Surface Chemistry, Kinetics & Catalysis Notes

Surface Chemistry, Kinetics & Catalysis

• Reference books: Atkins' Physical Chemistry & Essentials of Physical Chemistry by Arun Bahl
• UNIT 3: Surface Chemistry, Kinetics & Catalysis
  • Adsorption - Characteristics, Classification, Application
  • Adsorption isotherms - Freundlich, Langmuir & BET
  • Chemical Kinetics - Rate law, Arrhenius equation, Transition state theory, Collision theory; Complex reactions
  • Catalysis - Homogeneous and Heterogeneous Catalysis; Mechanism of Catalysis; Industrial Applications of catalysts

Adsorption

• Definition: Adsorption is a process whereby a substance (adsorbate or sorbate) is accumulated on the surface of a solid (adsorbent, or sorbent).
  • The adsorbate can be in a gas or liquid phase.
  • Adsorption refers to the existence of a higher concentration of any particular component at the surface of a liquid or a solid phase.
  • Example: Charcoal used in gas masks to remove poisons or impurities from a stream of air.

Adsorbent and Adsorbate

• Adsorbent: Solids that are used to adsorb gases or dissolved substances.
  • Examples: charcoal, alumina, silica gel
• Adsorbate: The adsorbed molecules.
  • Examples: gases like oxygen, nitrogen etc.

Adsorption vs. Absorption

• Absorption is a bulk phenomenon.
• Adsorption is a surface phenomenon.
• The word "adsorption" was coined in 1881 by German physicist Heinrich Kayser.

Surfaces for Adsorption

• Surfaces have various features like terraces, steps, adatoms, and kinks, which play an important role in surface growth and catalysis.

Characteristics of Adsorption

• Adsorption is accompanied by a decrease in the free energy change of the system when adsorption equilibrium is established.
• High surface area leads to more adsorbate molecules sticking to the surface.
• Adsorption is an exothermic process, meaning it releases heat ($\Delta H$ is negative).
• Adsorbate molecules' freedom of movement becomes restricted, resulting in a decrease in entropy.
• Adsorption is a consequence of surface energy, where surface atoms attract adsorbates because they are not fully surrounded by other atoms of the adsorbent.

Factors Affecting Adsorption

1. Nature of Adsorbate and Adsorbent
   • Greater surface area of the adsorbent leads to greater gas adsorption.
   • Different gases (adsorbates) are adsorbed differently by the same adsorbent at the same temperature.
2. Activation of Adsorbent
   • Increase the surface area of the adsorbent by making the surface rough or subdividing the adsorbent into smaller grains.
3. Experimental Conditions
   • Temperature: Adsorption generally decreases with an increase in temperature.
   • Pressure: At constant temperature, adsorption increases with an increase in pressure.

Classification of Adsorption

1. Physical Adsorption (Physisorption)
   • The force of attraction between adsorbate and adsorbent are Van der Waal’s forces.
   • Weak attraction, easily reversed by heating or decreasing the pressure.
2. Chemical Adsorption (Chemisorption)
   • The force of attraction between adsorbate and adsorbent is almost the same strength as chemical bonds.
   • Also known as Langmuir adsorption.
   • Strong attraction, not easily reversed.

Physisorption vs. Chemisorption

Applications of Adsorption

1. Silica Gel Packets: Used to keep moisture out of products by adsorbing moisture vapors.
2. Pollution Masks: Contain activated carbon granules or a filter sheet to adsorb dust and smoke particles.
3. Curing Diseases: Disease-causing germs get deposited on the surface of the drug and are later ejected from the body.
4. Charcoal Gas Masks: Used in mining to filter out toxic and poisonous gases.
5. Purification of Water: Alum is used to combine impurities into larger clusters that can be removed.
6. Removing Hardness from Water: Ion exchange resins are used to remove calcium and magnesium ions.
7. Misty Windows: Water vapor gets deposited on the surface of windows due to adsorption.
8. Decoloring of Matter: Fuller’s earth or charcoal solution is used to remove impurities and decolorize substances.
9. In Heterogeneous Catalysis: Reactants adsorb onto the surface of the catalyst, react, and then desorb.
10. Other Applications
    • Metallurgy: Froth floatation process for concentration of ore.
    • Chromatography: Separating pigments.
    • Virology: Viruses adsorb onto hosts.
    • Polymer Science: Non-stick coatings and biomedical devices.
    • Polyelectrolytes adsorption: Oil recovery, nutrition, concrete, etc.

Adsorption Isotherms

• The free gas and the adsorbed gas are in dynamic equilibrium.
• Fractional coverage ($\theta$) of the surface depends on the pressure of the overlying gas.
• Adsorption isotherm: The variation of ($\theta$) with pressure at a chosen temperature.
• Describes the amount of adsorbate on the adsorbent as a function of its pressure (gas) or concentration (liquid) at constant temperature.
• Types:
  1. Langmuir adsorption isotherm
  2. Freundlich adsorption isotherm
  3. BET adsorption isotherm

Langmuir Adsorption Isotherm

• Assumptions:
  1. Adsorption cannot proceed beyond monolayer coverage.
  2. All sites are equivalent and the surface is uniform.
  3. The ability of a molecule to adsorb at a given site is independent of the occupation of neighboring sites.
• Dynamic Equilibrium:
  • $A(g) + M(surface) \rightleftharpoons AM(surface)$
  • A(g) is gaseous adsorbate
  • M(surface) is solid adsorbent
  • AM(surface) is the material where the gaseous adsorbate is adsorbed onto the solid adsorbent surface.
  • $k<em>a$ is the rate constant for adsorption and $k</em>d$ for desorption.
• Rate of change of surface coverage due to adsorption:
  • Proportional to the partial pressure p of A and the number of vacant sites $N(1 - \theta)$, where N is the total number of sites.
• Rate of change of $\theta$ due to desorption:
  • Proportional to the number of adsorbed species, $N\theta$.
• At equilibrium, the rate of desorption is equal to the rate of adsorption.
• $K<em>1(1-\theta)P = K</em>2\theta$
• $K<em>1P - K</em>1\theta P = K_2 \theta$
• $K<em>1P = \theta(K</em>2 + K_1P)$
• Rate of adsorption depends on available sites on the adsorbent for adsorption i.e., $N(1-\theta)$ at partial pressure of the adsorbate P
  • $R<em>1 = K</em>1N(1-\theta)P$………………….(i)
• Rate of desorption depends on the fraction covered $\theta$
  • $R<em>2 = K</em>2N\theta$……………………..(ii)
  • $K<em>1$ and $K</em>2$ are adsorption and desorption constants respectively.
• $\frac{x}{m} = K_3\theta$ ……………………..(iii)
• $\frac{x}{m} = \frac{ap}{1+bp}$
  • $a = K_3b$ is constant.
• Equation (v) is the required Langmuir equation.
• A plot of $\frac{p}{x/m}$ Vs P gives a straight line.
  • Slope = $\frac{b}{a}$
  • Intercept = $\frac{1}{a}$
• Limitations of Langmuir Adsorption Isotherm
  1. Assumes monolayer adsorption, but many layers can be adsorbed.
  2. Assumes no interaction between adsorbed molecules, but interactions are observed.
  3. Works well at low pressure but fails at high pressures.
  4. The effect of temperature is not well considered.
  5. Relation between heat of adsorption and surface area not explained.
• In a nutshell:
  • Langmuir adsorption is applicable for monolayer adsorption onto a homogeneous (uniform/equivalent sites) surface when no interaction occurs between adsorbed species.
  • $x/m$ is the amount of adsorbate adsorbed per unit mass of adsorbent
  • $p$ is the pressure of the adsorbate gas
  • $a$ and $b$ are constants
  • $a = K_3b$
  • $b = \frac{K<em>1}{K</em>2} = \frac{K<em>a}{K</em>d}$

Freundlich Adsorption Isotherm

• In 1909, Freundlich provided an empirical relationship between the amount of gas adsorbed by a unit mass of solid adsorbent and pressure at a particular temperature.
• Expressed as: $\frac{x}{m} = k \cdot p^{\frac{1}{n}}$, where (n > 1)
  • $x$ is the mass of the gas adsorbed on mass $m$ of the adsorbent at pressure $P$.
  • $k$ and $n$ are constants that depend on the nature of the adsorbent and the gas at a particular temperature.
• At a fixed pressure, physical adsorption decreases with an increase in temperature.
• The curves reach saturation at high pressure.
• Taking the log of the equation:
  • $\log \frac{x}{m} = \log k + \frac{1}{n} \log P$
• To test the validity of the Freundlich isotherm, plot $\log \frac{x}{m}$ on the y-axis and $\log P$ on the x-axis.
  • If the plot shows a straight line, then the Freundlich isotherm is valid.
  • The slope of the straight line gives the value of $\frac{1}{n}$, while the intercept on the y-axis gives the value of $\log k$.
• Limitations of Freundlich Adsorption Isotherm
  • Based on the assumption that every adsorption site is equivalent.
  • Applicable to physical adsorption.

BET Adsorption Isotherm

• If the initial adsorbed layer can act as a substrate for further (e.g., physical) adsorption, then, instead of the isotherm leveling off, it can be expected to rise indefinitely.
• The most widely used isotherm dealing with multilayer adsorption was derived by Stephen Brunauer, Paul Emmett, and Edward Teller, and is called the BET isotherm.
• Salient features of BET isotherm:
  1. Gas molecules physically adsorb on a solid in layers infinitely.
  2. Gas molecules only interact with adjacent layers; and the Langmuir theory can be applied to each layer.
  3. The enthalpy of adsorption for the first layer is constant and greater than the second (and higher).
  4. The enthalpy of adsorption for the second (and higher) layers is the same as the enthalpy of liquefaction.
• A BET isotherm plots the amount of gas adsorbed as a function of the relative pressure.
• There are five types of adsorption isotherms possible from the surface adsorption analyses of materials using BET.
• The BET Equation uses the information from the isotherm to determine the surface area of the sample, where X is the weight of nitrogen adsorbed at a given relative pressure (P/Po), Xm is monolayer capacity, which is the volume of gas adsorbed at standard temperature and pressure (STP), and C is constant.
• (STP is defined as 273 K and 1 atm)

BET Isotherm Types

• Type I: Pseudo-Langmuir isotherm, depicts monolayer adsorption.
  • Obtained when P/Po < 1 and C > 1.
  • Characterizes microporous materials (pore diameters less than 2 nm).
  • The extent of adsorption increases with pressure until it reaches saturation.
• Type II: The most common isotherm, bilayer is formed only after the monolayer has been fully formed, C > 1.
• Type III: Formation of a multilayer, monolayers, bilayers, trilayers, and other layers all take place at the same time, C < 1.
• Type IV: Formation of a monolayer followed by the formation of multilayers; mesoporous materials (pore diameters between 2 - 50 nm).
• Type V: Obtained when intermolecular attraction effects are large, and adsorption takes place in pores and capillaries; very similar to type IV isotherms. The BET Equation uses the information from the isotherm to determine the surface area of the sample, where X is the weight of nitrogen adsorbed at a given relative pressure (P/Po), Xm is monolayer capacity, which is the volume of gas adsorbed at standard temperature and pressure (STP), and C is constant. (STP is defined as 273 K and 1 atm).