Job's Analysis of the Range of the "Dalton Syringe Rocket"

In the Classroom edited by

JCE DigiDemos: Tested Demonstrations

Ed Vitz Kutztown University Kutztown, PA 19530

Job’s Analysis of the Range of the “Dalton Syringe Rocket” submitted by:

Natalie Barto, Brandon Henrie, and Ed Vitz* Department of Physical Sciences, Kutztown University of Pennsylvania; *[email protected]

checked by:

Bruce Mattson Department of Chemistry, Creighton University, Omaha, NE 68178

Several demonstrations have been developed to illustrate how the power of an explosion can be harnessed to launch a projectile. Most notably, in the Austrian literature (1), a “lowcost kanone” launches a syringe plunger by igniting a combustible mixture of gases in the syringe. A similar device, which launches a piece of sponge, was described by Mattson (2). Piezoelectric igniters have been used to ignite mixtures in film canisters1 or in disposable pipet bulbs (3). In some cases semiquantitative data are used to relate the size of the explosion to the stoichiometry of the reaction.2 Surprisingly, the demonstration described here has a heritage that begins with Alessandro Volta (4) (1745–1827) and a device called “Volta’s Pistol”. We have developed a method that gives more quantitative data on reaction stoichiometry and that provides more insight into the combustion processes than previous methods. The syringe rocket is made with a modified plastic syringe that is filled with a combustible mixture of gases, whose composition is described in accordance with Dalton’s law. The syringe is inserted in a plastic pipe “launcher”, and its contents ignited electrically, propelling the syringe plunger, barrel, or both. The syringe projectile is directed into a bottle sliding on a monofilament line so that its travel was confined to a safe path, and its range (distance traveled) can be easily measured. We will see that stoichiometry is rocket science, and it is interesting to do! Surprisingly, the plunger may not be ejected from the syringe, and the entire syringe may be launched. As a matter of fact, if a total volume of 2 cm3 of gas is ignited in a 10cm3 syringe, the plunger is ejected from the syringe only for some mixtures that are close to optimal stoichiometry. The syringe is found intact in the sliding bottle in most cases after it has been “fired”. If we think of the syringe as a compressed spring that is quickly released as the ignited gases expand, it is less surprising that the plunger does not leave the barrel. This experimental artifact allows measurement of the residual gas volume and analysis by GC or other methods. In effect, the syringe is a eudiometer. The original experiments with eudiometers were done by Marsilio Landriani (5) (1751–1815) in 1775 and Volta in 1776 (6).

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a Meker burner flame, then used to slice off just enough of the barrel to remove the ridge, as shown in Figure 1.

Igniter Syringe Caps A 25–30-mm length of straightened paper-clip wire was inserted axially through a Luer-Lok cap3 to conduct a Tesla coil spark into the syringe (Figure 1). This was done by heating a needle or wire, which is slightly smaller than the paper-clip wire, and using it to melt the hole. The paper-clip wire was then pressed into the hole. Many caps have a large hollow on the non-Luer side that can be filled with hot melt glue, if necessary, to ensure a good seal (silicone glue does not adhere). The wire may be clipped off flush with the outside of the cap and extend a few millimeters into the syringe. Gas-Delivery Device A convenient device for delivering gases was constructed from a #2A Teflon stopcock mounted in 8-mm o.d. glass tubing4 (Figure 2). A 6-in. length of 3兾16-in. thick-walled latex hose was attached to one end of the stopcock tube, and a tubing clamp was attached to the end of the hose. A #3 one-

Figure 1. Modified syringe and Luer-Lok cap with wire inserted longitudinally: (A) photo and (B) schematic.

Equipment and Supplies

Syringe A 10-cm3 disposable plastic syringe was modified by cutting off the end of the barrel, which usually has finger tabs and a ridge to retain the plunger. This can be done with a hacksaw, or a microspatula can be heated to near red heat in www.JCE.DivCHED.org

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Figure 2. A length of latex hose is attached to a #2A stopcock mounted in 6-mm glass tubing and closed with a tubing clamp. A helium quality balloon is stretched over a one-hole #3 rubber stopper.

Vol. 83 No. 10 October 2006

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Journal of Chemical Education

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In the Classroom

hole rubber stopper was pushed, small end first, onto the other end of the stopcock tube. The neck of a balloon (heavy, helium grade is best) was pushed over the rubber stopper. The balloon was filled with gas from a tank by opening the stopcock and tubing clamp, attaching the hose to the tank and adding some gas, then removing the tube and allowing the gas to escape before reattaching the tube and filling the balloon completely with pure gas, then closing the tubing clamp. For gases normally delivered at pressures too low to fill the balloon, the latex hose with tubing clamp was pushed over the outside of the Luer-Lok joint of a 60- or 140-cm3 syringe, which was used to draw in the low-pressure gas and discharge it several times before final filling as above.5 The thick-walled latex tubing served as a septum, so that a syringe could be used to withdraw measured volumes of gas.

Sliding Bottle To make the sliding bottle (Figure 3), the neck was cut off of a 500-cm3 plastic soda or spring water bottle to make a ∼2-in. hole and four to five Kimwipes (or other light material) stuffed lightly inside to absorb the impact of the syringe and retain it. A 6-in. length of ∼6-mm-diameter plastic tubing (a plastic drinking straw or the barrel of a plastic pen) was glued or taped longitudinally to the outside of the bottle. The bottle and plastic tube that we used weighed only ∼16 g. A ∼20-ft length of 60-lb monofilament line was threaded through the plastic tube, and tied at each end to ring stands clamped to the bench. The launch tube was clamped to one of the stands just below the line so that the syringe was aligned with the opening of the bottle. The mouth of the sliding bottle was placed over the end of the syringe. Launch Tube A safety launch tube was constructed by cutting a 3.5in. piece of 3兾4-in. PVC pipe and using standard PVC cement to attach one end cap to the pipe. To conduct the spark from the Tesla coil (Figure 3) into the syringe igniter cap while it was inside the pipe, a 1兾8-in. hole was drilled in the center of the end cap, so that the wire in the end cap of the syringe was adjacent to the hole when the syringe was loaded

into the tube (plunger end out). Another 1兾8-in. hole was drilled on the side of the pipe at a distance from the end so that it was opposite the end of the igniter wire in the syringe. A 1兾4-in.-long machine screw or sheet-metal screw was inserted in the side hole (it should not extend inside the pipe), so an alligator clip of a patch cord could be attached to the screw, and the other clip could be attached to a pipe or other ground. When a Tesla coil6 was held near the hole in the pipe end cap, the spark jumped within the syringe to the grounded bolt, igniting the gas mixture.

Gases Butane was delivered from a commercial Ronson Multifill lighter fuel cylinder; carbon monoxide from a lecture bottle (99+%, Aldrich 29,511-6); and welding grade acetylene and prepurified hydrogen were obtained from a local industrial gas retailer. Propane from a disposable camp stove cylinder gave results that vary with manufacturer and lot, suggesting that the gas is often impure. Demonstration It is probably a good idea to lubricate the syringe plunger seal with silicone grease or lubricant before each trial. The syringe is filled by attaching an 18-gauge × 1.5-in. needle7 to the syringe and inserting it into the thick-walled latex tubing of the gas-delivery device, and slowly (over several seconds) withdrawing a small volume of the gas. This must be done slowly to allow the pressure to equilibrate, because of the restriction to gas flow through the hypodermic needle. The syringe is removed8 from the tubing and the gas is ejected once, then the syringe is reinserted and loaded with a little more than the final volume of gas. Finally, the syringe is again removed from the tubing and gas is ejected to give the required volume at atmospheric pressure. The second gas is then loaded from a similar delivery device. To ensure that volumes are measured precisely in the 10-cm3 syringe and, to minimize the effect of the “dead volume”, 10 cm3 of gas is mixed (e.g., 0.5 cm3 of acetylene and 9.5 cm3 of oxygen rather than attempting to measure 0.1 cm3 of acetylene and 1.9 cm3 of oxygen). The modified Luer-Lok cap is then applied to the syringe, and the plunger worked to mix the gases, although mixing is complete within a second or two.9 All but 2 cm3 of gas is then expelled by loosening the end cap, then the cap is retightened for the experiment. The loaded syringe is then inserted into the launch tube so that the closed end of the syringe is in contact with the closed end of the launch tube, the sliding bottle is brought up so that the syringe plunger is actually inside it, and the tip of a Tesla coil is brought adjacent to the end hole of the launch tube to ignite the gases. The distance that the bottle travels is measured with a retractable tape measure. Hazards

Figure 3. A sliding bottle with a plastic tube that slides along monofilament line receives the syringe that is ejected from the safety launch tube held in a three-finger clamp. The gas in the syringe is ignited by a spark jumping from the a Tesla coil to a ground wire.

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Tesla coil leak detectors can generate X-ray radiation and should be used intermittently only in the way described herein. Syringes with larger quantities of gases than specified here may explode, but the PVC launcher prevents the use of large syringes and protects users. Smaller (3 cm3) syringes were occasionally shattered when 2 cm3 of a stoichiometric mixture of oxygen and acetylene were exploded in them, so we


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In the Classroom

Results and Discussion

Job’s Analysis Job’s “method of continuous variation” is a common approach to determining reaction stoichiometry (7). A series of mixtures is prepared, each containing the same total amount of reactants, but with different mole ratios. Some measure of the amount of product formed, typically optical absorbance or enthalpy change (8), is plotted against the mole fraction of one substance in the reactant mixture or against the reactant mole ratio. The plot will show a maximum at the composition corresponding to the stoichiometric mole ratio. The method is easily implemented for gas mixtures in the syringe by keeping the total volume constant while varying the volume (or mole) ratio and using the range as an indicator of the amount of product formed (we suggest below that this is not completely accurate). Not surprisingly, there is a significant degree of scatter in a typical plot, but average ranges for several trials, which are shown in the plots, often

have a maximum value near the theoretical stoichiometric ratio for the thermodynamically favored reaction. It appears that the scatter is due to stochastic processes, so precise results for maxima are not a reasonable goal. Range is affected by a multitude of variables such as spark energy, residual water vapor in the syringe from previous runs, temperature of the syringe, and modification of the friction between the syringe barrel and plunger resulting from degradation of the rubber and plastic or deposition of soot. We measured ranges from zero to about 500 cm for a range of gas ratios with total volume of 2 cm3 for the gas mixtures we studied. The results are displayed graphically in Figures 4–8 and summa-

600

average values individual trials

500

Range / cm

recommend only the procedures prescribed here. It has been reported by the checker that mixtures of acetylene and oxygen in plastic syringes may explode without warning, possibly because of static discharge. Carbon monoxide is an inhalation hazard, and its use is not recommended unless it is confined to an efficient fume hood.

400

300

200

100

0 0.0

500 450

0.2

0.3

0.4

0.5

Mole Fraction Butane


400

0.1

Figure 6. Job’s plot for the butane/oxygen reaction.

300 120

250


100

200 150 100 50 0 0.0

0.2

0.4

0.6

0.8

1.0

Range / cm

Range / cm

350

80 60 40 20

Mole Fraction Acetylene Figure 4. Job’s plot for the acetylene/oxygen reaction.

0 0.0

0.2

0.4

0.6

0.8

1.0

Mole Fraction CO Figure 7. Job’s plot for the carbon monoxide/oxygen reaction. 500


450

60

300 250 200 150 100

50 40 30 20 10

50 0 0.0


70

350

Range / cm

Range / cm

400

0

0.2

0.4

0.6

0.8

0.0

0.2

Mole Fraction Propane Figure 5. Job’s plot for the propane/oxygen reaction.

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0.4

0.6

0.8

1.0

Mole Fraction Hydrogen Figure 8. Job’s plot for the hydrogen/oxygen reactions.


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In the Classroom Table 1. Results for the Syringe Rockets Figure

χmax (Theoretical)

χmax (Measured)

Maximum Range/cm

∆H/(kJ/mol)

2C2H2 + 5O2 → 4CO2 + 2H2O

4

2/7 = 0.29

0.30

380

᎑1304

C3H8 + 5O2 → 3CO2 + 4H2O

5

1/6 = 0.17

0.25

386

᎑2220

Reaction Equation

C4H10 + 13/2O2 → 4CO2 + 5H2O

6

1/7.5 = 0.13

0.18

478

᎑2879

2CO + O2 → 2CO2

7

2/3 = 0.66

0.66

112

0᎑283

2H2 + O2 → 2H2O

8

2/3 = 0.66

0.66

064

0᎑286

rized in Table 1. The expected stoichiometric ratio, χmax(theoretical) = (nfuel gas兾ntotal), for each assumed reaction equation and the measured χmax are given. Because the range for a given gas mixture may show a standard deviation of 10–30%, depending on the gas and mole ratio, we would estimate an error of at least ±0.03 in χmax values. The maximum in the Job’s plot may not be at the stoichiometric ratio for the assumed equation for some gas mixtures, notably for propane兾oxygen in this study. The deviation may be explained by thermodynamic or kinetic effects and most likely is a combination of both. The most important thermodynamic reason is that the range depends on the maximum temperature, which in turn depends upon the enthalpy of reaction (which is proportional to the amount of product as Job’s method requires), but also upon the total heat capacity of the gases. The latter is a very complex quantity that is virtually impossible to calculate accurately because a changing mixture of gases exists during the course of the reaction and their heat capacities are functions of temperature. The reaction mechanism may be a function of concentration so that the highest temperature may be achieved at unpredictable points in the process. The values of the enthalpies of reaction, provided in Table 1, do not correlate directly with the maximum ranges. More thermodynamic and kinetic explanations are provided in the Supplemental Material.W The most important kinetics explanation is that the Job’s plots may be telling us that the stoichiometry is not what we expect because competing reactions are faster than the assumed reaction, which is the thermodynamically favored one. Even in mixtures of optimal stoichiometry or excess oxygen, formation of carbon monoxide competes with formation of carbon dioxide, and carbon monoxide is detected by gas chromatography10 in the resulting gas mixtures. In the case of propane, combustion to CO by the equation,

tures, it seems, paradoxically, that we have the same amount of hydrogen and oxygen in the syringe. Dalton’s law resolves the paradox by describing gas mixtures in terms of the pressures of the component gases as if they were alone in the container. If the original pressure of the 4 cm3 of hydrogen was 1 atm,11 the pressure must have been reduced because the volume increased as the 6 cm3 of oxygen was added. According to Boyle’s law, the new pressure is P2 = (V1兾V2)P1 = 0.4 atm. This is the pure component pressure, equal to the partial pressure of hydrogen assuming ideal gas behavior (9). Since the total pressure in the syringe is still 1 atm, the pressure of oxygen is 0.6 atm. Since the only other parameter necessary to describe the gas, T, is constant, the amounts of hydrogen and oxygen must be in the ratio 0.4/0.6 = 2:3 = PV兾RT : PV兾RT. The volume percent, 60%v oxygen, can also be used to describe the composition, but it does not reflect any real volume of the oxygen gas in the mixture, in the sense that the mass percent reflects the real mass of hydrogen in the mixture. The volume percent requires historical knowledge about the preparation of the gas mixture, although it can be seen as a fictitious quantity identical to the mole percent. Our goal is to investigate the relationship between the mole ratio and the effectiveness of the gas explosion in doing work under conditions that might be related to an internal combustion engine or rocket motor.

Eudiometry The fact that the syringe plunger does not leave the barrel after the explosion, under some conditions, provides a rich opportunity for application of gas stoichiometry and eudiometry. If the final volume of gas in the syringe after the explosion is plotted against the mole fraction of hydrogen for the hydrogen兾oxygen experiment, a plot like Figure 9 is obtained, showing the expected minimum at 2兾3.

C3H8 + 3.5O2 → 3CO + H2O

Pedagogy

Dalton’s Law We often begin this demonstration of mixed gas reactions by stating what we call the “Dalton Paradox”: If 4 cm3 of hydrogen is drawn into a syringe and 6 cm3 of oxygen is added, then the final volumes of hydrogen and oxygen are the same! They are both 10 cm3, even though we know there are different amounts of gas present. This is a result of the defining property of gases: they expand to fill their containers. If volumes were a measure of the amount of gas in mix1508


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2.0

Residual Volume / mL

predicts χmax = 0.22, which is more consistent with our measured maximum (at χmax ≅ 0.25).

1.5

1.0

0.5

0.0 0.0

0.2

0.4

0.6

0.8

1.0

Mole Fraction Hydrogen Figure 9. Traditional eudiometric plot of the volume of residual gas in the syringe after the explosion against the initial mole fraction of hydrogen in hydrogen/oxygen mixtures.


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In the Classroom

In the case of the hydrogen兾oxygen reaction, residual gas volumes were never less than about 0.2 cm3, even when we measured gas ratios as close to the stoichiometric ratio as possible (where the residual gas volume would be zero). Unreacted gases were always detected by GC analysis. Other results give evidence for incomplete reaction or mixed stoichiometry. For example, if 1 cm3 of acetylene is mixed with 1 cm3 of oxygen, the balanced equation for complete combustion to CO2 (above) shows that the limiting reactant is oxygen, and only (2兾5)(1 cm3) = 0.4 cm3 of acetylene react, leaving 0.6 cm3. All of the oxygen is consumed, producing 0.8 cm3 of CO2, and 0.4 cm3 of water vapor, which condenses very rapidly. The final volume is thus 0.6 cm3 + 0.8 cm3 + 0.4 cm3 = 1.8 cm3 at room temperature in the unobservably short time before the water condenses, and 1.4 cm3 afterwards. The experimental final volume for this mixture is typically 3–4 cm3. Final volumes are difficult to measure accurately because of friction between the syringe barrel and plunger, but are usually larger than predicted. If the reaction produced just CO, and 1 cm3 of each gas was allowed to react, 0.33 mol of acetylene and 2 cm3 of products would remain (1.33 cm3 after water condenses). Thus it is plausible that too little gas is produced to expel the plunger, depending on the combustion temperature. The data allow us to estimate that the maximum temperature is about 1400 ⬚C, assuming that the residual gas thermally expands to no more than 10 cm3 from about 1.8 cm3 at 298 K, and that Charles’s law is obeyed.12 This is well below the reported maximum oxyacetylene flame temperature, 3100 ⬚C.

Explosive Limits Gas combustion is self-sustaining only between the lower and upper explosion (or explosivity) limits (LEL and UEL). The limits are usually given as percent by volume of the gas in air, but can sometimes be found for gases in pure oxygen. The Job’s plots give evidence for the limits of combustion in pure oxygen because the range falls abruptly to zero (there is no ignition) at very low or very high mole fractions of fuel gas. The LEL and UEL determined by this method may not match accepted values where they are available for several reasons, which are further explored in the Supplemental Material.W Conclusion These experiments will make excellent classroom demonstrations or investigations because they provide ample opportunity for students to make predictions about the range when the fuel to oxygen ratio is varied for a variety of fuels. Predicting the mole fraction that maximizes the range is an exciting challenge for students, so this demonstration is well suited to a “student inquiry” or interactive approach: An easily observed result, the range, may be related to stoichiometric ratios, total amount of fuel, heats of combustion, gas laws, combustion chemistry, kinetics, and type of fuel, with ranges from nil to around 500 cm. In most cases the classroom goal will be to show the effect of fuel兾oxygen ratios as related to stoichiometry, and a convincing demonstration might involve measuring ranges www.JCE.DivCHED.org

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for one or two far-from-stoichiometric mixtures followed by the stoichiometric mixture. We use 0.6, 0.5, and 0.2 mol fractions of propane in oxygen, respectively, and most students expect the first mixture to be most potent until they balance the equation and find that even the last is too fuel rich. Acknowledgments Useful advice of the Checker and fruitful conversations with Viktor Obendrauf are gratefully acknowledged. W

Supplemental Material

Construction details, thermodynamic and kinetic explanations, and information on limits of explosivity are available in this issue of JCE Online. Notes 1. Educational Innovations, Inc.; Piezo Popper Kit, #S-2A; http://www.teachersource.com (accessed Jul 2006)., 888.912.7474. 2. Flinn Scientific, Inc.; Micro Mole Rocket, #P6374; http:// www.flinnsci.com (accessed Jul 2006)., 800.452.1261. 3. BD #408531 Female Luer-Lok Caps were supplied by Fisher Scientific. Kendall monoject caps are less suitable because they are press fit, not Luer-Lok. Alternate instructions are provided in the Supplemental Material.W 4. Fisher Scientific #14-629-58A or any similar stopcock is appropriate. 5. Zipper-style plastic freezer bags may also be used to collect gases if they are punctured with a pencil tip or similar device so that lubricated 1兾8-in. i.d. latex tubing can be inserted tightly. [Mattson, B.; Meyer, A. Chem 13 News April 2003, 311, or http:// mattson.creighton.edu/Part22-ZiplocBag/Part22-ZiplocBag.html (accessed Jul 2006).] 6. Fisher Scientific NC9061498, VWR Scientific KT6915500000, or similar “high frequency coil vacuum tester”, or “vacuum leak detector”, or other high voltage supply capable of producing a 3兾4-in. spark in air was used to ignite the gas mixture. These products are manufactured by Electro-Technic, Inc. 7. The syringe may also be filled without a needle by attaching it to the end of the rubber hose while the gas is allowed to flow. 8. The needle may be left in the hose and the syringe removed without it to avoid handling a syringe with needle, or if 1兾8-in. i.d. latex tubing is used, it may be slipped over the Luer-Lok joint directly, with gas flowing, to avoid the use of a needle entirely. 9. This can be demonstrated by drawing 2 cm3 of bromine vapor into the syringe, and noting the uniformity of color as 4 cm3 of air is added 10. Gas chromatograms were obtained on a SRI 8610 GC controlled by a SRI Model 203 interface and software. A 6-ft × 1兾8in. 5A molecular sieve conventional column was maintained at 70 ⬚C with a helium flow rate of 1–2 mL兾min, the TCD detector was set at 200 ⬚C, and 1 mL samples were injected. The column was conditioned at 250 ⬚C under 1–2 mL兾min helium for 4 hours prior to first use. 11. The proper SI units, bar or Pascal, might be preferred here, but we use atmospheres because that unit is common in texts. 12. Given (V1兾V2) = (T1兾T2), (1.8 mL兾10 mL) = (298 K)兾T2, and T2 ≅ 1660 K ≅ 1400 ⬚C.


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Literature Cited 1. Victor Obendrauf has popularized many simple, low-cost gas demonstrations. See, for example, http://www.dasan.de/ lapaz/deutsch/Seminare/loxcost%20lima/lowcost.htm (accessed Jul 2006) or Obendrauf, V. Chemie und Schule 2004, 3, 12– 16. 2. (a) Mattson, B.; Lannan, J. Chem 13 News 1997, 254, 6–8. (b) Mattson, B. Microscale Gas Chemistry Experiments with Oxygen. http://mattson.creighton.edu/O2/index.html (accessed Jul 2006). 3. Mattson, B. M.; Anderson, M. Nguyen, J.; Harrison, B. Chem 13 News 1997, 257, 6–9. (b) Mattson, B. Microscale Gas Chemistry: Experiments with Ethyne. http:// mattson.creighton.edu/C2H2/index.html (accessed Jul 2006). 4. (a) Greenslade, T. B., Jr. Volta’s Pistol. Rittenhouse 1987, 1, 55–57. (b) Greenslade, T. B., Jr., Volta’s Pistol. http://

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5.

6.

7.

8.

9.

physics.kenyon.edu/EarlyApparatus/Static_Electricity/ Voltas_Pistol/Voltas_Pistol.html (accessed Jul 2006). Institute and Museum of the History of Science (Florence, Italy). Eudiometer. http://brunelleschi.imss.fi.it/catalogo/ genappr.asp?appl=SIM&xsl=approfondimento&lingua= ENG&chiave=100145 (accessed Jul 2006). Greenslade, Thomas B., Jr. Eudiometer. http://physics. kenyon.edu/EarlyApparatus/Thermodynamics/Eudiometer/ Eudiometer.html (accessed Jul 2006). (a) Harris, D. C. Quantitative Chemical Analysis, 4th ed.; W. H. Freeman & Co.: New York, 1995; pp 529–531. (b) Hill, Z. D.; MacCarthy, P. J. Chem. Educ. 1986, 63, 162. Rasmussen, Malcolm (for Project SERAPHIM). Job’s Method Thermal Titration of Acids and Bases. http://129.93.84.115/ Chemistry/DoChem/DoChem127.html (accessed Jul 2006). Missen, R. W.; Smith, W. R. J. Chem. Educ. 2005, 82, 1197– 1200.


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Job's Analysis of the Range of the "Dalton Syringe Rocket"

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