10
GAS-PHASE ADSORPTION
INTRODUCTION. In this experiment you will study the adsorption of gaseous nitrogen and dimethyl ether on a molecular sieve. Molecular sieves are commonly used as adsorbents and solid supports in chromatography. The mechanism of their mode of action is instructive in understanding the function of catalysts based on zeolites. The procedure is routinely employed in the characterization of catalysts since the adsorption of a substrate on a catalytic surface is the first step in the mechanism of catalysis. The experiment will also introduce you to manipulations on a vacuum line.
BASIS FOR THE EXPERIMENTAL PROCEDURE. The apparatus is displayed in Figure 1. Broadly speaking, it consists of a vacuum pump, pressure gauges, a ballast for storing the gas, a sample cell containing the adsorbent, a source of the gas, and a manifold that connects the components. The general approach is quite straightforward. One transfers a known amount of gas to the system and with the aid of a pressure gauge measures the amount of gas adsorbed by the adsorbent.
Figure 1. Components of the vacuum line. Key: A, stopcock A; B, stopcock B; ballast, ballast cell connected to the manifold via stopcock C; cell, tube with the adsorbent, connected to the manifold via stopcock D; MKS, MKS Baratron pressure gauge; MKS-C, controller for the MKS gauge; PT50, Leybold PT50 turbomolecular pump system; sample, cylinder of dimethyl ether with a regulator, connected to the manifold via tygon tubing and stopcock E; TC, thermocouple gauge; TC-C, controller for TC.
A detailed discussion of the vacuum system is necessary in order to understand the manipulations and the calculations that you will employ to analyze the data. The goal is to determine for a substance the number of moles adsorbed on an adsorbent as a function its partial pressure. One starts at the right with a Leybold PT50 turbomolecular pump system that has two components, a roughing pump and a turbomolecular pump. The latter component is routinely used in the semiconductor industry to achieve high vacuum. The PT50 system is connected to the glass manifold by a series of stainless steel elbows and a compression fitting. The vacuum system is isolated from the remainder of the system by stopcock A. Following stopcock A is a trap, normally cooled with liquid nitrogen, which functions to prevent condensibles from the manifold from reaching the vacuum pumps. The trap is connected to the remainder of the manifold by an O-ring junction.
Working to the left, one encounters a vent valve A' and the main valve B. You will require the volumes of the components to the left of stopcock B. In particular, the following volumes are relevant to the analysis: VB, the volume of the ballast which is connected to the manifold via stopcock C; VC, the free volume of the sample cell (total interior volume less the volume occupied by the adsorbent) that is connected to the manifold via stopcock D; and VM, the total volume of the remainder of the manifold to the left of stopcock B. The value of VB is 1.0454 liter. You will determine the values of VC and VM. The samples, nitrogen and dimethyl ether, are introduced via stopcocks E' and E, respectively. Pressures in the range of 0-1000 torr are measured using the MKS Baratron gauge at the right of the manifold. Its accuracy is 0.1 torr. Measuring pressures below 1 torr is achieved with the aid of the thermocouple gauge. It is not very accurate but allows one to measure pressure over several orders of magnitude.
One begins the procedure by completely evacuating all components of the system. The vent and stopcocks E and E' are closed during this step. Then one closes stopcocks B and D and via stopcock E or E' introduces gas into the manifold and ballast volumes (VM + VB) until a pressure pa is reached. Stopcock B will remain closed for the duration of the measurements. The total number of moles of gas in the system at this initial point is given by equation (1):
pa[1](VM + VB) = nT[1]RT (1)
The "1" in brackets indicates that this is the first measurement of the total number of moles of gas in the system prior to adsorption. One then opens stopcock D and waits until the system reaches equilibrium. The pressure reading will drop because of expansion into the sample cell and adsorption of the gas. Measuring the pressure, pp, is the last step of the measurement cycle which is repeated until the adsorbent is saturated.
The cycle is repeated N times. Each further cycle of the experiment consists of the following steps.
(1) Close stopcock D.
(2) Open stopcopck E(E') and introduce additional gas to the system.
(3) Measure the pressure, pa (a = ante or before exposure of the additional gas to the adsorbent).
(4) Open stopcock D and wait until the system has reached equilibrium.
(5) Remeasure the pressure, pp (p = post or after exposure of the additional gas to the adsorbent).
The manipulation of the data provides a wonderful illustration of gas laws and stoichiometry. The goal of this section is the derivation of an expression for nac[i], the total number of moles of gas adsorbed at each step i. At the end of cycle i-1, the total number of moles in the gas phase before the addition of more gas in the next cycle is given by equation (2):
pp[i-1](VM + VB + VC) = npT[i-1]RT (2).
This portion of this that is present in the ballast and the manifold is given by
pp[i-1](VB + VM) = npMB[i-1]RT (3).
Then stopcock D is closed. Cycle i is initiated and the additional gas fills just the ballast and manifold. The pressure at this point is given by
pa[i](VB + VM) = naMB[i]RT (2£i£N) (4).
By combining equations (3) and (4) obtains the following result for the number of moles of gas added in step i:
nadd[i] = naMB[i] – npMB[i-1] (2£i£N) (5)
Note that nadd[i] (the result for step i = 1) is given by equation (1). That is, nT[1] = nadd[1]. At this point the total number of moles of the gas in the gas phase is given by the sum of the amount in the ballast and manifold plus the amount in the cell. That is,
nT[i] = naMB[i] + pp[i-1]VC/RT (2£i£N) (6)
Note, however, that nT[1] is given by equation (1). Finally, stopcock D is opened and the gas in the ballast and manifold that was supplemented by the addition fills the cell and additional adsorption occurs. Once the system comes to equilibrium, the total number of moles in the gas phase is given by
pp[i](VB + VM + VC) = nTa[i]RT (1£i£N) (7).
The number of moles of gas adsorbed in step i is therefore given by
na[i] = nT[i] – nTa[i] (1£i£N) (8).
Finally, the required total number of moles of gas adsorbed at each step i is given by the sum of incremental contributions calculated from equation (8). That is,
i
nac[i] = S na[j] (1£i£N) (9).
j=1
MODELS FOR THE RESULTS. Various models have been proposed for the adsorption of gases. The are discussed in Adamson's monograph on surface chemistry. The simplest but yet effective model was proposed by Nobel Laureate Irving Langmuir. It works best when there is a strong interaction between the molecules and the adsorbent and the molecules in the high pressure regime, i.e. saturation, form a monomolecular layer on the adsorbent. It follows from a simple mechanism: M(g) + A(s) « MA(s).
Equation (10) expresses the Langmuir adsorption isotherm, the relationship between the pressure of the gas and the moles of adsorbed substance:
Q = n/n¥ = Kp/(1 + Kp) (10)
Q = fraction of total coverage
n = number of moles of adsorbed gas (nac[i] from equation (10) )
n¥ = number of moles of gas absorbed at saturation
p = partial pressure of the gas (pp[i], NOT pa[1])
K = ka/kb = binding equilibrium constant
ka = rate constant for the forward, adsorption step
kb = rate constant for the reverse, desorption step
Note that an identical relationship applies in the case of binding of a substrate to a protein in the case of non-cooperativity. If the adsorbent is a catalyst, adsorption (i.e. binding) is followed by the molecular transformation of the bound and therefore activated substrate to form the product. This Languir model for heterogeneous catalysis is identical with the Michaelis-Menten model for enzyme catalysis.
The model can be tested in several ways. If the term Kp is small (small binding constant and/or low pressure), equation (10) simplifies to its linear form, Q = Kp or n = n¥Kp. However, if binding is not weak, the full equation must be used to describe the data. The equation can be linearized in several ways. The simplest approach involves taking the reciprocal. After re-arranging terms, one obtains
1/n = (1/Kn¥)(1/p) + 1/n¥ (11).
Equation (11) is known as a Benesi-Hildebrand plot. Its equivalent in enzymology is the Lineweaver-Burke plot. It has been shown that this approach does not yield the most robust results. A statistically better approach is a Scatchard plot (equation (12)) which can be obtained from equation (10) by a few steps of algebraic manipulation:
n/p = n¥K – nK (12).
Although the Langmuir isotherm handles many cases well, it does not handle all due to factors such as multi-layer adsorption and interaction between binding sites, i.e. cooperativity. In level of sophistication, the next successful model was developed by Emmett, Brunauer, and Teller. Their relation, usually known as the BET isotherm, is
q = n/nmon = cz/{(1-z)[1-(1-c)z]} (13)
nmon = number of moles substrate required to form a monolayer (not necessarily the number of moles at saturation)
z = p/p* (calculable since p* is known)
p* = vapor pressure of the substrate
c » exp[(DH°des - DH°vap)/RT] (Since DH°des is always greater than DH°vap, the constant c is greater than one.)
The BET isotherm reduces to the Langmuir isoterm in the limit of low pressure if one associates c/p* with K. Equation (13) can be rearranged to yield equation (14) which is in a form that can be tested by the method of linear least squares.
z/[(1-z)n] = 1/cnmon + {(c-1)/(cnmon)}z (14)
EXPERIMENTAL PROTOCOL
SETUP OF THE SYSTEM
1) Do not perform any of these steps until you have first thoroughly read the entire handout for the experiment and have had the pre-lab orientation session with the instructor. In closing the stopcocks, don't turn them beyond their limits or you will crack the vacuum system. A black stripe has been drawn on each of the brown plastic plugs. The stripe will be close to the 12:00 position when the stopclock is closed. The instructor will point out the appearance of the plastic plug as it makes contact with the glass upon closing.
2) Secure a supply of liquid nitrogen from Room 21 in a large dewar. Do not close the door of the room while you are securing the cryogen. Asphyxiation is a real possibility in a closed room with limited ventilation.
3) Using the O-ring and the clamp, connect the trap to the manifold. Place the dewar in position but don't add any liquid nitrogen yet.
4) Close stopcock B and the stopcock connected to the vent and open stopcock A. Turn on the roughing pump but not the turbomolecular pump. When the switch on the PT50 controller is in the 12:00 position, the unit is completely off. When the switch is turned clockwise to the next position at roughly 2:00, the roughing pump is turned on.
5) Wait a few seconds for the pump to evacuate the trap and the manifold up to stockcock B. Slowly fill the dewar in which the trap is immersed with liquid nitrogen. Cover the top of the dewar with a towel to reduce the rate of evaporation of the liquid nitrogen.
Nota bene! You did not add the liquid nitrogen until after the trap was evacuated. Consider the following scenario. An open, unevacuated trap is immersed in liquid nitrogen. Since the boiling point of oxygen is greater than that of nitrogen, condensed oxygen will accumulate. This is a dangerous situation as flammable substances burn more readily in pure oxygen and high pressures will develop when the oxygen boils. In short, liquid nitrogen is a useful, non-toxic cryogen but must be used with caution.
6) Close the stopcocks to the inlet lines that drop down from the system, e.g. stopcocks D and E. Open stopcocks C and B and evacuate the ballast and the manifold. The stopcocks to both pressure gauges should be open.
7) Plug in the power cords for the controllers to the two pressure gauges. The units do not have on/off switches. The controller for the MKS gauge will require a few seconds for initialization. It reads in the range 0-1000 torr with an accuracy of 0.1 torr. The thermocouple gauge should give a reading in the vicinity of 50-80 mtorr.
8) Assemble the cell. Use Apiezon N stopcock grease. The instructor will demonstrate the proper method of using stopcock grease with standard taper joints. Attach the empty cell to the system using the male ball-and-socket fitting below stopcock D (cf. Figure 2). Attach a clamp to the socket and lightly support the cell. Then evacuate it by opening stopcock D.
9) When the cell has been evacuated, turn on the turbomolecular pump by turning the switch on its control panel to the 4:00 position. The thermocouple gauge should display a rapid decrease in pressure to 1-2 mtorr. If the MKS Baratron gauge does not read zero within its uncertainty of 0.1 torr, consult the instructor for an adjustment.
CALIBRATION OF THE VACUUM LINE
1) VB, the volume of the ballast up to stopcock C was determined to be 1.0454 liter with the aid of another flask with a known volume. The ballast tube will be the standard volume in the calibration of the system. Dry nitrogen gas will be used in the calibration.
2) Open the on-off valve of the nitrogen cylinder and slowly adjust the regulator so that the needle on the pressure gauge for the outlet pressure is barely moved. Also barely open the needle valve. Hence, nitrogen gas will flow slowly down the rubber tubing at a pressure slightly above atmospheric pressure. The tube is connected to the manifold via stopcock E', just to the left of stopcock E.