Simple and Low-Cost Setup for Measurement of the Density of a

Communication Cite This: J. Chem. Educ. XXXX, XXX, XXX−XXX

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Simple and Low-Cost Setup for Measurement of the Density of a Liquid Nima Noei,† Iman Mohammadi Imani,† Lee D. Wilson,‡ and Saeid Azizian*,† †

Department of Physical Chemistry, Faculty of Chemistry, Bu-Ali Sina University, Hamedan 65174, Iran Department of Chemistry, University of Saskatchewan, Saskatoon, Saskatchewan S7N 5C9, Canada

‡

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S Supporting Information *

ABSTRACT: A low-cost and simple setup to measure the densities of liquids is introduced herein. The results and reliability of this setup were evaluated for pure liquids, water−ethanol binary mixtures, and aqueous NaCl solutions. The constructed densitometer provided density values with acceptable relative errors (less than ±3.0%), which were compared to estimates of density from the literature. The favorable agreement is surprising for such a simple and low-cost setup. The facile design lends itself to use in diverse teaching environments to reinforce the ubiquitous concept of density at the secondary-school level and for undergraduate physical-chemistry teaching laboratories.

KEYWORDS: High School/Introductory Chemistry, Hands-On Learning/Manipulatives, Laboratory Instruction, Laboratory Equipment/Apparatus, Liquids, Physical Properties

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ments,19 and other advanced instrumentation. In this work, we report on the construction of a facile and low-cost apparatus for the measurement of liquid density that can be built in most secondary school or undergraduate laboratories using readily available materials. Some advantages of the present setup are its sustainability due to its simple construction, its low-cost design, its facile operation, its small sample requirements (99.9%), glycerol (purity >99%), ethylene glycol (purity >99.9%), n-octane (purity >99.9%), n-octanol Received: March 13, 2018 Revised: October 23, 2018

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DOI: 10.1021/acs.jchemed.7b00979 J. Chem. Educ. XXXX, XXX, XXX−XXX

Journal of Chemical Education

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the concept of density to address units of measurement and as a fundamental physical quantity in materials science. A key principle behind this technique is the change in vertical displacement (Δh) of the rubber band, which is influenced by the weight of the liquid sample added to the container with a known volume. Density is defined by eq 1, as follows: m ρ= (1) V where m is the mass of the liquid sample, and V is the volume of the liquid sample. It will be demonstrated by experiment that Δh (cm) is related to the sample mass by eq 2, where k is a proportionality constant (cm g−1). Δh = km

(2)

Combining eqs 1 and 2 results in Figure 1. Experimental setup for liquid density measurements.

Δh = kρV

(3)

Dividing eq 3 for the liquid sample, represented with subscript 2, by that of the reference liquid, denoted with subscript 1 (for an example with pure water, see Figure 2), one arrives at eq 4:

(purity >99.5%), toluene (purity >99%), n-decane (purity >99%), and NaCl (purity >99.9%) were all from Merck Company. Deionized water was used for the preparation of aqueous solutions, and 3 mL of liquid phase was needed for each measurement. The liquid mixtures were prepared independently by being weighed with a balance (IIAxis, ALN220) with an accuracy of ±0.0001 g. A detailed experimental procedure for the students using the proposed setup (Figure 1) is provided in the Supporting Information.

ρ V2 Δh2 = 2 Δh1 ρ1V1

(4)

For simplicity, if we use the same volumes for the reference and sample liquids (V1 = V2), eq 5 is obtained: ρ2 =

Apparatus and Procedure

Δh2 ρ Δh1 1

(5)

Therefore, the measurement of the vertical displacement of a container for a sample material (Δh2, Figure 2III) and for a reference material (Δh1, Figure 2II) is achieved for liquids by use of the basic setup shown in Figure 2. The use of eq 5 allows for the determination of liquid density. In this case, it is possible to find the density of a liquid by Δh ; with the use of a kV specific volume of reference liquid (e.g., 3 mL of water), one can estimate the k for the rubber band. Then, it is possible to measure the densities of other liquids (with the same volumes as that of the reference liquid) by use of the estimated k value.

The method of liquid-density measurement proposed herein is a facile method that employs readily available components found in any basic secondary school or university undergraduate laboratory. As shown in Figure 1, the setup requires a small plastic container suspended by a rubber band from a vertical stand with a ruler to measure the vertical height displacement with ±0.3 mm precision and a flat plate attached to the bottom of the container for measurement of displacement. The underlying principle of this apparatus relates to the vertical displacement of the container by addition of a known volume of a liquid, as illustrated in Figure 2. By use of this method, one can introduce and apply

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HAZARDS Materials such as ethanol (CAS# 64-17-1), ethylene glycol (CAS# 107-21-1), n-octanol (CAS# 111-87-5), toluene (CAS# 108-88-3), n-decane (CAS# 124-18-5), and sodium chloride (CAS# 7647-14-5) are not harmful but may cause moderate skin and eye irritation in the case of contact, when it is suggested to flush the eyes or skin with plenty of water for at least 15 min. Inhalation of high concentrations of ethanol may cause central-nervous-system effects characterized by nausea, headache, dizziness, and unconsciousness. Glycerol (CAS# 56-81-5) and n-octane (CAS# 111-65-9) can cause eye and skin irritation after contact and respiratorytract irritation in the case of inhalation. NaCl can also cause respiratory-tract irritation when inhaled. Note that glycerol and n-octane are also flammable in the liquid and vapor states, so they should be kept out of range of open flames, even in small amounts. Care should be taken to use safety gloves and glasses to avoid direct contact and chemical exposure. Waste-disposal considerations should be noticed for all materials. The

Figure 2. Container displacement by addition of a certain volume of a liquid. (I) Vertical displacement of the rubber band with an empty container (h0). (II) Vertical displacement of the rubber band with a small volume of reference liquid (h1). (III) Vertical displacement of the rubber band with the same volume of sample liquid (h2). B



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instructor is responsible for recognizing the hazardous points of other materials that may be provided to ensure safe practices and to enable the measurement of the liquid densities by students during class. Other equipment and usage procedures for the densitometer-setup preparation do not pose any significant hazards or safety risks.

Table 1. Comparison of Experimental Estimates of the Densities of Pure Liquids to Reported Values Relative Error, %

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RESULTS AND DISCUSSION Two key points were considered in the design of the present experimental setup. First, the container was selected to have minimal weight in order to optimize the accuracy of the measured vertical-displacement data. The second point was the choice of a rubber band as a tether with variable thickness, where its length changes measurably in accordance with the mass of the hanging liquid (Figure 3). According to the linear

Literature Density, g mL−1

Experimental Density, g mL−1 (SD)a

Average Δh2, cm

−0.8 2.2 0.9

0.789 1.261c 1.1133d

0.783 (±0.024) 1.289 (±0.035) 1.123 (±0.040)

0.80 1.32 1.15

−1.2 −1.9 −1.0 −2.6

0.698e 0.829f 0.862g 0.730h

0.689 0.813 0.854 0.711

0.70 0.80 0.87 0.73

b

(±0.010) (±0.034) (±0.034) (±0.023)

Material ethanol glycerol ethylene glycol n-octane n-octanol toluene n-decane

a

The values in parentheses represent the standard deviations (n = 27), where T = 293 K, ρ1 = 0.9982 g mL−1, and Δh1 = 1.02 cm. bSee ref 20. cSee ref 21. dSee ref 22. eSee ref 23. fSee ref 24. gSee ref 25. h See ref 26.

Figure 4. Density of water and ethanol binary mixtures at 303 K. Open circles are experimentally measured data; diamonds are reported literature values.27

Figure 3. Height change of the rubber band with different masses of water at 303 K.

relation between height changes of the rubber band and the mass of water, based on eq 2, the slope of this curve indicates the proportionality constant, k. To confirm the reliability of the present experimental setup for the measurement of liquid density, the densities of different pure liquids, binary liquid mixtures (water and ethanol), and NaCl solutions were measured and compared to their reported values from the literature. Nine undergraduate chemistry students at the first-year level were asked to use the setup and measure the densities of pure solvents in an independent fashion (triplicate measurements). It should be noted that each measurement takes less than 10 min. Table 1 lists the measured density values (averages of the 27 measurements taken by the students) of the pure liquids using the experimental densitometer setup in Figure 1. The experimental device was used successfully by several independent students, and it was found that the concept of density was readily reinforced through hands-on demonstration and an experimental approach with favorable student outcomes and success. Although the present apparatus is very simple, the measured displacement data provides reliable results that yield accurate estimates of liquid densities. The accuracy of the reported density values have relative errors below ±3%. The experimentally derived density values have notable accuracies for such a relatively simple densitometer device. The measured densities (triplicate averages) of binary mixtures of water and ethanol are presented in Figure 4 and

compared to the literature values. It is evident that there is good agreement between the density values of liquid mixtures measured by the relatively simple densitometer herein and the literature values reported from data obtained using highprecision densitometers. Moreover, the capability of this technique to measure the densities of aqueous NaCl solutions with variable concentrations was also evaluated. The average density estimates (triplicate measurements) obtained using the densitometer reported herein are presented in Table 2 and show favorable agreement with independent values obtained from the open literature.

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CONCLUSION Density is a key concept that is central to the chemical sciences. A knowledge of density allows for characterization of the physical states of materials, along with characterization of diverse chemical and physical processes that involve changes in volume.1−8 In this report, we outline the design of a facile and low-cost experimental setup introduced for the reliable measurement of liquid density. The apparatus can be readily built with locally available materials and does not require any specialized or advanced components such as an analytical balance. The setup is versatile in design for sustainable use in secondary schools and undergraduate chemistry laboratories with limited resources. This straightforward experimental setup C



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Aqueous Micelle Solutions of CTAB and CTAC as a Function of Surfactant Concentration and Temperature. J. Phys. Chem. 1994, 98 (16), 4368−4374. (6) Peterson, K. I. Measuring the Density of a Sugar Solution: A General Chemistry Experiment Using a Student-Prepared Unknown. J. Chem. Educ. 2008, 85 (8), 1089−1090. (7) Henderson, S. K.; Fenn, C. A.; Domijan, J. D. Determination of Sugar Content in Commercial Beverages by Density: A Novel Experiment for General Chemistry Courses. J. Chem. Educ. 1998, 75 (9), 1122−1123. (8) DeMeo, S. Beyond Density: An Inquiry-Based Activity Involving Students Searching for Relationships. J. Chem. Educ. 2001, 78 (2), 201−203. (9) Richardson, W. S.; Teggins, J. E. Measurement of Density: A first Laboratory Experiment for Beginning Chemistry Students. J. Chem. Educ. 1988, 65 (11), 1013−1014. (10) Keiter, R. L.; Puzey, W. L.; Blitz, E. A. Density Visualization. J. Chem. Educ. 2006, 83 (11), 1629−1632. (11) Emery, S. S. Baumé’s HydrometerAmerican Standard. J. Am. Chem. Soc. 1899, 21 (2), 119−132. (12) Heard, L. The Balanced Column Method for the Determination of the Density of Liquids. J. Chem. Educ. 1930, 7 (8), 1910− 1912. (13) Ledley, R. E., Jr. Pycnometer Holder. Ind. Eng. Chem., Anal. Ed. 1946, 18 (1), 72−72. (14) Singh, M. M.; Szafran, Z.; Pike, R. M. Construction of a Micropycnometer for Determination of Density and Specific Gravity of Liquids and Solutions. J. Chem. Educ. 1993, 70 (2), A36−A38. (15) Trinh, E. H.; Hsu, C. J. Acoustic Levitation Methods for Density Measurements. J. Acoust. Soc. Am. 1986, 80, 1757−1761. (16) Ashcroft, S. J.; Booker, D. R.; Turner, J. C. Density Measurement by Oscillating Tube. Effects of Viscosity, Temperature, Calibration and Signal Processing. J. Chem. Soc., Faraday Trans. 1990, 86, 145−149. (17) Yang, S. Determination of Density of Liquid by a Capillary with Two Pinhole Ends. J. Chem. Educ. 1998, 75 (3), 368−370. (18) Park, N. A.; Irvine, T. F., Jr. Liquid Density Measurements Using the Falling Needle Viscometer. Int. Commun. Heat Mass Transfer 1997, 24 (3), 303−312. (19) Adamowski, J. C.; Buiochi, F.; Simon, C.; Silva, E. C. N.; Sigelmann, R. A. Ultrasonic Measurement of Density of Liquids. J. Acoust. Soc. Am. 1995, 97, 354−361. (20) Abdussalam, A. A.; Ivaniš, G. R.; Radović, I. R.; Kijevčanin, M. Lj. Densities and Derived Thermodynamic Properties for the (nHeptane + n-Octane), (n-Heptane + Ethanol) and (n-Octane + Ethanol) Systems at High Pressures. J. Chem. Thermodyn. 2016, 100, 89−99. (21) Negadi, L.; Feddal-Benabed, B.; Bahadur, I.; Saab, J.; ZaouiDjelloul-Daouadji, M.; Ramjugernath, D.; Negadi, A. Effect of Temperature on Density, Sound Velocity, and Their Derived Properties for the Binary Systems Glycerol with Water or Alcohols. J. Chem. Thermodyn. 2017, 109, 124−136. (22) Kijevčanin, M. Lj.; Purić, I. M.; Radović, I. R.; Djordjević, B. D.; Š erbanović, S. P. Densities and Excess Molar Volumes of the Binary 1Propanol + Chloroform and 1-Propanol + Benzene and Ternary 1Propanol + Chloroform + Benzene Mixtures at (288.15, 293.15, 298.15, 303.15, 308.15, and 313.15) K. J. Chem. Eng. Data 2007, 52 (5), 2067−2071. (23) Abdussalam, A. A.; Ivaniš, G. R.; Radović, I. R.; Kijevčanin, M. Lj. Densities and Derived Thermodynamic Properties for the (nHeptane + n-Octane), (n-Heptane + Ethanol) and (n-Octane + Ethanol) Systems at High Pressures. J. Chem. Thermodyn. 2016, 100, 89−99. (24) Ye, C. W.; Li, J. Density, Viscosity, and Surface Tension of nOctanol-Phosphoric Acid Solutions in a Temperature Range 293.15− 333.15 K. Russ. J. Phys. Chem. A 2012, 86 (10), 1515−1521. (25) Luning Prak, D. J. Density, Viscosity, Speed of Sound, Bulk Modulus, Surface Tension, and Flash Point of Binary Mixtures of

Table 2. Densities of NaCl Aqueous Solutions with Different Concentrations as Measured by the Densitometer Apparatus Reported Herein and Compared to Literature Values Molality, mol kg−1

Average Δh2,a cm

5.0080 4.0283 3.2144 2.2113

1.87 1.73 1.67 1.63

Experimental Density,b g mL−1 (SD)c 1.184 1.150 1.106 1.084

(±0.019) (±0.038) (±0.019) (±0.019)

Literature Density,d,e g mL−1

Relative Error, %

1.1647 1.1354 1.1130 1.0831

1.6 1.3 −0.6 0.1

a

For n = 6. bAt 303 K. cThe values in parentheses represent the standard deviations (n = 6). dSee ref 28. eAt 298 K.

allows for the reliable measurement of liquid density, and it allows students to gain conceptual understanding of this fundamental concept by enabling interactive engagement with hands-on experiential learning. A key learning outcome of this activity reinforces that liquids with equal volumes may possess different densities, as illustrated by the reliable measurement of vertical displacement of a liquid with a known volume. The setup allows for accurate measurements of differences in liquid density and a comparative analysis of liquids and solutions from the chemical literature.

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available on the ACS Publications website at DOI: 10.1021/acs.jchemed.7b00979. Instructor and student instructions for the experimental setup (PDF, DOCX)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] or [email protected]. ORCID

Lee D. Wilson: 0000-0002-0688-3102 Saeid Azizian: 0000-0003-0040-3478 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors acknowledge the support of Bu-Ali Sina University, which allocated a research grant. REFERENCES

(1) Hawkes, S. J. The Concept of Density. J. Chem. Educ. 2004, 81 (1), 14−15. (2) Wilson, L. D.; Verrall, R. E. A Volumetric and NMR Study of Cyclodextrin-Inhalation Anesthetic Complexes in Aqueous Solutions. Can. J. Chem. 2015, 93 (8), 815−821. (3) Wilson, L. D.; Verrall, R. E. A Volumetric Study of βCyclodextrin/Hydrocarbon and β-Cyclodextrin/Fluorocarbon Surfactant Inclusion Complexes in Aqueous Solutions. J. Phys. Chem. B 1997, 101 (45), 9270−9279. (4) Wen, X. G.; Verrall, R. E.; Liu, G. Effect of Anesthetic Molecules (Halothane and Isoflurane) on the Aggregation Behavior of POEPOP-POE Triblock Copolymers. J. Phys. Chem. B 1999, 103 (14), 2620−2626. (5) Wang, L.; Verrall, R. E. Apparent Molar Volume and Apparent Molar Adiabatic Compressibility Studies of Anesthetic Molecules in D



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Butylcyclohexane with Toluene or n-Hexadecane. J. Chem. Eng. Data 2016, 61 (10), 3595−3606. (26) Estrada-Baltazar, A.; Bravo-Sanchez, M. G.; Iglesias-Silva, G. A.; Alvarado, J. F. J.; Castrejon-Gonzalez, E. O.; Ramos-Estrada, M. Densities and Viscosities of Binary Mixtures of n-Decane + 1Pentanol, + 1-Hexanol, + 1-Heptanol at Temperatures from 293.15 to 363.15 K and Atmospheric Pressure. Chin. J. Chem. Eng. 2015, 23 (3), 559−571. (27) Perry, R. H.; Green, D. Perry’s Chemical Engineers’ Handbook, 6th ed.; McGraw-Hill, Inc.: New York, 1984. (28) Hai-Lang, Z.; Shi-Jun, H. Viscosity and Density of Water + Sodium Chloride + Potassium Chloride Solutions at 298.15 K. J. Chem. Eng. Data 1996, 41 (3), 516−520.

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Simple and Low-Cost Setup for Measurement of the Density of a

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