The weight of water evaporated per 100 g feed in the evaporator is 84.0 g.

Step-by-step solution

Determine the mass of caustic soda in the feed

The feed contains 4% caustic soda by mass. So, for every 100 g of feed, the mass of caustic soda will be 4 g.

Calculate the mass of feed after evaporation

After evaporation, the lye contains 25% solids, which is the caustic soda. Thus, to find the mass of feed after evaporation, let the mass of the caustic soda remain constant at 4 g (\(x\) g of the lye contain 4 g of caustic soda), implying \(x = \frac{4}{0.25} = 16\) g.

Determine the weight of water evaporated

The initial weight of the feed is 100 g. The final weight after concentrating is 16 g. The weight of water evaporated is the difference, \(100 - 16 = 84\) g.

Key concepts

Caustic Soda Concentration

Understanding caustic soda concentration is crucial when working with chemical solutions. Caustic soda, also known as sodium hydroxide, is a commonly used chemical in the textile industry for processes like cleaning and bleaching. Its concentration in a solution is usually expressed as a percentage by mass. This percentage signifies the amount of caustic soda in a given mass of the whole solution and is crucial for ensuring the effectiveness of the chemical process while maintaining safety standards.

For instance, in the exercise problem provided, the 'weak liquor' initially contains 4% caustic soda by mass. It's important for students to grasp that this figure is not arbitrary but rather calculated taking into account the specific requirements of the process it is being used for. Changes in concentration, achieved through evaporation in this example, are aimed at enhancing the caustic soda effectiveness for its intended purpose in the textile mill.

Mass Percentage Calculation

Mass percentage calculation is a fundamental concept in chemistry and chemical engineering, representing the concentration of a component in a mixture. It’s defined as the mass of a specific component divided by the total mass of the mixture, multiplied by 100%.

In our problem, the mass percentage of caustic soda needs to be increased from 4% to 25%. To understand this transition, one must be able to calculate the new mass of the solution after water has been evaporated. The mass percentage ensures accuracy in the resulting chemical concentration, which is essential for the quality and effectiveness of the products being manufactured, such as the lye in the textile industry.

Evaporative Concentration

Evaporative concentration is a process used in industries to increase the concentration of a particular substance in a solution. This is done by evaporating the solvent—in most cases, water—leaving behind a more concentrated solution of the solute. This process can be seen in the provided exercise where water is evaporated from the weak liquor to increase the concentration of the caustic soda.

It involves careful control of temperature and pressure to ensure efficient evaporation. By understanding the principles of evaporative concentration, students are able to predict and calculate the outcomes of such processes, as seen in chemical engineering problems where precision is paramount.

Chemical Engineering Problems

Chemical engineering problems, like the one in our textbook exercise, often involve calculations related to mass balances and concentrations. These problems require a methodical approach to solving, which typically includes defining the problem, identifying the known variables, setting up the equations, and then performing calculations.

For example, knowing the principles of mass balance, one can deduce the quantity of water evaporated in an evaporator system by keeping the mass of the caustic soda constant and calculating the loss in mass of the overall solution. Such problems not only test the student’s understanding of theoretical concepts but also their ability to apply these concepts in practical, real-world situations.