T Plot Adsorption

 
  1. T Plot Adsorption Meaning
  2. T Plot Adsorption Isotherm
  1. Indian Institute of Technology Kanpur.
  2. The t-plot is considered to be the graph of Vadsvs. If both reference and sample isotherm are identical, as is the case for nonporous solids, a straight line passing through or passing close to the origin, should result (Fig.
  3. The amount of adsorption at time t was calculated by (Bulut and Ozacar (2008) q t ¼ ðÞC 0 C t v w ð2Þ where C 0 and C t (mg/L) are the liquid phase concentrations of dyes at initial time and time t, respectively.

In order to test the validity of Freundlich adsorption isotherm plot log (x/m) against log Ce. The slopes and intercepts of the plot will give 1/n and log k respectively and hence n and K can be calculated. Validity of Langmuir adsorption equation can be tested by plotting Ce/(x/m) Vs Ce. A linear plot obtained shoe the applicability of the.

Overview of BET Theory

The BET theory was developed by Stephen Brunauer (Figure (PageIndex{1}) ), Paul Emmett (Figure (PageIndex{2}) ), and Edward Teller (Figure (PageIndex{3}) ) in 1938. The first letter of each publisher’s surname was taken to name this theory. The BET theory was an extension of the Langmuir theory, developed by Irving Langmuir (Figure (PageIndex{4}) ) in 1916.

The Langmuir theory relates the monolayer adsorption of gas molecules (Figure (PageIndex{5}) ), also called adsorbates, onto a solid surface to the gas pressure of a medium above the solid surface at a fixed temperature to ref{1} , where θ is the fractional cover of the surface, P is the gas pressure and α is a constant.

[ Theta = frac{alpha cdot P}{1 + (alpha cdot P)} label{1} ]

The Langmuir theory is based on the following assumptions:

  • All surface sites have the same adsorption energy for the adsorbate, which is usually argon, krypton or nitrogen gas. The surface site is defined as the area on the sample where one molecule can adsorb onto.
  • Adsorption of the solvent at one site occurs independently of adsorption at neighboring sites.
  • Activity of adsorbate is directly proportional to its concentration.
  • Adsorbates form a monolayer.
  • Each active site can be occupied only by one particle.

The Langmuir theory has a few flaws that are addressed by the BET theory. The BET theory extends the Langmuir theory to multilayer adsorption (Figure (PageIndex{1}) ) with three additional assumptions:

  • Gas molecules will physically adsorb on a solid in layers infinitely.
  • The different adsorption layers do not interact.
  • The theory can be applied to each layer.

How does BET Work?

Adsorption is defined as the adhesion of atoms or molecules of gas to a surface. It should be noted that adsorption is not confused with absorption, in which a fluid permeates a liquid or solid. The amount of gas adsorbed depends on the exposed surface are but also on the temperature, gas pressure and strength of interaction between the gas and solid. In BET surface area analysis, nitrogen is usually used because of its availability in high purity and its strong interaction with most solids. Because the interaction between gaseous and solid phases is usually weak, the surface is cooled using liquid N2 to obtain detectable amounts of adsorption. Known amounts of nitrogen gas are then released stepwise into the sample cell. Relative pressures less than atmospheric pressure is achieved by creating conditions of partial vacuum. After the saturation pressure, no more adsorption occurs regardless of any further increase in pressure. Highly precise and accurate pressure transducers monitor the pressure changes due to the adsorption process. After the adsorption layers are formed, the sample is removed from the nitrogen atmosphere and heated to cause the adsorbed nitrogen to be released from the material and quantified. The data collected is displayed in the form of a BET isotherm, which plots the amount of gas adsorbed as a function of the relative pressure. There are five types of adsorption isotherms possible.

Type I Isotherm

Type I is a pseudo-Langmuir isotherm because it depicts monolayer adsorption (Figure (PageIndex{6}) ). A type I isotherm is obtained when P/Po < 1 and c > 1 in the BET equation, where P/Po is the partial pressure value and c is the BET constant, which is related to the adsorption energy of the first monolayer and varies from solid to solid. The characterization of microporous materials, those with pore diameters less than 2 nm, gives this type of isotherm.

Type II Isotherm
Adsorption

A type II isotherm (Figure (PageIndex{7}) ) is very different than the Langmuir model. The flatter region in the middle represents the formation of a monolayer. A type II isotherm is obtained when c > 1 in the BET equation. This is the most common isotherm obtained when using the BET technique. At very low pressures, the micropores fill with nitrogen gas. At the knee, monolayer formation is beginning and multilayer formation occurs at medium pressure. At the higher pressures, capillary condensation occurs.

Type III Isotherm

A type III isotherm (Figure (PageIndex{8}) ) is obtained when the c < 1 and shows the formation of a multilayer. Because there is no asymptote in the curve, no monolayer is formed and BET is not applicable.

Type IV Isotherm

Type IV isotherms (Figure (PageIndex{9}) ) occur when capillary condensation occurs. Gases condense in the tiny capillary pores of the solid at pressures below the saturation pressure of the gas. At the lower pressure regions, it shows the formation of a monolayer followed by a formation of multilayers. BET surface area characterization of mesoporous materials, which are materials with pore diameters between 2 - 50 nm, gives this type of isotherm.

Type V Isotherm

Type V isotherms (Figure (PageIndex{10}) ) are very similar to type IV isotherms and are not applicable to BET.

Contents

T Plot Adsorption Meaning

Adsorption Isotherm

The adsorption on a given surface generally increases with increase in pressure (for gases) and concentration (for solutions) at a constant temperature.

The extent of adsorption of a gas per unit mass of adsorbent depends upon the pressure of the gas. The relation between the amount of substance adsorbed by the adsorbent and the equilibrium gas pressure (or concentration for solutions) at constant temperature is called an adsorption isotherm.

The extent of adsorption is usually expressed as x/m where x is the mass of adsorbate and m is the mass of the adsorbent.

The extent of adsorption (x/m) increases with pressure and becomes maximum corresponding to pressure ps called equilibrium pressure. Since adsorption is a reversible process, the desorption also takes place simultaneously. At this pressure (ps) the amount of gas adsorbed becomes equal to the amount of gas desorbed so that the extent of adsorption becomes constant even though the pressure is increased. This state is also called saturation state and ps is called saturation pressure.

Freundlich Adsorption Isotherm

The variation of extent of adsorption (x/m) with pressure (p) at a particular temperature was given mathematically by Freundlich in 1909.
(i) At low pressure, the graph is almost straight line which indicates that x/m is directly proportional to the pressure.
x/m ∝ pz
x/m = Kp
where K is constant.
(ii) At high pressure, the graph becomes almost constant which means that x/m becomes independent of pressure. This may be expressed as:
x/m = constant
x/m ∝ p0
x/m = K p0
(iii) Thus, in the intermediate range of pressure, x/m will depend upon the power of pressure which lies between 0 to l i.e., fractional power of pressure (probable range 0.1 to 0.5).
where n can take any whole number value which depends upon the nature of adsorbate and adsorbent. The above relationship is also called Freundlich’s adsorption isotherm.

Calculation of K and n of adsorption isotherm

Taking logarithms on both sides of Equation, we get
Log {x/m} =log K + 1/n log p
If we plot a graph between log (xlm) on y-axis (ordinate) and log p, on x-axis (abscissa), straight line will be obtained. The slope of the line is equal to 1/n and the intercept is equal to log K.
Freundlich’s adsorption isotherm fails at high temperature.

Adsorption Isobars

With the increase in temperature at constant pressure the extent of adsorption (x/m) will decrease. The graph between extent of adsorption and temperature at constant pressure is called adsorption isobar.
In case of chemisorption, the adsorption initially increases with rise in temperature and then decreases. Like all chemical reactions, some activation energy is required for chemisorption.

T Plot Adsorption Isotherm

b) As temperature is increased the molecules of the adsorbate gain energy and become equal to activation energy so that proper bonds are formed with the adsorbent molecules.
c) Therefore, initially amount of gas adsorbed increases with rise in temperature. Further
increase of temperature will increase the energy of molecules which have already been adsorbed.
d) This would increase the rate of desorption and, therefore, decrease the extent of adsorption.
The adsorption isobar graphs can be used to distinguish between physical and chemical adsorptions. In physical adsorption, there is a regular decrease as temperature increases. However, in chemisorption, there is initial increase and then it decreases.

Adsorption from solution

The process of adsorption can take place from solutions also.
1) When solution of acetic acid in water is shaken with charcoal, a part of the acid is adsorbed by charcoal and therefore, the concentration of acetic acid decreases in the solution.
2) When magnesium is precipitated as magnesium hydroxide, in the presence of magneson reagent, it attains blue colour. The colour is due to adsorption of magneson.
3) The litmus solution when shaken with charcoal becomes colourless because of adsorption from solution phase.
Solid adsorbents adsorb certain solutes from solution in preference to other solutes and solvents.
For example : animal charcoal decolourises impure sugar solution by adsorbing colouring dye in preference to sugar molecules.
Adsorption
The following observations are made in case of adsorption from solution phase:
(1) The extent of adsorption depends upon the concentration of the solute in the solution. It increases with increase in concentration of solute in the solution.
(2) The extent of adsorption decreases with increase of temperature.
(3) The extent of adsorption also depends upon the nature of adsorbent and adsorbate.
(4) The extent of adsorption increases with an increase in the surface area of the adsorbent.
The Freundlich’s adsorption isotherms obtained for the adsorption of gases on the surface of solid adsorbents have also been found to be approximately applicable to the adsorption of solutes from the solutions. Here, the equilibrium pressure in the adsorption of gases has been replaced by the equilibrium concentrations (c) of the adsorbates in solution.
The adsorption isotherm may be represented as:
x/m = Kc1/n
Taking log, it becomes
log {x/m}= log K + 1/n log c
A graph between x/m and c has been found to be similar to one shown for x/m and p for gases on solid . From the graph, the values of 1/n and log k can be calculated as slope and intercept respectively.