Dr Renu Nayar Department of Chemistry DPVipra College Bilaspur CG Capillary Rise in cylindrical tube Capillary Rise for liquid like water Its depend on two type of forces 1 Downward direction ID: 1021526
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1. Capillary Rise in cylindrical tube Dr Renu Nayar Department of Chemistry D.P.Vipra College Bilaspur C.G
2. Capillary Rise in cylindrical tube Capillary Rise for liquid like water Its depend on two type of forces 1 Downward direction Due to weight of liquid[wetting liquid] 2 Upward direction Due to Tensile Forces in opposite direction
3. Capillary action in different thickness and Diameter of Tube
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5. Capillary Rise in cylindrical tube Determination for formulae 1 in the downward direction Weight= x V X g =Density of Water (h x a) x g v=Volume of Rising liquid which is equal to area and hight of liquid In Cylindrical tube
6. Capillary Rise in cylindrical tube In Cyllindrical Tube The volume of a cylindrical tube is equal to hight rise for the liquid and area covered by the liquid which is equal to Volume of a cylindrical Tube = X Hight for liquid [h]
7. Capillary Rise in cylindrical tube Tensile forces in capillary = x circumferences of liquid x cos {circumferences of liquid = }So we can write hereTensile forces in capillary = x x cos Now After achiving at equllibrium both forces are equal so… (h x a) x g = x x cos
8. Capillary Rise in cylindrical tube (h x a) x g = x x cos (h x ) x g = x x cos h = x x cos / . .g h= 4 x cos / .d. g For water lquid due to cos =0
9. Capillary Rise in liquid final equation [ h= 4 / .d. g ]
10. Hight of liquid in Capillary action Hight[h] for the liquid =
11. Capillary action in nonwetting liquid [Hg]
12. Capillary Fall in liquid Due to Hydrostatic forces [pressure exerted by a liquid that depends on how liquid deep in it Hydrostatic force = pressure x area Hydrostatic force = P x Hydrostatic force = h x g x
13. Capillary Fall in liquid Due to Tensile forces Tensile forces in capillary = x circumferences of liquid x cos {circumferences of liquid = }Tensile forces in capillary = x x cos Now After achiving at equllibrium both forces are equal so…h x g x = x x cos
14. Capillary Fall in liquid h x g x = x x cos hight = x x cos / . .g h= 4 x cos / .d. g For in case of mercury[Hg] due to cos =1280 We can use the value of cos =1280 in numericals
15. Capillary Fall in liquid Formulae for capillary fall in liquid Hight[h] for the liquid =
16. Laplace equation This concept is based on two factorsPressure inside the liquid PiPressure outside the liquid Por-radius of curverc -radius of capillary When liquid rise in a capillary there are two type of forces creating on the surface of liquid 1 force due to pressure difference 2.Forces due to surface tension
17. FORCE DUE TO PRESSURE DIFFERENCE FORCE = PRESSURE x AREA PRESSURE =PRESSURE INSIDE –PRESSURE OUTSIDE P= Pi – Po Area = r 2 Force due to pressure difference = [Pi - P0] . rc2
18. FORCE DUE TO THE SURFACE TENSION AT UNIT LENGTH SURFACE TENSION = SO WE KNOW THAT AT dl length surface tension force = dl x At z-axis force = dl x cos ----------1 When we see on the figure Cos = rc/r Put the value of Cos in equation no 1 Force = dl x rc/r This equation is only for dl length
19. Laplace equationNow we will do summation in dl length of liquid For the whole surface = dl = 2 rcForce = dl x x rc/r Put the value of summation dl Force = 2 rc x x rc/r Force due to surface tension = 2 rc2 /r
20. Laplace equationAt equilibrium Force due to pressure difference = force due to surface tension [Pi - P0] . rc 2 = 2 rc2 /r [Pi - P0] = 2 /r [Laplace Equation ]
21. BET EQUATION WHY BET CONCEPT COMES ?Langmuir adsorption isotherm is applicable for mono-molecular layer of adsorption and in this concept only monolayer is formed .In BET concept we will see multilayer formation of the gas molecule on the adsorbent surface .
22. BET EQUATION Langmuir adsorption low pressure and high temperature[monolayer] BET THEORY High pressure and low temperature[multilayer ]
23. BET EQUATIONIn 1938BRUNAUER EMMETT TELLERIT EXPLAINS MULTILAYAR ADSORPTION PHENOMENONIT IS USEFUL TO CALCULATE SURFACE AREA OF ADSORBENT
24. The BET theory applies to systems of multilayer adsorption and usually utilizes probing gases that do not chemically react with material surfaces as adsorbates to quantify specific surface area. Nitrogen is the most commonly employed gaseous adsorbate used for surface probing by BET methods.
25. BET EQUATIONTHIS THEORY IS BASED ON TWO ASSUMPTIONS THE ADSORBED LAYER MAY BE POLYMOLECULAR IN THICKNESS. LANGMUIR ASSUMPTION APPLIES TO EVERY LAYAR. 2 THERE IS A DYNAMIC EQUILIBRIUM BETWEEN SUCCESSIVE LAYARS.SO THE RATE OF EVAPORATION FROM THE FIRST LAYAR IS EQUAL TO THE RATE OF CONDENSATION ON THE PRECEDING LAYER.3 THE HEAT OF ADSORPTION IN EACH LAYAR EXCEPTING THE FIRST LAYER IS INVOLVED IN EACH OF THE EVAPORATION PROCESSES. AFTER THE FIRST LAYER ,THE HEAT OF ADSORPTION IS EQUAL TO LATENT HEAT OF CONDENSATION OF VAPOUR BET EQUATION AND DERIVATION IS BASED ON THE KINETICS CONCEPT
26. BET EQUATION Gaseous molecules behave ideally Multiple molecules can be adsorbed to each site Each adsorbed molecule provides a site for the adsorption of the molecule in the layer above it All sites on the surface are equivalent No adsorbate - adsorbate interactions An adsorbed molecule is immobile
27. BET EQUATIONThe adsorption involves the formation of multimolecular layer of adsorbate molecules on the surface of the solid adsorbent.The multilayer adsorption takes place in the following Steps Gas + Adsorbent Surface Single complex Gas + Single complex Double complexGas + Double complex Triple complex Multilayer formation
28. BET EQUATIONThe interactions between the adsorbate molecules in the adsorbed layer are neglected.The forces that produce condensation are responsible for binding energy in the successive layersThe heat of adsorption in the first layer is constant. After the formation of first layer, the heat of adsorption is assumed to be equal to the latent heat of condensation of vapors. Kinetic behavior of the adsorption process so rate of arrival of adsorption is equal to the rate of desorption
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31. Derivation of BET adsorption isotherm On the basis of above postulates, Brunauer, Emett and Teller derived the BET equation as follows. We can represent the formation of multilayer of gas molecules on the adsorbent surface with the help of following equilibrium equations:
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37. Overall concept with derivation of BETAdsorption is the sticking of gas molecules onto the surface of a solid… all available surfaces including that surface inside open pores. • Increasing the pressure of gas over a solid causes increasing adsorption. • Temperature dependent • Desorption is the removal of gas molecules from the surface of a solid… all available surfaces including that surface inside open pores. • Decreasing the pressure of gas over a solid causes increasing desorption. • Done at same temperature as adsorption.
38. When the interaction between a surface and an adsorbate is relatively weak only physisorption takes place. • However, surface atoms often possess electrons or electron pairs which are available for chemical bond formation. • This irreversible adsorption, or chemisorption, is characterized by large interaction potentials which lead to high heats of adsorption. As is true for most chemical reactions, chemisorption is usually associated with an activation energy, which means that adsorbate molecules attracted to a surface must go through an energy barrier before they become strongly bonded to the surface.
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40. APPLICATION OF BET It is Powerful method of surface area determination
41. Limitations • BET theory ignores inhomogeneities of the surface and lateral adsorbate- adsorbate interactions High energy sites will be occupied at lower relative pressures Reason for the nonlinearity of BET plots at p/p0 0.3 • The BET equation is applicable for surface area analysis of nonporous materials Difficulties to separate mono-multilayer adsorption from pore filling Filling of micropores is completed at p/p0 0.1. however, linear BET plot are found at even lower relative pressures