Assignment 4. Adsorption Isotherms

Institute of Process Engineering

RATE CONTROLLED SEPARATIONS

HS 2017 – PROF. DR. MARCO MAZZOTTI

IN FINE CHEMISTRY

Assignment 4. Adsorption Isotherms

Part A: Competitive adsorption of methane and ethane In large scale adsorption processes, more than one compound from a mixture of gases get adsorbed, leading to competitive adsorption: The different compounds compete for the empty adsorption sites of the adsorbent. The purpose of this exercise is to show how also the classical Langmuir isotherm, basically valid only for one-component adsorption, can be extended to multi-component adsorption, and to compare to the Ideal Adsorbed Solution (IAS) theory. Exercise A1 Determine the parameters NA, NB, kA und kB of the Langmuir isotherm equation for the given data for pure methane (A) and ethane (B) on activated carbon, e.g. by using the isotherm in its inverse form and performing a linear regression: Data for methane (A) on activated carbon:

Data for ethane (B) on activated carbon:

 nA (mol/g)

pA (kPa)

nB (mol/g)

pB (kPa)

0 4.21E-03 7.91E-03 1.17E-02 1.48E-02 1.82E-02 2.12E-02 2.43E-02 2.71E-02 2.95E-02 3.28E-02

0 8.435 17.559 26.547 36.390 45.934 56.002 66.013 76.238 87.175 101.30

0 3.80E-02 4.61E-02 5.60E-02 6.70E-02 7.71E-02 8.54E-02 9.40E-02 1.02E-01 1.07E-01 1.08E-01

0 7.483 11.383 19.084 27.787 37.653 49.969 61.827 75.199 90.783 98.301

Source: Adsorption of Binary and Ternary Hydrocarbons on Activated Carbon: Experimental Determination and Theoretical Prediction of the Ternary Equilibrium Data, E. Costa, J.L. Sotelo, G. Calleja, AIChE Journal Vol.27, p. 5 -12 , (1981)

Exercise A2 Put up the binary Langmuir adsorption isotherm from the determined parameters of the two Langmuir adsorption isotherms for the pure components.

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Assignment3_Adsorption_Isotherms.docx




IN FINE CHEMISTRY

Exercise A3 Draw the following diagrams: a)

Amount adsorbed (nA respectively nB) vs. partial pressure (pA respectively pB) for the pure components A and B (Langmuir isotherm and data points).

b)

Amount adsorbed (n) vs. partial pressure (pA) using the binary Langmuir isotherm for 80% methane / 20% ethane and 70% methane / 30% ethane.

c)

Mole fraction in the adsorbed phase (xA) vs. partial pressure (pA) using the binary Langmuir isotherm and the data given below. The total pressure is P = 101.3 kPa.

The following list contains equilibrium data for the adsorbed and gas phase. xA is the mole fraction of component A in the adsorbed phase: xA = nA(pA) / ntotal(pA) . On the other hand, yA is the mole fraction of component A in the gas phase: pA = yA  P. xA yA

0.00 0.00

0.380 0.975

0.116 0.790

0.051 0.580

1.00 1.00

Source: Adsorption of Binary and Ternary Hydrocarbons on Activated Carbon: Experimental Determination and Theoretical Prediction of the Ternary Equilibrium Data, E. Costa, J.L. Sotelo, G. Calleja, AIChE Journal Vol.27, p. 5 -12 , (1981)

Exercise A4 Determine the binary adsorption isotherm of methane and ethane on activated carbon using the Ideal Adsorbed Solution (IAS) theory. For the pure adsorption isotherms, the Langmuir isotherms calculated in exercise A1 should be taken. Compare the prediction of binary adsorption by the IAS theory with the binary Langmuir isotherm by adding another curve to the corresponding diagram of exercise A3. Again the total pressure is P = 101.3 kPa. Exercise A5 Besides the Langmuir isotherm, which has been used up to this point, there are many other adsorption isotherms found in the literature. Another frequently used isotherm represents the Anti-Langmuir isotherm, whose equation is shown below: ni 

Ni ki pi 1  ki pi

Langmuir

ni 

Ni ki pi 1  ki pi

Anti-Langmuir

Using the Ideal Adsorbed Solution theory, analytically derive the expressions for the binary isotherms using the following combination of pure adsorption isotherms of the two components: Component A: Anti-Langmuir

Component B: Anti-Langmuir

Assume that the saturation capacities are equal for both components (N = N A = NB) and that kB > kA.

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IN FINE CHEMISTRY

Hint: one can prove that IAS leads to: a)

ni 

Nki pi 1  k A p A  k B pB

i = A, B

b)

ni 

Nki pi 1  k A p A  k B pB

i = A, B

c)

but not ni 

Nki pi 1  k A p A  k B pB

i = A, B

Part B: Determination of Specific Surface Area of a Silica Gel For many materials, the surface to volume ratio is an important quality-related parameter (adsorbents, catalysts). Adsorption according to the BET isotherm is the basis for an important analytical technique for the measurement of the specific surface area of materials. This is shown in the following example, where Langmuir and BET isotherm are compared. Exercise B1 Nitrogen adsorption is used to determine the surface area of a silica gel sample (mass: 30 g): The temperature used in the experiment is the normal boiling point of N2 (77 K). In the following list, the adsorbed volume of N2 is given at different pressures: p (kPa) Vads (ml)

0.8

3.3

5.0

6.3

7.5

9.0

11.2

18.7

30.7

38.0

42.7

3.1

6.4

6.7

7.0

7.2

7.4

7.7

8.5

9.9

10.7

11.5

Write down a one-component Langmuir isotherm using volumetric instead of molar units (we assume implicitly a constant density of the adsorbed phase). In particular, use as maximal loading (saturation capacity) a volume Vmono that represents the volume of a fully occupied monolayer of adsorbed N2 molecules on the surface of the given sample. Use the data presented above to determine the parameters k and Vmono by linear regression. It is assumed that the density of the adsorbed phase corresponds to that of liquid N2 at 77K (0.808 g/cm3), and that one N2 molecule occupies a specific surface area of 16.2  10-20 m2. Calculate the surface of the sample corresponding to Vmono as derived from the Langmuir isotherm. Also give the specific surface area of the silica gel sample in [m2/g].

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IN FINE CHEMISTRY

Exercise B2 For comparison to the Langmuir isotherm, we use a BET isotherm with the following functional form:

n

c N prel 1  prel 1  (c  1) prel 

As in the case of the Langmuir isotherm, n is the adsorbed amount of gas, N is the saturation capacity and prel is the pressure relative to the vapor pressure: prel = (p / pV). At 77K, the vapor pressure pV of nitrogen equals the atmospheric pressure, i.e. 101.3 kPa. Also this isotherm may be written in its inverse form, and using volumetric instead of molar parameters. Hence, we obtain:

prel 1 c 1   prel Vads 1  prel  cVmono cVmono As in the previous case, Vads is the adsorbed volume of nitrogen, and Vmono is the volume of the fully occupied N2 monolayer on the surface of the given sample. Use the data presented in B1 together with this linearized equation and extract the parameters c and Vmono by linear regression. It is again assumed that the density of the adsorbed phase corresponds to that of liquid N2 at 77K (0.808 g/cm3), and that one N2 molecule occupies a surface area of 16.2  10-20 m2. Calculate the surface of the sample corresponding to Vmono as derived from the BET isotherm. Also give the corresponding specific surface area of the silica gel sample in [m2/g]. Exercise B3 Draw a diagram of the adsorbed volume vs. the pressure. Include experimental data points and curves according to the Langmuir isotherm and the BET isotherm. Compare the two isotherms with respect to their ability to describe the experimental data.

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IN FINE CHEMISTRY

Part C: multi-component BET isotherm In the scope of this lecture, we have described how a single species can undergo multilayer adsorption on a solid surface, we have written equations that describe interactions of the adsorbed molecules with the solid surface and with each other, and we have eventually derived from this the BET isotherm for a single adsorbing species. Exercise C1 – Optional project assignment As an optional project assignment, you may repeat the study that leads to the derivation of the BET isotherm, now describing the case of multilayer adsorption for two species that adsorb simultaneously on a solid surface. Extend the set of equations required and explore the possibility of deriving the binary adsorption isotherm accordingly.

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Assignment 4. Adsorption Isotherms

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