Adsorption Concept and Laws

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Questions and Answers

At low pressure, how is the volume of gas adsorbed (V) related to the pressure (P)?

V is proportional to P²

V is inversely proportional to P

V is independent of P

V is proportional to P (correct)

What happens to the adsorption at high pressure according to the given information?

Adsorption remains constant

Adsorption decreases

Adsorption tends to have a limiting value (correct)

Adsorption increases indefinitely

How is V related to P at intermediate pressure?

V is proportional to $x P$ (correct)

V is proportional to $P^2$

V is inversely proportional to P

V is independent of P

At what conditions is V = constant * $P^1$?

Low pressure Signup and view all the answers

At high pressure, what is the exponent of P in the equation relating V and P?

0 Signup and view all the answers

Which of the following is an assumption of the Langmuiu Model?

The surface contains a fixed number of adsorption sites Signup and view all the answers

What does θ represent in the Langmuiu Adsorption Isotherm?

The fraction of the surface area covered by adsorbed molecules Signup and view all the answers

At equilibrium, what is the relationship between the rate of condensation and the rate of evaporation in the Langmuiu model?

The rate of condensation is equal to the rate of evaporation Signup and view all the answers

How does the fraction of the surface area covered, θ, change at very high pressures in the Langmuiu model?

θ approaches 1 Signup and view all the answers

According to the Langmuiu Adsorption Isotherm, what happens at low pressure?

θ is proportional to the pressure, P Signup and view all the answers

Which of the following equations describes the Langmuiu Adsorption Isotherm?

$θ = \frac{KP}{1 + KP}$ Signup and view all the answers

What does $V$ represent in the BET equation?

volume of gas adsorbed at pressure $P$ Signup and view all the answers

Which of the following represents the constant $C$ correctly?

$C= ext{exp}(rac{ ext{-d}H_o}{RT})$ Signup and view all the answers

What is $P_o$ in the BET equation?

saturation vapor pressure at experimental temperature Signup and view all the answers

In the BET equation, what is $V_m$?

volume of gas adsorbed at a monolayer formation Signup and view all the answers

In the adsorption isotherms equation, what does $K_1$ represent?

rate constant for adsorption Signup and view all the answers

What is the phenomenon of adsorption?

Accumulation of molecules of a gas or liquid on a solid surface Signup and view all the answers

Which factors affect the amount of substance adsorbed?

Nature of adsorbent, nature of adsorbate, temperature Signup and view all the answers

What is the equation of the Freundlich isotherm when the adsorbate concentration is expressed in terms of molarity?

$x/m = kC^{1/n}$ Signup and view all the answers

Who introduced the Freundlich adsorption isotherm?

Freundlich, Hinshelwood and Taylor Signup and view all the answers

In the Freundlich isotherm equation, $x/m = kP^{1/n}$, what does P represent?

Equilibrium pressure of the gas Signup and view all the answers

Which type of adsorption is characterized by the surface not being saturated even at higher pressures?

Type 2 Signup and view all the answers

What does the variable 'P' represent in the Freundlich adsorption isotherm equation?

Equilibrium pressure Signup and view all the answers

When logarithms are taken on both sides of the Freundlich equation, what is the equation obtained?

$log x = log k + (1/n)log P$ Signup and view all the answers

What does 'n' indicate in the Freundlich adsorption isotherm equation?

Measure of adsorption intensity Signup and view all the answers

Which of the following best describes the behavior of the Freundlich adsorption isotherm graph at higher pressures?

Concave downward Signup and view all the answers

What does the plot of $log(x/m)$ vs. $log P$ indicate in the Freundlich Isotherm?

A straight line with slope $1/n$ and y-intercept $log k$ Signup and view all the answers

What is the usefulness of the Freundlich isotherm at low pressures?

It gives a good approximation to the adsorption process Signup and view all the answers

What type of adsorption behavior does the Freundlich isotherm equation describe?

Non-ideal Signup and view all the answers

What is one of the primary applications of the Freundlich equation?

Estimating the specific surface area of solids Signup and view all the answers

Which limitation does the Freundlich equation face?

It does not account for the saturation of the adsorbent Signup and view all the answers

Which of the following is true about the surface of the adsorbent in the Freundlich equation?

The surface is heterogeneous and adsorption energy is not uniform Signup and view all the answers

For what range of P/P values does the BET equation fit experimental data?

0.05 to 0.35 Signup and view all the answers

What is the Brunauer, Emmett, and Teller equation commonly abbreviated as?

BET equation Signup and view all the answers

What does the y-axis label represent in the BET isotherm graph?

V (Volume adsorbed) Signup and view all the answers

How much area does the ultimately adsorbed nitrogen cover according to the image?

16.2 A Signup and view all the answers

Which subheading is NOT mentioned in the document?

Langmuir Model Signup and view all the answers

What are the x-axis labels in the BET isotherm graph?

P/P^o Signup and view all the answers

Which type of adsorption isotherm typically exhibits a linear increase in adsorption with pressure followed by a plateau at high pressures?

Type I Signup and view all the answers

Which type of adsorption isotherm is represented by a sigmoid curve with an initial slow increase in adsorption, followed by a steep increase and a plateau?

Type II Signup and view all the answers

In the Langmuir Adsorption Isotherm equation $n_a = n_m \theta = n_m \frac{K_p}{1+K_p}$, what does $K_p$ represent?

Equilibrium constant for adsorption Signup and view all the answers

Which type of adsorption isotherm shows a concave curve with an initial steep increase in adsorption followed by a gradual increase towards a plateau?

Type III Signup and view all the answers

Which type of adsorption isotherm features a hysteresis loop?

Type IV Signup and view all the answers

Which of the following statements about Type VI adsorption isotherms is correct?

They feature multiple steps and plateaus, indicating adsorption at different sites. Signup and view all the answers

Study Notes

The Concept of Adsorption

Adsorption is the phenomenon of accumulation of molecules of a gas or liquid on a solid surface.
The amount of substance adsorbed is affected by the nature of the adsorbent and adsorbate, as well as the temperature of the system.

Laws Governing Adsorption

Freundlich isotherm is a mathematical equation that relates the amount of gas adsorbed to the concentration of the gas in the solution.
The equation is: $x/m = kP^{1/n}$, where x is the mass of gas adsorbed, m is the mass of adsorbent, P is the equilibrium pressure, and k and n are constants.

Freundlich Isotherm

The Freundlich isotherm is especially useful in describing adsorption with porous adsorbents.
There are two types of adsorption isotherms:
- Type 1: represents adsorption where the surface is saturated at higher pressures.
- Type 2: represents adsorption where the surface is not saturated even at higher pressures.

Taking Logarithms

Taking logarithms on both sides of the Freundlich equation yields: $log x = log k + (1/n)log P$
This equation is a linear equation with slope $1/n$ and intercept $log k$, which can be used to determine k and n.

Langmuir Model for Adsorption

The Langmuir model is based on the following assumptions:
- The surface contains a fixed number of adsorption sites.
- All sites are equivalent.
- The adsorption is localized.
- There is no interaction between adsorbed molecules.
The Langmuir equation is derived from the condensation and evaporation of gas molecules.
The resulting equation is: $θ = \frac{k_c P}{k_e + k_cP} = \frac{KP}{1 + KP}$, where K = $k_c/k_e$.

Three Limiting Cases

At low pressure, θ = KP, so θ is proportional to P.
At very high pressure, θ = 1, so the surface is completely covered.
At intermediate pressure, the equation yields a curved line.

The Freundlich Adsorption Isotherm

The Freundlich equation is: $x/m = kP^{1/n}$, where x is the mass of adsorbate, m is the mass of adsorbent, P is the equilibrium pressure, and k and n are constants.
The equation assumes that the adsorption process is not restricted to one molecule thick.
The graph of the Freundlich isotherm is sigmoidal, showing the relationship between the amount of adsorbate adsorbed and the pressure at a constant temperature.

Assumptions of the Freundlich Equation

The equation is empirical and based on experimental data.
The adsorbent surface is heterogeneous and adsorption energy is not uniform.
The adsorbate is physically adsorbed onto the adsorbent surface.

Limitations of the Freundlich Equation

It does not account for the saturation of the adsorbent surface.
It is not valid for high pressures or for adsorption of very large molecules.

Applications of the Freundlich Equation

To study the adsorption of gases on solids.
To study the adsorption of liquids on solids.
To study the adsorption of dyes from solution.
To design adsorption processes for the removal of pollutants from air and water.

Adsorption Isotherms

The BET equation is: $\frac{P}{V(P_o-P)} = \frac{1}{V_mC} + \frac{C-1}{V_mC} \frac{P}{P_o}$
The BET equation can be used to fit experimental data for values of P/P from 0.05 to 0.35.

Classification of Adsorption Isotherms

Brunauer made a useful classification of adsorption isotherms, including:
- Type I: linear increase in adsorption with pressure, followed by a plateau at high pressures.
- Type II: sigmoid curve with an initial slow increase in adsorption, followed by a steep increase and finally a plateau.
- Type III: concave curve with an initial steep increase, followed by a gradual increase towards a plateau.
- Type IV: sigmoid curve similar to type II, but with a hysteresis loop.
- Type V: sigmoid curve similar to type III, but with a hysteresis loop.
- Type VI: stepped curve with multiple plateaus, indicating adsorption at different sites.

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Description

Learn about the concept of adsorption, factors affecting it, and the different types of adsorption. Discover the laws governing adsorption, including the Freundlich Isotherm.