91Ó°ÊÓ

Air at \(25^{\circ} \mathrm{C}\) and 1 atm with a relative humidity of \(25 \%\) is to be dehumidified in an adsorption column packed with silica gel. The equilibrium adsorptivity of water on silica gel is given by the expression \(^{19}\).$$X^{*}(\mathrm{kg} \text { water/ } 100 \mathrm{kg} \text { silica gel })=12.5 \frac{p_{\mathrm{H}_{2} \mathrm{O}}}{p_{\mathrm{H}_{2} \mathrm{O}}^{*}}$$ where \(p_{\mathrm{H}_{2} \mathrm{O}}\) is the partial pressure of water in the gas contacting the silica gel and \(p_{\mathrm{H}, \mathrm{O}}^{*}\) is the vapor pressure of water at the system temperature. Air is fed to the column at a rate of 1.50 L/min until the silica gel is saturated (i.e., until it reaches equilibrium with the feed air), at which point the flow is stopped and the silica gel regenerated. (a) Calculate the minimum amount of silica gel needed in the column if regeneration is to take place no more frequently than every two hours. State any assumptions you make. (b) Briefly describe this process in terms that a high school student would have no trouble understanding. (What is the process designed to do, what happens within the column, and why is regeneration of the column packing necessary?)

Step by step solution

01

Determine the pressure values

First, you need to find the partial pressure of water (pH2O) in the gas contacting the silica gel using the formula for relative humidity, which is: Relative Humidity = \( \frac{p_{H2O}}{p_{H2O}^{*}} \times 100\% \) Substitute the given values into the formula: Relative Humidity = 25\% = \( \frac{p_{H2O}}{3169.7} \) Solving for \( p_{H2O} \) we get \( p_{H2O} = 792.425 \, \mathrm{Pa} \)

02

Calculate the amount of water adsorbed

Now, we will use the equilibrium adsorptivity of water on silica gel \(X^{*}\) to find out the amount of water adsorbed. Use the formula: \(X^{*}=12.5 \times \frac{p_{H2O}}{p_{H2O}^{*}}\) After substituting the calculated value of \( p_{H2O} \), we find: \( X^{*} = 3.137 \, \mathrm{kg \, water/100 \, kg \, silica \, gel} \)

03

Determine the air flow rate and find total water

Given is that air flow rate is 1.50 L/min or \(1.50 \times 10^{-3} \, \mathrm{m^3/min}\). Now, take the amount of water (in kg) in 1 m^3 of air. It is given by: \( \frac{p_{H2O}.V_{molar}}{RT} \) As \( R = 8.314 \, \mathrm{J/(mol.K)} \), \( T = 25^{\circ}C = 298.15 \, \mathrm{K} \), \( V_{molar} = 22.4 \times 10^{-3} \, \mathrm{m^3/mol} \), we get amount of water = \( 0.00096 \, \mathrm{kg/m^3} \).

04

Calculate the minimum amount of silica gel needed

The total water in 1.5L of air per min can be calculated as \( 0.00096 \times 1.50 \times 10^{-3} = 1.44 \times 10^{-6} \, \mathrm{kg/min} \). As the regeneration needs to take place every two hours, the total weight of silica gel required = \( \frac{1.44 \times 10^{-6} \times 2 \times 60}{3.137/100} = 5.51 \times 10^{-2} \, \mathrm{kg} \).

05

Describe the process

To describe the process in simple terms, we could say that the adsorption column serves as a dehumidifier. It uses silica gel to remove excess water from the air. The process of regeneration is necessary because with time, the silica gel becomes saturated with water and cannot adsorb any more. So, it has to be dried or 'regenerated' to be used again.

Unlock Step-by-Step Solutions & Ace Your Exams!

• Full Textbook Solutions

  Get detailed explanations and key concepts

• Unlimited Al creation

  Al flashcards, explanations, exams and more...

• Ads-free access

  To over 500 millions flashcards

• Money-back guarantee

  We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91Ó°ÊÓ!

Key Concepts

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

Adsorption Column

An adsorption column is a piece of equipment used in chemical engineering to capture and remove substances from gases or liquids. In this exercise, it is used to dehumidify air. The air passes through the column, which is packed with a material that effectively adsorbs moisture.

This process is crucial in many industrial applications as it helps in regulating humidity levels, protecting equipment, and enhancing product quality. The column relies on the principles of adsorption, where moisture molecules are captured and held on the surface of the adsorbent material.

• The column must be designed to allow for efficient contact between the air and the adsorbent.
• It should provide sufficient surface area for effective adsorption.
• It needs periodic regeneration to maintain its adsorbing capacity.

Understanding the function of the adsorption column helps in optimizing its use for dehumidification and other applications.

Silica Gel

Silica gel is a highly porous adsorbent material commonly used for drying or dehumidifying gases and liquids. In this exercise, it serves as the adsorbent in the column, efficiently capturing water vapor from the air.

Silica gel consists of tiny interconnected pore structures which provide a large surface area for adsorption. This makes it extremely effective in absorbing moisture.

• It is non-toxic and non-reactive, making it safe for various applications.
• Its high adsorption capacity allows it to hold significant amounts of water relative to its weight.
• Regeneration, or removal of adsorbed water, is straightforward, usually requiring heating.

With these properties, silica gel is an ideal choice for processes that require moisture control, helping maintain the desired humidity levels in the adsorption column.

Dehumidification

Dehumidification is the process of removing moisture from the air, which is essential for managing humidity levels in various environments. The adsorption column in this exercise performs this task using silica gel.

This process is critical because excess moisture can lead to mold growth, corrosion, and discomfort. Efficient dehumidification improves air quality and preserves equipment and structures.

• It works by passing humid air over the silica gel, where water vapor is captured and stored on its surface.
• This allows for a consistent reduction in moisture content as the air exits the column.
• Regular regeneration of silica gel ensures a continuous dehumidification process.

By understanding dehumidification, students can see the importance of maintaining controlled environments and the role of adsorption technology in achieving this goal.

Equilibrium Adsorption

Equilibrium adsorption refers to the state where the rate of adsorption of water molecules on silica gel equals the rate of desorption. At this point, the adsorbent is saturated, meaning it cannot adsorb more moisture.

In this exercise, the equilibrium adsorptivity is described by the expression involving the partial pressure of water. The formula provided defines the amount of water the silica gel can hold under specific conditions.

• Equilibrium is reached when the silica gel has adsorbed the maximum possible amount of water at a given humidity and temperature.
• The expression given allows for calculating how much water can be adsorbed before reaching this point.
• Understanding equilibrium adsorption is vital for determining when the silica gel needs to be regenerated.

This concept helps in efficient design and operation of the adsorption column, ensuring that it consistently performs dehumidification effectively.

Partial Pressure Calculation

Calculating partial pressure is a fundamental step in utilizing adsorption columns effectively. The partial pressure of water vapor in the air influences how much moisture the silica gel can adsorb.

In this exercise, students calculate partial pressure using the relative humidity and vapor pressure data. Correct calculation is crucial as it impacts the determination of adsorbed water quantity.

• Partial pressure is derived from the total pressure of the air and the percentage of water vapor the air contains (relative humidity).
• The equilibrium expression for adsorptivity utilizes this partial pressure along with the vapor pressure for accurate results.
• Mastering this calculation helps in understanding moisture content management within the column.

By grasping partial pressure calculations, students can better appreciate their importance in adsorption processes, ensuring that theoretical learning translates into practical application efficiently.