Chem 367-2/ Physical Adsorption 63 PHYSICAL ADSORPTION (S&G 5th ed. Expt 27, 6th, 7th & 8th eds. Expt 26) The sample used in this experiment needs to be conditioned for at least two hours before the experiment; see Pre-Lab prep. 1. Purpose In this experiment, the so-called BET surface area of a powder sample (silica gel, alumina or any other sample assigned by the instructor) is to be measured by physical adsorption of N 2, as described in S&G 5th ed. Expt 27 (6th & 7th eds. Expt 26). 2. Safety Wear eye protection at all times in the laboratory, but in particular when working next to a glass vacuum line. Wear protecting gloves when handling liquid nitrogen, 3. Pre-Lab Preparation Read Appendix II and the chapter on vacuum apparatus in S&G before coming to the lab. At some time during the morning of the lab session, the powder sample which is to be used has to be baked to clean the surface (mostly adsorbed water). Obtain from the instructor a small glass bulb reserved for this experiment. First, weigh on the analytical balance the empty bulb, then filled it with about 1 g of the powder sample (1/4 to 1/3 full) and weigh again to determine precisely the mass of the powder. Insert a plug of glass wool in the neck of the sample tube to prevent the powder from being sucked into the line when the vacuum is applied. The bulb is attached to the apparatus, evacuated and heated to 250 C for 2 hours under vacuum before starting the experiment. Attach the bulb containing your sample to the vacuum line as depicted in Fig. 1. Ensure that there is liquid N 2 in the cold trap, otherwise fill it up with liquid N 2. Make sure that all the valves are shut (valves A, B, C and D in Fig. 3).
64 Chem 367-2/ Physical Adsorption Open slowly valve A (see Fig. 3) until vacuum is applied to the sample (the powder will start jumping and the mechanical pump will make gurgling noises). Leave valve A open and attach the small tube oven around the sample bulb. Switch ON the rheostat controlling the oven; do not adjust the rheostat setting which has been preset to obtain the required temperature. Figure 1. Diagram of CAJON TM O-ring fitting used to connect the sample bulb to the vacuum line. 4. How to Perform the Experiment Many students have found the description of experimental method in S&G to be obscure. A hopefully clearer one follows. Your immediate experimental objective is to measure an adsorption isotherm; that is, the amount adsorbed as a function of pressure, which is then analysed by the BET theory to find the surface area. The adsorption isotherm will look something like Fig. 2. The vertical axis can be in any units which are proportional to amount of gas. S&G use cm 3 at STP as their unit for amount adsorbed. This may be confusing as there are several volumes (cm 3 ) which enter the calculation. It is, therefore, much better to use moles as the quantity unit throughout. In addition to the above problem, the S&G derivation of amount adsorbed (Eq. 11) is singularly obscure. A (hopefully) clearer derivation is given below.
Chem 367-2/ Physical Adsorption 65 Figure 2. Typical adsorption isotherm. Remember that one is always trying to find the total amount of gas adsorbed. In a volumetric experiment, such as the present one, this is always obtained from Nads = Ntotal N gas (1) where N ads is the number of moles adsorbed. N total is the total number of moles admitted to the adsorption system and N gas is the number of moles still present in the gas phase. This is obtained from N gas V = Pgas (2) RT Thus, the experiment is performed by starting out with an evacuated adsorption system, admitting a known amount of gas, allowing equilibrium to be established and calculating N ads from (2) and (1). This process is repeated several times so that, after each addition, a larger amount of gas is adsorbed and the gas phase pressure is higher. For the present experiment, at least 8 points should be obtained in the range 0.05 (P/P 0 ) < 0.3 where P 0 is the saturation vapour pressure of the adsorbing gas at the temperature of the adsorbent (P 0 1 atm for N 2 at liquid nitrogen temperature). 4.1 VOLUME CALIBRATION The apparatus looks something like Fig. 3. It is very similar to the one pictured in S&G, except that the present set-up is fitted with teflon O-ring valves instead of stopcocks.
66 Chem 367-2/ Physical Adsorption Make sure you understand how to use these valves when there are open and when they are closed. Be careful not to undo these valves too far as the stem will come off creating a disastrous leak into your vacuum system. Also, over-tightening may break the glass screw thread. Note that the S&G labelling of the gas burette bulbs is opposite to our labelling; also in Fig. 3 the valve labelling of S&G (A, B... etc.) is indicated in parenthesis. Figure 3. Diagram of the vacuum line used to measure the BET surface area of powder sample. The volumes of the gas burette are accurately known as they were determined prior to the construction of the apparatus (top bulb V 1 = 65.1 ml, bottom bulb V 2 = 63.2 ml. In order to conduct the experiment, it is necessary to know V A and V B, the volumes of the connecting tubing on either side of stopcock S2. For all measurements, the Hg in the left side of the manometer should always be brought to a same reference level (chosen at the beginning of the session), so that V A is constant. Calibration is performed by using Boyle s law with He as the calibrating gas (Why?). To calibrate V A, put Hg to the bottom of V 2 with S 2 closed. Admit He ( 100 to 150 torr) via S1, close S1, adjust the Hg level in the left-hand side of the manometer and read the pressure (P 1 ). Raise Hg to fill V 2 (and V 1 if necessary) re-adjust the Hg level in the left-hand side of the manometer and read the new pressure (P 2 ). V A is obtained by solving Eq. (3).
Chem 367-2/ Physical Adsorption 67 ( ) ( ) P1 V1 + V2 + VA = P2 v + VA (3) where v = 0 or V 1 depending whether or not V 2 was filled with Hg when P 2 was measured. A similar measurement enables V B to be obtained. V B should be measured with liquid N 2 around the sample. If Boyles law is used as above for the calibration and, again, in the same way during adsorption measurements, the effect of the low sample temperature will cancel out, and need not be considered explicitly in the calculation. Make sure that the liquid N 2 level stays reasonably constant for all measurements. 4.2 MEASUREMENT OF AMOUNT ADSORBED Depending on the powder assigned (ie., depending on the BET surface area of the sample) the size of successive doses of gas will be different; consult with the instructor. 4.2.1 First dose of gas Start with an evacuated system. Close S 2. Admit the adsorbate gas via S 1 with Hg in the gas burette at the position suggested by the instructor*. Close S 1. Re-adjust the left side of the manometer to the reference level and read the pressure P init(1). N total (1) P = init (1) ( v + V ) RT A where v = 0, or V 1 or V 1 + V 2 depending on your situation. Open S 2. Some gas adsorbs and the pressure drops. Wait for the pressure to equilibrate, readjust the left hand side of manometer to the reference level and read the equilibrium pressure P eq(1). N gas( 1) = Peq( 1) Then, ( v + V + V ) A RT B Nads( 1) = Ntotal N gas( 1) (6) (4) (5) 4.2.2 Second dose of gas Close S 2 and admit more gas via S 1. Re-adjust the left side of the manometer and read the new pressure P init(2). The total amount of gas in the system now consists of the amount adsorbed in the previous step, plus the *At the bottom of V 2, or at the bottom of V1, or at the top of V1, depending on the sample assigned
68 Chem 367-2/ Physical Adsorption amount in the gas phase to the left of S 2 (at pressure P eq(1) ), plus the amount in the gas phase to the right of S 2 at pressure P init(2). Thus, N total ( v + V ) VB A ( 2) = N ads(1) + Peq(1) + Pinit (2) (7) RT RT S 2 is now opened and equilibration again allowed to take place, giving pressure P eq(2). Then, Nads( 2 ) = Ntotal Peq( 2 ) ( v + V + V ) A RT B Subsequent doses are handled in the same way as the second dose, with repeated use of Eqns. 7 and 8. It is helpful to carry out the calculations for each step as you conduct the experiment. You can also collect all the data and go away for later analysis, but you will not have a chance to back track if something goes wrong. An attempt to reduce everything algebraically to a single master equation for the nth of dose (as in S&G) will not be good for your sanity. It should be noted that a suitable set of data for BET analysis will look something like Fig. 1. Usually, nearly a complete mono-layer must be adsorbed to produce a P eq /P o value of 0.05. Thus, if you do not know the approximate area and are admitting small doses at first, the first few doses may result in such a low relative pressure as to not be useful. Once a suitable point has been obtained, however, the pressure up to P eq /P o = 0.3 is covered with only a small (typically 20%) increase in the amount absorbed, so you must admit small doses and go carefully in this region. When all your data have been collected, close all the valves around the sample (shut A and B), remove the liquid N 2 dewar then disconnect the cold sample promptly (before the nitrogen desorbs as the powder sample warms up). Do not forget to record the atmospheric pressure of the day with the barometer available in the laboratory. This experiment is an excellent example of the disasters which can occur if you come to the lab without thinking in advance about what you are going to measure. You have been warned. Data analysis can be greatly facilitated by the use of a spreadsheet program. (8) 5. Extra problem In your discussion, indicate how the results from the present experiment can be used to determine the heat of absorption of a gas on a solid. Using your data estimate the heat of adsorption of N 2 for the sample studied (see in Atkins[1], how one of the parameter describing the BET isotherm can provide information on this heat of adsorption). How does the surface area
Chem 367-2/ Physical Adsorption 69 found for the present powder compare with typical values found in the literature? 6. References [1] P. Atkins et al., Physical Chemistry, WH Freeman, NY, (any edition)
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