Application of a Differential Respirometer to the undergraduate Chemistry laboratory Ken Curnrnins Mount Royal College, Calgary, Canada Geoffrey Stedman University College of Swansea, Swansea, UK The apparatus shown in Figure 1can he used to measure low gas pressures over a range of temperature and can be easily used in the undergraduate teaching laboratory. The apparatus, consisting of two Florence flasks connected by rubber tubing to both manometer arms containing manometer oil, is based on the respirometric method (I)previously applied to studies of respiration, fermentation, and photosynthesis. The volume of air in the flasks and the manometer arm's cross-sectional area can be adjusted depending upon the sensitivity required. Because hoth flasks can he kept a t the same temperature, the effect of any changes in temperature upon the pressure of the air originally enclosed in the flasks can he nullified. However, additional pressure created by changes occurring in only one flask (e.g., formation of additional quantities of gas) can he measured over an appropriate temperature range. Three applications of this manometer are presented in this paper: the verification of pressure-temperature relationships for an enclosed gas, the measurement of vapor pressure, and the kinetics of the iodide-catalyzed decomposition of hydrogen peroxide. These applications demonstrate that the differential manometric method compares favorably with other established methods (2) for the measurement of low pressures. Pressure-Temperature Relatlonshlps The manometer oil level difference ( H cm) to he expected when the temperature of the two flasks are different (T and To)can he predicted using eq 1 below. Using the general gas equation, and taking into account the pressure change due to the compression and expansion of the enclosed gas in the flasks due to the movement of the manometer oil, the difference in height ( H ) of the manometer oil level can he expressed by H=
nRd2(TV- TAV - ToV- ToAW 1.333d, ( V 2- (AW2)
(1)
where dl and d* are the densities of manometer oil and of mercurv. res~ectivelv.n is the number of moles of gas initially enclosed ih both flasks a t a temperature To an; pressure Po in the volume V of the flasks and tubing, and AV is the change in volume of the enclosed gas due to manometer oil movement. Since AV is very small compared to V , then ( A m 2 in eq 1 can he neglected. Substituting the values of AV = HCl2000 and nR = PoVI To into eq 1, we obtain
B
Figure 1. Differentialmanometer.
temperature To and c is the cross-sectional area of manometer arm. Equation 2 permits the prediction of manometer oil level difference ( H ) when the temperature of one of the flasks is changed. Vapor Pressure Curves An expression that permits the calculation of the vapor pressure (PL)of aliquid introduced into one of the flasks can be similarly derived and is shown in eq 3. Equation 3 assumes that the volume of the liquid introduced is insignificant compared to the total volume V . P THC 1.333Hd,
+-
p,,= I 103ToV
where Po is the pressure of gas enclosed in hoth flasks at
' Visiting Scientist, University of Swansea. Author to whom corre-
spondence should be addressed. 88
Journal of Chemical Education
d,
(3)
For vapor pressure measurements, both flasks are kept at the same temperature (T). To is the initial temperature of the flasks when enclosing dry air a t atmospheric pressure Po. Klnetlcs The rate of decomposition of hydrogen peroxide
Experimental Procedure for the Measurement of the Vapor Pressure Curve of a Liquid (Hexane) I'lace both flasks in a water bathat 12'C (To).After 5 min, close clamps C and D.Measure atmospherle pressure (Po).With clamp K rlos~d.fill the tubinr above clam^ E with hexana 12 mL). wine a paste& pipet, and thin place anotier clamp at the end of the tubing at F. Open clamps C and D to ensure that the manometer water levels are equal. Open clamp E and squeeze the tubing to allow hexane to enter flask A. Close clamp E, and record the height (H cm) of the equilibrium water level difference in the manometer over the temperature range 2-12 'C. Thirty minutes will he required for equilibriumto he established after initial addition of hexane. Thereafter, approximately 5 min is required for equilibrium to be established at decreasing temperature values. Note: Flasks, tubing, and enclosed air must be initially dry when measuring aqueous vapor pressures; otherwise, low values will he obtained. Water should be used as the manometric fluid when measuring vapor pressures of nonpolar liquids.
-
Figure 2. Variation ot oil level difference(Mwith injected gas volume (VJ.
can be measured a t a temperature To from the rate of pressure increase caused by the evolution of oxygen gas. Hydrogen peroxide solution ( x mL) is placed in one of the flasks, and the subsequent oxygen pressure (Po,) calculated from the manometer oil level difference ( H ) by P&c 1.33Hdl P Ox- 103(V-X) d2
+-
The concentration of hydrogen peroxide left ([Hz02])in the solution a t any given time can be calculated using
where Ha is the maximum constant height of the oil level differences after complete decomposition has occurred. Substituting (Ha - H ) for [Hz021 can provide information concerning the kinetics of the decomposition, since, for a given experimental run, [H202]is directly proportional to (He
H). Pressure changes due to the effect of changing oxygen partial pressure upon oxygen solubility in the hydrogen peroxide solutions can he neglected because the volumes of rhe solutions are small. Determination of Volume (V) A manometer oil level difference ( H cm) results from the injection of VgmL of air a t atmospheric pressure (Po) into one flask. I t can be shown that
Experimental Procedure for Kinetics Add 1.00 mL of 6% Hz02 to flask A and 11 mL distilled water to flask B. Connect the flasks to the apparatus, and place into water at temperature To(20 "C). Close spring clamps C, D, and E. After 5 min open and then close spring clamps C and D to equalize the pressures in each flask. Open spring clamps D and E, and then add 10 mL potassium iodide solution through the funnel connected at F into flask A. The potassium iodide solution should be temperature equilibrated before adding to the hydrogen peroxide solution. Immediately close spring clamps D and E and start the clock. Shake the contents of flask A at approximately1 min intervals. A magnetic stirrer is preferred for continuous stirring, which will produce an even evolution of oxygen gas as well as ensure constant temperature in this exothermic reaction. Record the height iH cml of oil st " appropriate intervals. Measure the atmospheric pressurePoand the water bath temperature To. Note: Do not wait for complete decomposition to occur in the solutions containing low iodide concentrationsin order to obtain the maximum manometric height (H,).H., once determined using higher iodide concentrations (e.g., 0.1 mol L-'), can he used for the kinetics at lower iodide conc&trations Results and Discussion Errors quoted are statistical and represent the 20, 95% confidence limit. Figure 2 shows the linear relationship predicted by eq 6. V (0.225 L) can he calculated from the slope of the line when c (0.007855 cm2), PO(87.5 KPa), d l (0.8274 g mL-I), and d2 (13.59 g mL-l) are known. Volumes calculated from the slope of the line are in good agreement (3%) with the calibrated volume. Figure 3 shows the good agreement between the theoretical value of H (line only shown) predicted by eq 2 and the experimentally observed value of H. Equation 2 may be simplified by inserting the constant experimental values for
where
and dl and dz are the densities of manometer oil and mercury, respectively. The volume V can be calculated from the slope of the graph of H versus V,. Experimental Procedure for Pressure-Temperature Measurements The spring clamp E attached to flask A must be kept closed throughout this experiment. Open spring clamps C and D,and place flasksA and B in a water bath at temuerature Tn (20 OC). Measure barometric pressure PCI. Aiter closing spring rlampsC and D,place flask A in wnterat different tamperntures ( T ,5-40T1,and measure the corresponding differ~nce( H cm, in the levels uf or1 in the manmxter fur each temperature. At the end of the experiment remwe spring dip D. The theoretical values for H predicted by eq 2 fur each value of Tcan he ccmpared with the experimental values uf H.
TEMPERATURE (K)
Figure 3. Experimenlaland the~retlcslvalues of Hfor an enclosed gas sample at different temperatures.
Volume 65
Number 1
January 1988
89
Table 1. Vapor Pressure Curves for Water and Aqueous Ethylene Glycol (50% vlv) H (cm
Temperature
aqueous
water
ethylene glycol
293
16.8
298
21.7
303
28.7 38.3 49.0
10.0 14.2 19.5 25.9 32.9 42.6 53.9 65.2
(K)
308
313 318 323
328
61.9 79.8 99.9
b
paw (KPa)
(KPa)
2.21 2.88 3.82 5.13
1.30 1.86 2.58 3.45
6.61
4.41
8.39 10.85 13.74
7.32
5.75 8.90
To (296 K), PO(88.0 KPa), c (0.1257 cm2), and V (0.225 L). Hence, the theoretical value of H for agiven temperature can be calculated using
Deviations from ideality are attributable to the temperature of the enclosed eas in the rubber tubinr beina different from the temperature of the gas in the flas'k. As expected, these deviations become more significant as the tempera_ture of the gas in the rubber tubing becomes increasingly different from the temperature of the rest of the gas. The volume (VJ can also be calculated from Figure 3, the slope of which can be shown to t ~ e
for a temoerature ranee eauidistant above and below To. Hence, fo; a temperature range 296 i 11K, the slope (2.13) of Fieure 3 enables Vto be calculated (0.189 L). This value is lowe; than V determined from Figure 2 because the ruhber tubine is not a t the same temperature as the flasks. vapor pressure curves for water, 50% (vlv) aqueous ethylene glycol, and hexane can be calculated using eq 3. For a given experiment, eq 3 can be simplified by inserting the constant experimental values for To, Po, c, dl, dl, and V. For example, the vapor pressure of water a t different temperatures shown in Table 1can be calculated from the value of H by inserting the experimental values of To (293 K), Po (89.8 KPa), c (0.1257 cm2),dl (0.8274 g mL-I), dz (13.59 g mL-I), and V (0.225 L). Hence, eq 3 simplifies to
Figue 5. Plol of l q 9 v m u a 1lTtw water (a). 50% (vlv) aqueous ethylene glycol (b), hexane (c), and cyclohexane (d).
The vapor pressure curves for water and 50% (vlv) aqueous ethvlene alvcol are shown in Figure 4. For water, satisfactory agreeme&-with literature vapor pressure values were obtained a t ambient temperatures with cooling effects on the rubber tubing causing increasing discrepancies (lower experimental values) a t elevated temperatures. The heatofwpmization for water, calcuEte?l from Figure 5, was found to be 41.9 f 0.5 mol-1 in water and 43.8 f 1.9 kJ mol-I in 50% (vlv) aqueous ethylene glycol. These values are in good agreement with the literature (40.6 kJImol). The expected linear relationship between the vapor pressure of water ( P o ~ , o )and the vapor pressure of aqueous ethylene glycol ( P H ~ Ois) shown in Figure 6. The slope of the line indicates that Raoult's Law is not obeyed at the high solute concentration used and that deviations from ideality are similar over the temperature range studied.
Flgure 6. Vapw pressure relationship between water (Pow) and aqueous ethylene glycol (%) over lernperahrm ran* 284-296 K.
Table 2. Vapor Pressure Cuwea lor Hexane and Cyclohexane over 275-285 K Ternperatwe
I 290
300
310
320
330
TEMPERATURE (K)
Figure 4. Vapor pressure curves fawater (a) and 50% vlv a glycol (b). Literature vapor pressure curve for water (c). 90
Journal of Chemical Education
(K)
Heme
285
73.8 68.3 62.0 56.6 51.3 46.2
283 281
q w s ethylene
279 277 275
H(cm) Cyclohexane 46.1 41.9 38.3
35.0 31.5 28.3
Hexane
9 Cyclahexane
9.81 9.09 8.24 7.51
6.16 5.59 5.10 4.66
6.79 6.11
4.18
3.75
TIME (MINI Figure 7. Variatim in reanion rate at 20 OC fw decomp&tion of hydrogen peroxide in the presence of different iodide concentrations: 0.01 mol L-' (a); 0.02 mol L-' (b): 0.06mol L-' (c): 0.10mol L-' (d).
Figure 9.Anhsnius plot for the decomposition of hydrogen peroxide In p r e r ence of 0.02 mol L-' iodide.
0.356 L cvclohexane). The data from Table 2 is included in Figure 5 from which the heat of vaporization of hexane (30.4 i 0.8 KJ mol-') and cvclohexane (32.1 f 0.4 K.1 mol-'J can be calculated. These values are in satisfactory agreement with literature values (31.9 and 32.8 K J mol-I, respectively). Results of the iodide-catalyzed decomposition of hydrogen peroxide are shown in Figures 7 and 8 and confirm the tatelaw (3,4) for the decomp&ition, rate = -k'd[HzOz]ldt
where k' = k[I-1. Typical data for the decomposition is shown in Table 3. For this experiment, the values of Po (88.0 KPa), V (0.225 L), c (0.1257 cm2), x (0.011 L), dl (0.8274 g mL-I), d2 (13.59gmL-I), and To(293 K) can be inserted into eq 5, which simplifies to [H202]= 2.12 X
TIME (MINI Figure 8.FirstQrder plasfw me decampositlonat 2beC of hydrogenperoxide in the presence of iodide. Refer to Figure 7 for key.
Table 3.
Decornposltlon ot Hydrogen Peroxide In 0.01 mol L-I K I at 20 OC
time (min) 0
4 6 10 17
H(cm)
0 2 4 8 14.2
Ha
- H(cm)
[H&]
100.5 98.5 96.5 92.5 86.2
( m i LK')
0.213 0.209 0.204 0.196 0.183
(H, - H)
The activation energy for the decomposition, calculated from the data shown in Figure 9, was found to he 56.7 f 3.4 kJ mol-1, whichis in good agreement with the previously reportedvalue of 56.5 kJmol-I (5).The frequency factor was found from Figure 9 to be 2.22 X 108mol-1 L s-1. The slope and log k' intercept of the line shown in Figure 10 permits the calculation of the order in iodide (0.95 f 0.05 at 20 "C, 0.94 0.09 at 25 OC) and the specific rate constant mol-'L s-'at 20 'C, (1.90 f 0.59) X lo-= (1.42 f 0.25) X mol-I L s-I a t 25 OC, which is in satisfactory agreement with the previously reported value of 2.2 X 10-= mol-I L s-' at 25 "C (4). Taking into account the value of the specific rate constant and the initial concentration of hydrogen peroxide used.
*
The vapor pressures of hexane and cyclohexane shown in Tahle 2 can be calculated using eq 3 which can be simplified to
+
PL = 9.81 x 10-=H(AT 1)
The value of A depends upon experimental values of To (285 K hexane, 288 K cyclohexane), Po (102 KP.), C (0.1257 cm2), dl (1.00 g mL-I), d2 (13.59 g mL-9, and V (0.362 L hexane,
Figure lo.Variation of lag k' with log [I-] at 20 ' C and 25 OC,
Volume 65 Number 1 January 1988
91
Figure 11. Variation of initial rate of decomposition of hydrogen peroxide with iodide concenbation at 20 OC.
Figure 11 shows the anticipated dependence of the initial rate of decomposition ( R ) upon the iodide concentration. The order in iodide (0.96 f 0.07) was calculated from the
92
Journal of Chemical Education
slope of this plot as well as the specific rate constant (1.2 f 0.4) X mol-I L s-I a t 20 O C . The iodide-catalyzed decomposition of hydrogen peroxide was measured in solutions buffered with phosphate buffer (pH 6.9 and 9.2) as well as in unhuffered solutions. Yo pH effect upon the rate of decomposition wasobserved over this uH ranee. indicatine that the acid-catalvzed oxidation ( 6 )of lodide rb; hydrogen peroxide to be ins"ignificant, althbigh the pale yellow coloration of iodine was observed in the solutions. The kinetics of hydrogen peroxide decomposition, the heat of vaporization of nonpolar liquids and the pressuretemperature relationship can he measured using water as the manometric fluid. The use of water permits the linking together of the manometer arms with rubber tubing so that students, supplied with l-m lengths of 4-mm-i.d. glass tubing, can easily assemble their own manometer. Literature Clted
1. UmBmiZ W. W.;Bunis,R.H.:Stauffor, J.F.Monomct"eTeehniouoa,3rdd.:Burs~: Minoeapolis, 1959; p 79. 2. Weissburger. A,, Ed. Phyaieol Methois of organic Chomlatry, 3rd d.: Wilcy (Inttseiene): Near York. 1960: P u t I. Chaofarj VIll and IX. . C ~ ~ ~ . 1iiz,1o.i61. R ~ L . ' 3. B ~ ~wY. c. ' 4. Bmde J.Z.Phya. Chem. 1904,49,M8-216. 5. Lsid1er.K. J. ThaChomicalKinaficsofEnzyme A~fioio;O.I.~rdUniiiiity:1958:p199. 6. Liebhafsky, H.A,: Mohammed, A. J.Am. Chom. Soc. 1933,55,3971.
