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Physical Chemistry II
Unit 6 Overview: Surface Chemistry and Catalysis
6.1 Adsorption Isotherms
6.2 Langmuir-Hinshelwood and Eley-Rideal Mechanisms
6.3 BET Theory and Surface Area Determination
6.4 Heterogeneous Catalysis and Catalyst Characterization
6.5 Enzyme Catalysis and Michaelis-Menten Kinetics

🧂physical chemistry ii review

6.3 BET Theory and Surface Area Determination

Last Updated on August 14, 2024

BET theory expands on Langmuir adsorption, allowing for multilayer gas adsorption on solid surfaces. It's crucial for determining surface area and pore size distribution in porous materials, especially those with mesopores or macropores.

The BET equation, derived from adsorption-desorption equilibrium, helps calculate specific surface area. This is vital for characterizing materials used in catalysis, adsorption, and energy storage, where high surface area often means better performance.

BET Theory for Multilayer Adsorption

Principles and Assumptions

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  • BET theory extends the Langmuir adsorption model to multilayer adsorption
    • Allows for the determination of surface area and pore size distribution of porous materials
  • Assumes gas molecules can adsorb onto a solid surface in an infinite number of layers
    • No interaction between each adsorption layer
  • First adsorbed layer has a heat of adsorption equal to the heat of condensation of the adsorbate
    • Subsequent layers have a heat of adsorption equal to the heat of liquefaction
  • Introduces the concept of a statistical thickness of the adsorbed film
    • Ratio of the amount of adsorbate in each layer to the amount required to form a monolayer

Applicability and Adsorption Isotherms

  • BET theory is most applicable to Type II and Type IV adsorption isotherms
    • Exhibit multilayer adsorption and capillary condensation in mesopores (pores with diameters between 2 and 50 nm)
  • Type II isotherms are characteristic of non-porous or macroporous materials (pores with diameters greater than 50 nm)
    • Show unrestricted monolayer-multilayer adsorption
  • Type IV isotherms are characteristic of mesoporous materials
    • Exhibit a hysteresis loop associated with capillary condensation in mesopores

BET Equation Derivation and Limitations

Derivation of the BET Equation

  • Derived by considering the equilibrium between the rates of condensation and evaporation for each adsorption layer
  • Resulting equation: 1/[v((P0/P)−1)]=(c−1)/(vmc)∗(P/P0)+1/(vmc)1/[v((P_0/P)-1)] = (c-1)/(v_mc) * (P/P_0) + 1/(v_mc)
    • vv: volume of gas adsorbed at pressure PP
    • P0P_0: saturation pressure
    • vmv_m: volume of gas required to form a monolayer
    • cc: BET constant related to the heat of adsorption
  • BET equation can be linearized to obtain vmv_m and cc from the slope and intercept of a BET plot
    • Plot of 1/[v((P0/P)−1)]1/[v((P_0/P)-1)] versus P/P0P/P_0

Assumptions and Limitations

  • Assumes the surface is energetically homogeneous
    • No lateral interactions between adsorbed molecules
  • BET equation is valid only for a limited range of relative pressures
    • Typically between 0.05 and 0.35, where multilayer adsorption is dominant
  • May not accurately describe adsorption in microporous materials (pores with diameters less than 2 nm)
    • Pore filling rather than layer-by-layer adsorption occurs in micropores

Surface Area Determination Using BET

Specific Surface Area Calculation

  • Specific surface area of a porous material can be calculated from the monolayer volume vmv_m obtained from the BET equation
  • Surface area is given by: SBET=(vm∗NA∗σ)/(V∗m)S_{BET} = (v_m * N_A * σ) / (V * m)
    • NAN_A: Avogadro's number
    • σσ: cross-sectional area of the adsorbate molecule
    • VV: molar volume of the gas
    • mm: mass of the sample
  • Nitrogen is the most commonly used adsorbate for BET surface area measurements
    • Typical cross-sectional area of 0.162 nm2 per molecule at 77 K

Experimental Procedure

  • BET method requires the measurement of an adsorption isotherm
    • Typically using a volumetric or gravimetric technique
    • Obtains the volume of gas adsorbed at different relative pressures
  • Sample is degassed to remove adsorbed contaminants
    • Cooled to liquid nitrogen temperature (77 K) for nitrogen adsorption
  • Adsorption isotherm is measured by incrementally dosing the sample with nitrogen gas
    • Measuring the equilibrium pressure after each dose

Importance of Specific Surface Area

  • Specific surface area is an essential characteristic of porous materials
    • Influences their performance in various applications (catalysis, adsorption, and energy storage)
  • High specific surface area materials (activated carbons, zeolites, and metal-organic frameworks) are desirable for adsorption and catalysis
    • Provide more sites for adsorption and reaction
  • Specific surface area can be used to compare the effectiveness of different porous materials
    • Optimize their synthesis and processing conditions

BET Isotherm Analysis and Surface Area Calculation

Adsorption Isotherm Interpretation

  • BET adsorption isotherm plots the volume of gas adsorbed (vv) against the relative pressure (P/P0P/P_0) at a constant temperature
  • Shape of the isotherm provides information about the pore structure and adsorption behavior of the material
    • Type II isotherms indicate non-porous or macroporous materials
    • Type IV isotherms indicate mesoporous materials with capillary condensation
  • Linear region of the BET plot (typically between relative pressures of 0.05 and 0.35) is used to determine the monolayer volume vmv_m and the BET constant cc
    • Slope and intercept of the linear fit are used to calculate vmv_m and cc

Surface Area Calculation from Experimental Data

  • Specific surface area is calculated from vmv_m using the appropriate values for the adsorbate cross-sectional area and molar volume
  • Example calculation for nitrogen adsorption at 77 K:
    • vmv_m = 10 cm3/g (from BET plot)
    • NAN_A = 6.022 × 1023 mol-1
    • σσ = 0.162 nm2
    • VV = 22414 cm3/mol
    • mm = 0.1 g
    • SBET=(10∗6.022×1023∗0.162×10−18)/(22414∗0.1)=43.8m2/gS_{BET} = (10 * 6.022 × 10^{23} * 0.162 × 10^{-18}) / (22414 * 0.1) = 43.8 m^2/g

Additional Information from BET Analysis

  • BET constant cc is related to the heat of adsorption
    • Provides information about the strength of the adsorbate-adsorbent interactions
    • Higher values of cc indicate stronger interactions and a more energetically homogeneous surface
  • Deviations from linearity in the BET plot at low or high relative pressures may indicate the presence of micropores or mesopores, respectively
    • Alternative analysis methods (Langmuir, Dubinin-Radushkevich, or Barrett-Joyner-Halenda) may be required for accurate characterization of these materials
  • Pore size distribution can be obtained from the adsorption isotherm using methods such as the Barrett-Joyner-Halenda (BJH) analysis
    • Based on the Kelvin equation and the assumption of cylindrical pores

Key Terms to Review (25)

Paul Emmett: Paul Emmett was a prominent American physical chemist known for his groundbreaking work in the field of surface science, particularly for developing the BET (Brunauer-Emmett-Teller) theory. His contributions have been crucial in understanding the adsorption of gases on solid surfaces, which has important applications in determining surface area and porosity of materials.
Stephen Brunauer: Stephen Brunauer was a prominent chemist known for his contributions to the field of physical chemistry, particularly in the development of the Brunauer-Emmett-Teller (BET) theory, which is used for determining surface areas of solids. His work helped establish a crucial understanding of gas adsorption on solid surfaces, a key concept for characterizing materials in various scientific fields including catalysis and material science.
Nitrogen adsorption: Nitrogen adsorption is the process by which nitrogen gas (N₂) molecules adhere to the surface of a solid material, often used in the context of measuring surface area and porosity of materials. This technique is fundamental in understanding the properties of materials like catalysts and adsorbents, as the amount of nitrogen that can be adsorbed is directly related to the available surface area. By analyzing the adsorption isotherms, valuable information about the texture and pore structure of a material can be obtained.
Gas adsorption: Gas adsorption is the process where gas molecules adhere to the surface of a solid or liquid, forming a thin film. This phenomenon is crucial for understanding various applications in physical chemistry, including catalysis, separation processes, and gas storage, as it highlights how the properties of materials can change based on their interactions with gases.
Relative Pressure: Relative pressure is a measure of pressure that compares the pressure of a gas to a reference pressure, typically atmospheric pressure. In the context of gas adsorption, particularly in BET theory, relative pressure is crucial because it allows scientists to assess how gas molecules interact with solid surfaces by normalizing pressures to understand adsorption behavior across varying conditions.
Heat of adsorption: The heat of adsorption refers to the amount of energy released or absorbed when a gas or liquid molecules adhere to a solid surface. This process is crucial in understanding how adsorbates interact with adsorbents, influencing the overall effectiveness of materials in various applications such as catalysis and gas storage. The heat of adsorption is essential for interpreting isotherm data in BET theory, which helps determine surface area and porosity of materials.
Type IV isotherm: A type IV isotherm is a specific adsorption isotherm characterized by a distinctive hysteresis loop, indicating the presence of mesoporous materials with a pore size typically between 2 and 50 nanometers. This type of isotherm reflects capillary condensation and evaporation phenomena occurring in these mesopores, which can be critical in understanding the adsorption properties and surface area of materials used in various applications, including catalysis and gas storage.
Surface Porosity: Surface porosity refers to the presence of tiny voids or pores on the surface of a material, which can significantly affect its physical and chemical properties. This characteristic plays a critical role in processes such as adsorption, catalysis, and diffusion, as the available surface area is enhanced by the existence of these pores. Understanding surface porosity is essential for applications that depend on surface interactions, including the measurement of surface area using techniques like BET theory.
Adsorbate: An adsorbate is a substance that adheres to the surface of another material, typically a solid. In the context of surface chemistry, adsorbates play a crucial role in understanding how molecules interact with surfaces, influencing properties such as reactivity, catalysis, and surface area measurements. The interactions between adsorbates and substrates can provide insights into the physical and chemical behavior of materials.
Statistical Thickness: Statistical thickness refers to the effective thickness of a layer of adsorbed molecules on a surface, derived from statistical considerations based on the arrangement and distribution of these molecules. This concept is essential for understanding how adsorbate layers interact with surfaces and helps in interpreting experimental data related to surface area and adsorption isotherms.
Type II Isotherm: A Type II isotherm is a specific adsorption isotherm shape that represents the adsorption of gases onto non-porous or macroporous solids at high pressures. This type of isotherm typically exhibits a sigmoidal shape, indicating multilayer adsorption, and is associated with materials that have significant surface area but lack fine porosity. Understanding Type II isotherms is crucial for analyzing the adsorption behavior of materials in various applications, particularly in the context of surface area determination.
Specific Surface Area: Specific surface area refers to the total surface area of a material per unit mass or volume, commonly expressed in units such as m²/g or m²/cm³. This measurement is essential in various scientific fields because it significantly affects the reactivity, adsorption properties, and overall performance of materials, especially in contexts like catalysis and adsorption phenomena where surface interactions are key.
Catalyst characterization: Catalyst characterization refers to the process of determining the physical and chemical properties of a catalyst, including its composition, structure, surface area, and reactivity. This characterization is essential for understanding how a catalyst functions in chemical reactions and for optimizing its performance. By examining these features, scientists can assess the effectiveness of catalysts and improve their design for various applications.
Adsorption-desorption equilibrium: Adsorption-desorption equilibrium refers to the dynamic balance between the process of adsorption, where molecules from a gas or liquid phase adhere to a solid surface, and desorption, where those adhered molecules detach back into the gas or liquid phase. This equilibrium is crucial for understanding how surface interactions influence various physical and chemical processes, particularly in the context of measuring surface area and material properties.
Adsorption isotherms: Adsorption isotherms describe the relationship between the amount of a substance adsorbed on a surface and the concentration of that substance in the surrounding phase at a constant temperature. These isotherms provide crucial insights into how molecules interact with surfaces, influencing surface area determination and the thermodynamics involved at surfaces and interfaces.
Macropores: Macropores are large pores within a material, typically defined as having a diameter greater than 50 nanometers. These structures play a significant role in the adsorption process and surface area determination, as they can influence the capacity of a material to hold gas or liquid and affect the overall porosity.
Langmuir Adsorption: Langmuir adsorption describes a model for the adsorption of molecules onto a solid surface, where the adsorbate forms a monolayer without interactions between the adsorbed molecules. This concept highlights the importance of surface coverage and saturation, directly connecting to how surface area is determined through the BET theory, which expands on Langmuir's ideas to account for multilayer adsorption.
Multilayer gas adsorption: Multilayer gas adsorption is the process where gas molecules adhere to the surface of a solid in multiple layers, rather than just a single layer. This phenomenon is critical for understanding the interaction between gases and solid surfaces, especially when determining surface area and porosity through techniques like BET theory.
BET Theory: BET Theory, or Brunauer-Emmett-Teller Theory, is a method used to measure the surface area of materials, particularly porous substances, through the physical adsorption of gas molecules. It extends the Langmuir theory by accounting for multilayer adsorption and provides a mathematical model that relates the volume of gas adsorbed to the pressure and allows for the calculation of specific surface areas of solids. This theory is crucial in fields like material science and catalysis where understanding surface area is key to performance.
Mesopores: Mesopores are void spaces within materials that have diameters ranging from 2 to 50 nanometers. These pores play a significant role in the surface area and porosity of materials, particularly in the context of adsorbents and catalysts, where they can influence the interaction between the surface and adsorbate molecules. Understanding mesopores is essential for analyzing material properties related to gas adsorption and catalysis efficiency.
BET Equation: The BET equation is a mathematical model used to determine the surface area of porous materials through gas adsorption. It connects the volume of gas adsorbed on a solid to the pressure of the gas, allowing for the calculation of specific surface areas based on the behavior of adsorbates. The equation is named after its developers, Brunauer, Emmett, and Teller, and is foundational in physical chemistry for characterizing materials like catalysts and adsorbents.
Activated carbon: Activated carbon is a highly porous material derived from carbonaceous sources that have been treated to create an extensive surface area, allowing it to adsorb various substances. This unique property makes activated carbon an essential component in processes such as filtration, purification, and separation in both environmental and industrial applications.
Pore size distribution: Pore size distribution refers to the range and frequency of pore sizes present within a material, particularly in porous solids. This concept is essential in understanding how materials interact with liquids and gases, influencing adsorption properties, permeability, and the overall surface area available for interaction. By analyzing pore size distribution, one can determine how efficiently a material can capture and retain molecules, which directly ties into adsorption isotherms and surface area determination methodologies.
Adsorption capacity: Adsorption capacity refers to the maximum amount of a substance that can adhere to a surface or interface under specific conditions. This concept is crucial for understanding how various materials, like activated carbon or zeolites, interact with gases or liquids. It helps in determining the effectiveness of adsorbents in processes like purification and catalysis by quantifying how much of a particular substance can be captured at equilibrium.
Surface Area: Surface area refers to the total area that the surface of a solid object occupies. In the context of adsorption and catalysis, it plays a crucial role in determining the amount of material that can interact with surrounding substances, significantly affecting reaction rates and adsorption phenomena.
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Glossary
6.4 Heterogeneous Catalysis and Catalyst Characterization