LABORATORY EXPERIMENT pubs.acs.org/jchemeduc
Kundt’s Tube: An Acoustic Gas Analyzer Natasha Aristov, Gehsa Habekost, and Achim Habekost* Department of Chemistry, P€adagogische Hochschule Ludwigsburg, Reuteallee 46, D-71634 Ludwigsburg, Germany
bS Supporting Information ABSTRACT: A Kundt tube is normally used to measure the speed of sound in gases. Therefore, from known speeds of sound, a Kundt tube can be used to identify gases and their fractions in mixtures. In these experiments, the speed of sound is determined by measuring the frequency of a standing sound wave at a fixed tube length, temperature, and pressure. This resonant frequency is dependent only on the properties of the gas, namely, its heat capacity ratio (adiabatic index) and molar mass. We discuss the capabilities of a Kundt tube for use as an instructional device to identify gases on the basis of their acoustic spectra and to use these spectra to determine the fractions of components of a binary mixture or to study the kinetics of gas-generating or gas-depleting reactions. KEYWORDS: First-Year Undergraduate/General, Upper-Division Undergraduate, Laboratory Instruction, Physical Chemistry, Hands-On Learning/Manipulatives, Gases, Kinetics, Laboratory Equipment/Apparatus, Physical Properties
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The tube has been tested for two years by second- and third-year chemistry education students during their physical chemistry laboratory. These students saw several didactical uses for the gas sensor in chemistry and physics instruction for 10th to 12th-graders and college students. First, the chemistry education students noted the possibility of demonstrating the connection between the two sciences: a physical phenomenon (acoustic waves), induced with physical (electronic) hardware, is used to identify a chemical substance. This is, of course, just physical chemistry, but it is an aspect of science that is not often presented at the secondary school level. Second, the chemistry education students were impressed with the apparatus itself because they are not typically confronted with chemical laboratory equipment much beyond the usual pipets and test tubes and an occasional pH-meter, conductivity tester, or fully automated spectrometer. The students reported that understanding the vacuum and gas conducting systems was initially challenging. Third, the chemistry education students insisted that the gas sensor should not be introduced without prior explicit visualization of the standing acoustic waves, for example, by putting cork powder or sand into the tube. Alternatively, by pulling a stick microphone through the tube when the speaker is tuned to an overtone, one can hear the varying amplitude of the standing sound wave.
number of chemical reactions studied in high school and college general chemistry courses produce gases. The quick identification of these gases is part of many experiments, for example, the burning splint test for oxygen gas, the “squeaky pop” test for hydrogen, or the clouding of a limewater solution for carbon dioxide. Identifying gases, especially toxic ones, is an expanding industry, with new types of gas sensors coming on the market regularly. The more common sensors are based on potentiometric methods, with a voltage change being measured across a semiconductor chip in the presence of the gas in question. Although rather sophisticated, these gas sensors have the practical disadvantage of being useful, for the most part, for only one kind of gas, as well as a didactical disadvantage for students who may not yet be familiar with the properties of semiconductors and gassurface interactions. Acoustic phenomena of gases, on the other hand, are generally familiar even to younger students. That the shape, size, and filling material of a vessel can change its tone can also be easily demonstrated with a few wine glasses, first empty, then filled with water, and struck as a bell or rubbed on the edge with a moistened finger tip. Helium- and SF6-distorted voices are further examples that students can be referred to when told that the speed of sound is different in different (gaseous) media. We present a device for the identification of all sorts of gases— from as light as hydrogen to at least as heavy as sulfur dioxide—based on their resonant acoustic frequency. The device is a glass tube, fitted with a loudspeaker at one end and a microphone at the other: a variation of a Kundt tube.1 Whereas Kundt devised his apparatus to measure the speed of sound in various media from the observed sound wavelength, in our device, the measured sound wavelength (actually the frequency) is used to identify the medium (a gas). Copyright r 2011 American Chemical Society and Division of Chemical Education, Inc.
’ EXPERIMENTAL SETUP The acoustic gas analyzer device is capable of analyzing gases and vapors of low-boiling-point liquids, such as methanol, Published: March 31, 2011 811
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Figure 2. Acoustic spectra for oxygen taken at different pressures. The theoretical resonance position is at 335 Hz. The ripples toward low and high frequencies are an artifact of the measurements being taken while the gas was still flowing. They do not appear when the gas is stationary.
fluctuations of the gas at the position of the microphone generate the detected voltage signal. Moving the microphone along the axis of the gas-filled resonance tube allows one to see, via an oscilloscope, and to hear the nodal structure of the standing wave.5 With the microphone position fixed at the end of the tube, the maximum signal amplitude corresponds to that of an antinode (i.e., maximum wave amplitude) of a standing wave. Both a fundamental and the lowest overtones can be seen. Monitoring the microphone response while scanning the loudspeaker frequency results in an acoustic resonance spectrum. The acoustic spectra of oxygen taken at various pressures are shown in Figure 2. The acoustic spectra should be independent of the pressure of the gas in the tube (see the discussion in Theoretical Background section); however, the peak position moves gradually from higher frequencies toward the theoretically expected value of 335 Hz at 1000 mbar with increasing pressure. All gases that we tested behaved in this way. This behavior can be attributed to the loudspeaker acting as a damped, driven oscillator, where the gas in the tube provides the damping force. Increasing the pressure beyond 1000 mbar, to a maximum of 1300 mbar, does not affect the resonance. All measurements reported below were carried out at 1000 mbar. A factor affecting the microphone response is the driving voltage (that is, the volume) of the loudspeaker. The data were obtained with the driving voltage set as low as possible (0.08 V) without entire loss of signal intensity. We have tested two ways of driving the speaker and reading the microphone signal: one using external components and one using typical hardware installed in most computers, namely, a soundcard. Figure 1 shows the setup using a wobbler signal generator (B€urklin PeakTech 4080) in which the frequency is varied by a dc voltage ramp from a power CASSY (LD Didactic 524 011). The rms value of the microphone signal is digitized by a sensor CASSY (LD Didactic 524 010) and sent to a computer.b Standard CASSY lab software (LabVIEW) is used to control the voltage ramping (that is, the speaker frequency) and to display the resulting signals, that is, the amplitude of the microphone response, and also the measurements of the pressure and temperature gauges. The spectra obtained are displayed as a function of time, that is, the start and end time of the voltage ramp, which correlates to an initial and final dc voltage of the power CASSY. The actual frequency of the loudspeaker for a given dc voltage is read directly off the wobbler signal generator and noted, manually, postexperiment. We believe this setup to be the more easily understood
Figure 1. The setup of the acoustic gas analyzer device. In a version involving less hardware, the power CASSY and wobbler are replaced by the output of a computer soundcard and the microphone signal is led to the input of the same soundcard rather than to the sensor CASSY.
ethanol, or acetone, and binary mixtures of gases.2 The setup is shown in Figure 1. The design details are described in the Supporting Information. Alternative designsa of similarly conceived inventions have been proposed.3,4 The experimental center of the device is a custom-made acoustic resonance tube, 500 mm long and 45 mm o.d., made of double-walled 2 mm thick glass. There are ports for pressure and temperature gauges. The temperature of the tube is controlled by water flowing between the double walls. The water temperature is externally controlled via a thermostat (Haake SC 100; not shown in Figure 1). The pressure inside the tube is controlled by a mechanical vacuum pump (Alcatel, Annecy 2012) connected via a T-joint to the gas inlet. All valves and joints are standard laboratory glassware; no high-vacuum equipment was used. The best vacuum attained is about 1 mbar, the leak rate about 1 mbar in 20 s. The maximum pressure that the sound components and glass tube can handle is about 1.5 bar. The ends of the acoustic resonance tube are flanged to allow easy clamping of the loudspeaker (B€urklin 38 M380) to one end and a piezo crystal microphone (B€urklin MC 9)d to the other. The loudspeaker membrane is perforated with a 0.1 mm diameter needle in six places along the perimeter of a 20 mm diameter circle centered on the membrane to equilibrate the pressure on both sides. The loudspeaker and microphone were each mounted in a polyethylene-plastic holder, with a milled groove for fixing the Viton O-rings (45 mm o.d., 4 mm thick). The O-rings ensure a vacuum seal between the glass flange and the sound components. A 1 mm diameter hole is drilled through the holder for the electrical cable throughput. After mounting the sound component in the holder and threading the cable through the hole, twocomponent glue (Pattex, Stabilit extra, Henkel KGaA, D€usseldorf, Germany) is used to vacuum-seal the hole. The holder design is also provided in the Supporting Information. During the experiment, the resonance tube is filled with a gas, the loudspeaker is driven at a given frequency, and the pressure 812
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Journal of Chemical Education variation because each electronic component has a unique function: power CASSY (ramp generation); wobble frequency generator and loudspeaker (sound generation); microphone (sound pickup); and sensor CASSY (signal conversion). An alternative that requires less hardware but removes direct access of the students to the separate steps of signal production and retrieval is to use a computer soundcard to generate the acoustic signals and process them. We used the Visual Analyzer shareware program6 to drive the Realtek AC 97 audio soundcard in our PC. This software includes a wave generator function that can produce single-frequency signals, a frequency sweep, and also white (and pink) noise between 0 and 4 kHz to the speaker output of a soundcard. This signal was passed to the loudspeaker on the acoustic resonance tube, eliminating the need for the power CASSY and the wobbler. The microphone is connected to the input of the soundcard. The sensor CASSY is retained but only to monitor the temperature and pressure measurements. An even more technically elegant alternative is to use the white noise generating function of the software to drive the speaker. This introduces, however, a “magical” component because the incoming microphone signal must be Fourier transformed by the software to reveal the resonant frequency. The Fourier transformation is comparatively fast: the recording of a complete spectrum takes less than 0.1 s at a sampling depth of 4096 samples, a sampling frequency of about 40 kHz, and 16-bit resolution. Sample data using the soundcard are given in the Supporting Information. The fast signal acquisition allowed by Fourier transformation permits kinetics measurements and measurements on transitory systems in which the pressure or temperature might be varying rapidly. This was done for the data shown in Figure 1, in which the spectra were taken with the stopcock to the gas inlet cracked open slightly and the oxygen gas leaking in. As can be seen, this method of measurement, although yielding clear resonance lines, also introduces “ripples”. We are not clear as to how the ripples are actually generated, but they are clearly connected with the gas being not stationary during the 2-s measurement: the ripples do not appear when the gas is not flowing. The device was initially tested and calibrated with commercialgrade gases and later, in reaction kinetics studies, with chemically generated gases. Unfortunately, because the loudspeaker and the microphone are exposed directly to the gas, this setup is not suited to measurements with reactive (e.g., caustic) gases.c The gas generator is a two-neck, 250 mL, round-bottom flask, with one neck attached to the vacuum line and acoustic tube, and the other to a separate dropping funnel. One (nonvolatile) reagent is placed in the flask and the other (liquid) reagent in the funnel, in nonstoichiometric quantities, until measurements are begun. After the system (Kundt tube and flask) has been evacuated, the stopcock to the dropping funnel is opened to allow the liquid reagent to drip into the first, and the evolved gas diffuses into the Kundt tube. A student laboratory procedure is included in the Supporting Information.
’ THEORETICAL BACKGROUND The speed of a sound wave, in an ideal gas, is given by c = (γRT/M)1/2, where γ = CP/CV, the ratio of the heat capacities, sometimes known as the adiabatic index; R is the ideal gas constant; M is the molar mass; and T is the absolute temperature. The speed of sound is also equal to the wavelength of the sound
LABORATORY EXPERIMENT
multiplied by the frequency: c = λf. At resonance, the length of the tube a is equal to a multiple n/2 of the wavelength λ of the standing wave, thus, cres ¼ ðγRT=MÞ1=2 ¼ ð2=nÞafres
ð1Þ
Rewriting this equation in terms of fres shows that, for a given temperature and fixed tube length, it is only proportional to (γ/ M)1/2 and is independent of the gas pressure. (The pressure dependence of γ is negligible.) For a binary gas mixture, the frequency will be dependent on some effective molar mass and effective γ (given by ref 5) Meffective ¼ x1 M1 þ x2 M2 γeffective ¼ x1 γ1 þ x2 γ2
ð2Þ
where xi is the molar fraction of component i, Mi the molar mass, and γi its adiabatic index. Thus, by following the position of the resonance frequency, it is always possible to see whether the gas in the tube is a single component or a mixture. The actual length of the tube, a, was calibrated using room temperature (24 °C) air in two different ways: (i) A 100 MHz oscilloscope measured the jitter between the microphone and the loudspeaker signals (the scope was triggered by the loudspeaker) as 0.148 ms. The known speed of sound in air at 24 °C, 343 m/s, thus yields a tube length of 0.507 m. (ii) The measured resonance frequency for air is 353 Hz. Taking γ = 1.4 gives 0.49 m for the length of the tube. In the calculations, a was set to 0.50 m.
’ HAZARDS The hazards are minimal with this experiment. The MSDS sheets should be examined for the gases used. ’ RESULTS The acoustic resonance tube was tested using gases as light as hydrogen and as heavy as sulfur dioxide. Tests with sulfur dioxide had to be abandoned as the electronic components were quickly corroded. The resonance frequencies expected for the gases (with n = 1 in eq 1) and the actual measured values7 are listed in Table 1. As can be seen, the agreement between predicted and measured values is excellent. A typical spectrum, for CO2, showing the fundamental and the first overtone is shown in Figure 3. The relative intensities of the lines are an artifact of the loudspeaker performance, not a property of the gas. The line widths are about 10 Hz at half-maximum. Line broadening is due to the thermal speed distribution of the gas particles, as can be seen from the Gaussian line shape, and also from the enhancement of the broadening at higher temperatures (about 18% between 8 and 58 °C, not shown here). The resonance frequency will shift with the effective mass of the gases present in the tube. In Figure 4, we show the change in frequency for various mixtures of CO2 and CH4 along with the theoretical resonance frequencies, as calculated using the effective molar mass of the mixture and the effective adiabatic index (eq 2) and eq 1. It is obvious that the tube can be used to determine the relative fractions of a binary gas mixture. The maximum discrepancy is about 2% and could be accounted for by air leaking into the apparatus, reducing Meffective and γeffective and slightly raising the resonance frequency. This mode of the tube has been used by students to determine the CO2:CH4 ratio 813
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Table 1. Predicted and Measured Resonance Frequencies, fres Gas Hydrogen Helium Methane Acetylene Nitrogen Air (dry)d NO Oxygen Methanol Carbon dioxide Ethanol NO2 Acetone Sulfur dioxide N2O4
Adiabatic Indexa γ
Calculated fres /Hz
Measured fres /Hz
1.41 1.66 1.194 1.23 1.404c 1.40 1.40 1.397 1.33 1.266
1306 1033 438 349 349 353 337 335 318.5 272
1300 1028 438 350 350 353.5 338 335 320e 272
1.33 1.33 1.33 1.29c
266 266 236 228
268e -f 238e 226
1.33
188
-f
Values of γ at 293 K were taken from ref.7. Frequencies measured at 293 K and 1000 mbar. c Value of γ at 288 K. d Effective molar mass for dry air is 28.85 g/mol. e Vapor pressure at 10 mbar. f Not measured experimentally as a pure gas; seen only in gas mixtures. a
of the gaseous reactants and products are different. In these experiments, we follow the pressure-dependent shift of the resonance frequency (as shown in Figure 2) as a function of time. Fourier-transformed spectra are taken every second and then the intensities of the resonance frequencies obtained from each spectrum are plotted as a function of time. Preliminary measurements have been made for several simple reactions such as the production of acetylene from calcium carbide and water, NO2 dimerization, oxygen produced from the decomposition of hydrogen peroxide, and hydrogen production from acids reacting with metals. We have provided a brief procedure used by students to look at NO2 dimerization, qualitatively, in the Supporting Information.
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’ FURTHER WORK The Kundt tube gas analyzer could possibly be made much smaller, on the order of typical test tube dimensions, to reduce overall costs and space requirements. Testing with water aspiration in place of the mechanical pump could put the device within reach of most schools and allow several devices to be set up on a typical lab bench. Finding corrosive-resistant electronic components will significantly enhance the tube’s versatility, for example, to study the chemistry of ozone. Work is proceeding on chemically reactive systems to see whether equilibrium and rate constants can be accurately determined with this method. ’ ASSOCIATED CONTENT
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Supporting Information A sample student laboratory procedure for the dimerization of NO2 to N2O4; complete design details for the Kundt tube and speaker and microphone mounting flanges; sample spectra taken using a computer soundcard to generate the speaker signal and read the microphone response. This material is available via the Internet at http://pubs.acs.org. Figure 3. Acoustic resonances of CO2 showing the fundamental (272 Hz) and one overtone frequency (544 Hz).
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected].
’ ACKNOWLEDGMENT We would like to thank Anke Rothgang for her initial testing of the device.
Figure 4. Comparison between the measured frequency dependence of a binary mixture of CH4 and CO2 and the theoretical values derived using eqs 1 and 2. The error bars represent the scatter of five sets of data. Total gas pressure is the same for all measurements, 1000 mbar.
generated by fermenting silage in experiments concerning biogas generation.8 Most interesting is the possibility of using the tube to look at kinetics of gas-phase reactions or of reactions producing or depleting gases. This can be done under the provision that the effective masses
’ ADDITIONAL NOTE a The alternatives proposed in refs 3 and 4 have several disadvantages: In those instruments, ultrasound velocity is measured to identify the components of a gas mixture. This requires precise time measurements and is thus more sensitive to experimental error. In addition, the piezoelectric ultrasound transmitter used there must be acoustically insulated from all other instrument components. This makes the measurements exceedingly sensitive to all kinds of pressure instabilities. In our device, these difficulties are overcome by measuring resonant acoustic frequencies, rather than sound velocities. This negates the need for soundproofing the device and lowers the requirements on the sensitivity of electronic parts. CASSY, “Computer-Assisted Science System” (that is, computerassisted experimenting) is a product group made by LD Didactic,
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located in H€urth, Germany. It comprises interfaces between various standard sensors and devices (e.g., power supplies, photometers, pH-meters) and the associated software, intended for instructional use. Generated data files can be exported to the usual spreadsheet programs such as Excel. Analogous interfaces for data logging can be obtained from the Vernier company (www.vernier.com), for example, the Universal Lab Interface, or LabPro. c
Efforts are currently underway in collaboration with Beyerdynamic (http://www.beyerdynamic.de/ Heilbronn, Germany) to develop speakers and microphones that can be used reliably in this device in caustic atmospheres. d
The B€urklin MC9 is no longer available for sale. Alternative microphones are currently being sought and tested.
’ REFERENCES (1) Kundt, A. Ann. Phys. 1866, 127 (4), 497–523. (2) Habekost, A. G., German Gebrauchsmuster 20,2009,003,553.0 27, 2009 (3) Cadet, G., Valdes, J. L. Acoustic Analysis of Gas Mixtures. U.S. Patent 5,392 635, 1995. (4) Douglas, D. W. Method and Apparatus for Monitoring the Content of Binary Gas Mixtures. U.S. Patent 5,060,506, 1991. (5) Tipler, P. A. Physik; Spektrum, Akademischer Verlag: Heidelberg, 1994; p 480. (6) Visual Analyzer Software. http://www.sillanumsoft.org (accessed Mar 2011). (7) Table of physical properties of gases. http://www.energie.ch/et/ grundlagen/thermodynamik/gas.htm (accessed Mar 2011). (8) Rothgang, A. unpublished Bachelor’s Thesis 2009, P€adagogische Hochschule Ludwigsburg, Manuscript available (in German) from the authors upon request.
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