Lab Report on Density Measurement

Introduction

1. 1 Background of the Experiment

Mass density describes how heavy an object is. Defined by the Greek letter ρ, read as rho, density is a basic yet important physical property of matter. For a bulk body without accounting its existing pores and voids, density is represented by the ratio of its mass and volume. It is given by the equation ρ = mass/volume [1]. The SI unit of density is kg/m3. However, its CGS units, g/cm3, or g/ mL, are the most commonly used ones in the laboratory. The conversion is given by 1 gcm3=1gmL=1000 kg/m3 [1]. The density of a homogeneous liquid is also defined by the amount of mass per unit volume. The liquid is usually confined in a container, so its volume is relative to the volume of its container [2]. There are various instruments that are used to accurately measure the density of substances; the most commonly used are the densitometers, pycnometer, and hydrometers [3]. In this experiment, the density of selected liquid samples will be measured using a pycnometer.

1. 2 Objectives of the Experiment

1. To determine the density of low boiling point liquid samples by measuring their mass at controlled volume;

2. to determine the density of alumina by measuring the mass and volume of variously shaped alumina balls; and

3. to compare the density calculated from the given samples with the standard density at room temperature.

1. 3 Significance of the Experiment

At the end of the experiment, the laboratory performer is expected to learn the following;

1. the density of selected liquids and material at a given temperature; and

2. the proper method of measuring the volume and consequently the density of irregularly shaped objects using water displacement method.

Review of Related Literature

Density is one of the most important and commonly used physical properties of matter. It is an intrinsic property which is represented by the ratio of a matter’s mass to its volume [3]. Density was purportedly discovered by the Greek scientist Archimedes in an unusual circumstance. According to stories, King Hiero of Syracuse asked Archimedes to determine whether his new crown is made of pure gold or not. It was seemingly impossible to identify the gold percentage that composed the crown because chemical analysis was still unstudied in those times.

One day, when Archimedes was enjoying himself to a bath, he observed that the further he went down the tub, the lesser he weighed and the higher the water level rose up. He then came to the realization that he could determine the ratio of the mass of the crown and the volume of water displaced by the crown, and compare it to the value measured from the pure gold sample. Hence, density and the principle behind it were revealed [4]. Density is dependent on many factors, one of which is temperature. It specifically decreases with increasing temperature.

This is because an object’s volume undergoes thermal expansion at increasing temperature while its mass remains unchanged. This results to a decrease in density [1]. When matter undergoes a transformation to a different phase, it undergoes an abrupt change in density. The transition of molecules of matter to a less random form, say from gas to liquid or from liquid to solid, causes a drastic increase in the density. However, there are substances which behave differently from this density-temperature relationship, by which one example is water. The greatest density achieved by water molecules is at 4°C.

At temperatures higher or lower than 4°C, its density slowly decreases. This makes ice less dense than water, a property not commonly exhibited by other liquids [3].

Methodology

3. 1 Materials A. Pycnometer, 25-mL B. Graduated cylinder, 1000-mL C. Graduated cylinder, 250-mL D. Beaker, 250-mL E. Low boiling point liquids (acetone, 70% solution ethyl alcohol, 70% solution isopropyl alcohol), 30 mL F. Distilled water G. Two sets of alumina balls (small cylindrical, large cylindrical and large spherical balls) H. Analytical balance beam

3. 2 Determining the Mass of a 25-mL Liquid [5] A.

Carefully clean and dry the pycnometer. B. Weigh the empty pycnometer and its stopper in the balance beam and record the mass. C. Fill the pycnometer with the liquid sample up to its brim, and insert the stopper carefully. Wipe off any excess fluid on the sides of the pycnometer with a clean cloth or tissue. D. Balance and record the mass of the filled pycnometer plus the stopper. E. Empty the contents of the pycnometer in a clean beaker. F. Make three trials for each liquid.

3. 3 Determining the Mass and Volume of Alumina Balls [5] A. Measure the mass of each alumina ball in the balance beam. B. Add distilled water to the graduated cylinder and record its initial volume. C. Carefully drop an alumina ball to the graduated cylinder and measure the new volume. Do this by slightly tilting the cylinder and gently sliding the ball to its side. D. Use the 250-mL graduated cylinder for small cylindrical alumina balls while the 1000-mL cylinder for the large cylindrical and spherical alumina balls. E. Do the same procedure for the two sets of alumina balls. 3. 4 Calculating the Density of Liquid [5] A. Calculate the mass of the liquid by computing the difference between the recorded mass of the pycnometer when empty and filled with liquid. B. Calculate the density of the liquid by dividing its obtained mass by the volume indicated on the pycnometer. C. Record and compare the resulting density of the liquid with the standard value at room temperature. 3. 5 Calculating the Density of Alumina Balls [5] A. Compute for the volume of the alumina balls by subtracting the initial volume from the final volume of water in the graduated cylinder. B. Calculate for the density of the alumina balls by dividing the measured mass by the volume. C. Record and compare the resulting density of the alumina balls with the standard value at room temperature. 3. Data and Analysis Table 1. The mass of the four 25-mL liquid samples measured in three trials

Liquid| Volume (mL)| Mass (grams)| | | 1ST Trial| 2nd Trial| 3RD Trial| Water| 25. 0| 25. 244| 25. 348| 25. 359|

Acetone| 25. 0| 20. 131| 20. 147| 20. 163|

Ethyl Alcohol| 25. 0| 22. 313| 22. 330| 22. 337|

Isopropyl Alcohol| 25. 0| 22. 025| 22. 035| 22. 049|

Table 2. The volume and mass of the two sets of alumina balls Alumina

Ball (based on Size)| Set 1| Set 2|

|Volume (mL)| Mass (grams)| Volume (mL)| Mass (grams)|

Small cylindrical| 2. 0| 5. 813| 2. 0| 5. 742|

Large cylindrical| 8. 5| 24. 042| 9. 5| 23. 42|

Large spherical| 10. 0| 22. 975| 9. 0| 19. 747|

Table 3. Calculation of density of the four liquid samples

Liquid| Density (grams/mL)| | 1st Trial| 2ND Trial| 3rd Trial|

Water| 25. 244 ? 25 = 1. 00976| 25. 348 ? 25. 0 = 1. 01392| 25. 359 ? 25. 0 = 1. 01436|

Acetone| 20. 131 ? 25. 0= 0. 80524| 20. 147 ? 25. 0 = 0. 80588| 20. 163 ? 25. 0 = 0. 80652|

Ethyl Alcohol| 22. 313 ? 25. 0= 0. 89252| 22. 330 ? 25. 0= 0. 89320| 22. 337 ? 25. 0= 0. 89348|

Isopropyl Alcohol| 22. 025 ? 25. 0= 0. 88100| 22. 035 ? 25. 0= 0. 88140| 22. 049 ? 25. 0= 0. 88196|

Table 4. Calculation of density of the alumina balls

Alumina Ball (based on Size)| Density (grams/mL)|

| Set 1| Set 2| Small cylindrical| 5. 813 ? 2. 0 = 2. 9065| 5. 742 ? 2. 0= 2. 8710| Large cylindrical| 24. 042 ? 8. 5= 2. 8285| 23. 942 ? 9. 5= 2. 5202| Large spherical| 22. 975 ? 10. 0= 2. 2975| 19. 747 ? 9. 0= 2. 1941|

Table 5. The mean values of the density calculated from the four liquid samples

Liquid| Mean Value (g/mL)| Water| 1. 00976 + 1. 01392 +1. 014363| =1. 01268| Acetone| 0. 80524 + 0. 80588 + 0. 806523| =0. 80588| Ethyl Alcohol| 0. 89252 + 0. 89320 + 0. 893483| =0. 89307| Isopropyl Alcohol| 0. 88100 + 0. 88140 + 0. 881963| =0. 8145|

Table 6. The mean value of the density calculated for the alumina balls Alumina Ball (based on Size)| Mean Value (g/mL)| Small Cylindrical| 2. 9065 + 2. 87102| =2. 8888| Large Cylindrical| 2. 8285 + 2. 52022| =2. 6744| Large Spherical| 2. 2975 + 2. 19412| =2. 2458| Average| 2. 8888 + 2. 6744 + 2. 24583| =2. 6027|

Results and Discussions

The table below shows the obtained densities of the samples in four decimal places. Table 7. Summary of experimental densities of the samples

Liquid/Material| Density (g/mL) at 25°C|

Acetone| 0. 8059|

Alumina| 2. 6027|

Ethyl Alcohol| 0. 8931|

Isopropyl Alcohol| 0. 8815|

Water| 1. 0127|

Table 8. Accepted values of the density of certain materials at 25°C [6]

Liquid/Material| Standard Density (g/mL) at 25°C|

Acetone| 0. 7846|

Alumina| 2. 7300|

Ethyl Alcohol| 0. 8651|

Isopropyl Alcohol| 0. 8493|

Water| 0. 9970|

Accuracy of the result, or the agreement of the experimental value to the accepted value, is defined by its percentage error. An experimental result with a percentage error of less than 5% is considered to be accurate. This indicates that the laboratory procedure performed in obtaining the said result is scientifically reliable [7].

The next table shows the calculation of the percentage errors of the densities obtained from the experiment relative to the accepted values represented in Table 8. Table 9. Calculation of the percentage error of the experimental densities of the samples

Liquid/Material|- |

Acetone | 0. 7846 — 0. 8059 0. 7846| ? 100 = 2. 643%|

Alumina| 2. 7300 — 2. 6027 2. 7300| ? 100 = 4. 663%|

Ethyl Alcohol| 0. 8651— 0. 8931 0. 8651| ? 100 = 3. 237%|

Isopropyl Alcohol| 0. 8493—- 0. 88150. 8493| ? 100 = 3. 791%|

Water| 0. 9970 — 1. 0127 0. 9970| ? 100 = 1. 550%|

Table 9 shows the percentage of errors of the experimental densities computed from the samples. The values indicate that the experimental densities of acetone, alumina, ethyl alcohol, isopropyl alcohol, and water at 25°C are within 5% error from accepted values, thereby implying that these results are accurate and the procedure used in performing the experiment is correct, consistent and reliable. Small disagreements in the values of experimental and accepted densities can be accounted for factors that could slightly change the density of a material, in which one of these is temperature.

The actual room temperature was not actually measured due to personal negligence and was just assumed to be 25°C. Thus, the standard values that are used to compare with the results might not be the most appropriate ones relative to temperature. Other factors that could lead to slight discrepancies in density could be unavoidable systematic errors, particularly instrumental and human errors.

Conclusion and Recommendation

In general, the experimental densities of all the samples used are significantly close to the standard densities at 25°C. Thus, the laboratory procedure was done correctly and consistently. Small deviations of the results from the accepted values might be due to systematic errors. One of which can be caused by the lack of precision of the analytical balance beam. Human errors such as incorrect or inconsistent readings and interpretations of results might also cause these slight disagreements between the standard and experimental values. It is recommended for future laboratory performers to measure the actual room temperature before, while, and after conducting the same experiment, to make sure that the temperature is constant all throughout.

Temperature is a vital factor that could affect the results of the experiment. Hence, this must not be neglected. Nevertheless, the method of using a pycnometer to measure the density of the liquids and water displacement method for the irregularly shaped solids yields accurate and reliable results.

References:

1. Gallova, J. (2006). Density determination by pycnometer. Retrieved July 8, 2012 from Comenius University of Bratislava at http://www. fpharm. uniba. sk/fileadmin /user_upload/english/Fyzika/Density_determination_by_pycnometer. pdf
2. University of Massachusetts Boston, College of Science and Mathematics (2005). Measurement of Density and Archimedes’ Principle. Retrieved July 4, 2012 from http://www. physicslabs. umb. edu/Physics/sum07/181_Exp9_Sum07.
3. Johnston, J. (2011). Density Definition. Retrieved July 7, 2012 from http://www. densitydefinition. com/#
4. Bell, E. T. (1937). The mathematical achievements and methodologies of Archimedes [Electronic version]. Men of mathematics. Retrieved July 8, 2012 from http://mathdb. org/articles/archimedes/e_archimedes. htm#Bk03
5. Skyline College, Chemistry 210 Laboratory Manual (2010). Determination of the density of water and unknown solid sample. Retrieved July 7, 2012 from http://www. smccd. edu/accounts/batesa/chem210/lab/labmanual/Density2010. pdf
6. Walker, R. (1998). Density of Materials. Retrieved July 8, 2012 from http://www. simetric. co. uk/index. htm
7. Brooks P. R. , Curl R. F. , Weisman R. B. (1992). Investigating the relationship between the mass of a liquid and its volume [Electronic version]. Introductory Quantitative. pages 16-19. Retrieved July 8, 2012 from http://www. terrificscience. org/lessonpdfs/MassVolumeofLiquid. pdf