# Density

In Measuring and Understanding Density, several experiments were performed to find density of regularly shaped objects, irregularly shaped objects, liquids and gasses. An additional experiment was done to find the specific gravity of a sampling of liquids. The purpose of the experiment was to provide a better understanding of density and to be able to extrapolate unknowns based upon these calculations. The experiments yielded data in keeping with Kinetic-molecular theory in regards to the density of water versus its temperature.Key measurements and formulae were also used to determine densities of metal and plastic objects as well as irregularly shaped rocks.

It is possible to find the density of an object (be it liquid, gas or solid) by the use of only a select few measurements and the formulae contained herein. Introduction In observing oil floating on water one unknowingly observes a difference in density. Encyclopedia Britannica describes density as offering “a convenient means of obtaining the mass of a body from its volume or vice versa. Density calculations are used in a number of ways that impact daily life. They are used in the preparation of ballistics gelatin for testing the actual damage a bullet might do to a human body in order to provide information to forensic scientists (C.

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J. Shepherd et. al. 2009). Density calculations are also vitally important to ship builders in order to allow them to calculate how much weight a ship with a given sized hull can hold without sinking (Smith, and Jewett 342).

Density (d) is relative to mass (m) and volume (V) in as much as d=m/V.This experiment uses this equation in different fashions to analyze certain substances and extrapolate unknown measurements from known measurements. Through the techniques used in this experiment, one can easily determine differing factors about regularly or irregularly shaped materials as well as liquids and gasses, and thereby determine their densities. In knowing the density of an object, further hypotheses can then be made. These hypotheses include which liquids will layer themselves if put in a column relating to density as well as which solids may be heavier or more dense than others.

With regard to gasses, one can use the information herein to realize the amount of gas contained within a container and thereby its density. Procedure In the first of five stages in this experiment, the density of several regularly shaped objects (in g/cm3) was determined. The objects used were: a small metallic rectangle, two small metallic cubes of slightly different size, and two small, solid plastic spheres. The cubes were differentiated by marking them “1” and “2” with a marker. The spheres were dark and so could not be marked but one had a small dent in it and that was used as differentiation.The objects were weighed to a hundredth of a gram on a scale and the mass for each was recorded.

In order to obtain a volume for these objects, a formula of length x width x height was used for the rectangle and cubes. In order to obtain the volume of the spheres, a formula of 4/3 pi • r3 was used where r = radius of the sphere. All measurements were done in mm with a ruler and so were converted to cm3 at the end. Once volumes and masses were calculated, they were used in the d = m/V formula to determine densities and these were recorded in g/ml.In the second stage of this experiment, the density of two irregularly shaped objects was determined.

Two small rocks were obtained that differed in size by roughly half. The small rock was labeled rock “A” and the larger was labeled rock “B. ” Each rock was weighed on a scale and their masses were recorded. A graduated cylinder was then used that the rocks would fit into and filled with a specific volume of water sufficient to cover the rocks. This volume was recorded and the rocks were then added to the water one at a time with the increase in volume being recorded after each one.This displacement of water gave a way to measure the volume of the irregularly shaped rocks by subtracting the initial amount of water from the amount obtained after the first rock was inserted into the cylinder (measuring at the bottom of the meniscus) and then subtracting the amount of water with the first rock in it from the amount obtained after the second rock was inserted.

With volume and mass determined, the density formula (d = m/V) was used to determine the densities of each rock and recorded in g/ml. In the third stage of this experiment, the density of a liquid was determined and compared to known standards.A 100ml beaker was filled to about half-full with room-temperature distilled water. The temperature of the water in ? C was recorded in order to compare to known standards later. A 50ml beaker was then weighed on a scale in order to determine mass and recorded. A sample of the distilled water with an exact volume of 10ml was then placed in the 50ml beaker using a volumetric pipette.

The 50ml beaker with the 10ml of water was then weighed again and the initial mass of the beaker was subtracted from this mass to obtain the mass of the 10ml of water.With the volume and the mass of the water now known, density was calculated using d = m/V and recorded in g/ml. This process was then repeated to check for precision and compared to standard values to check for accuracy. Standard values were obtained from CRC Handbook, 88th Ed. In the fourth stage of this experiment, the density of a gas was determined.

A 250ml flask was weighed with an empty rubber balloon and the mass was recorded. A small piece of dry ice was placed inside the flask and the balloon was fitted over the top of the flask to seal it.The flask with the dry ice and the balloon were weighed together and this mass was also recorded. By subtracting the first weight from the second, the mass of the dry ice was determined. This provided a known mass for the gas that the subliming dry ice would create.

Once the dry ice had fully sublimed and was no longer visible, the circumference of the balloon was measured in cm using a flexible tape measure. This measurement was used in the following formulae: circ. = 3. 1415 x diameter, radius (r) = ? diameter, volume of a sphere = 4/3 pi • r3.In this way, the volume of the gas filling the balloon was obtained. By using this volume and the recorded mass of the dry ice, the d = m/V formula was used to determine the density of the gas in g/L.

In the fifth and final stage of this experiment, specific gravity of three different liquids was determined. Distilled water, Coke and Diet Coke were used in the experiment. The instructions for this lab called for 7-Up and a synthetic “urine” sample to be tested as well, but these were unavailable at the time of the experiment.An empty graduated cylinder was weighed and the mass was recorded. 10ml of each liquid were put into the cylinder with a volumetric pipette and the cylinder was weighed with each liquid and then cleaned and dried before the next liquid was weighed. In this manner, the masses for 10ml of each liquid were obtained and recorded.

These volumes and masses were used in the d = m/V formula to determine their individual densities. These individual densities were then compared as a ratio to the density of water known to be 1. 00g/cm3 @ 4? C.If the ratio was above one, the liquid had a higher specific gravity than water and if the ratio was less than one, the object had a lower specific gravity than water. As an aside, it had been planned to perform an experiment involving a density column during this exercise. However, since time and materials were prohibitive, this part was omitted.

Data Stage 1 – Density of Regularly Shaped Objects Object| Mass| Vol. Formula (mm)| Volume| Density Formula| Density| Rectangle| 33. 07g| 7. 49 x 2. 43 x . 50| 9.

10mm3| d= 33. 07g/9. 10mm3| 3. 63x103g/cm3| Cube 1 | 5. 37g| 1.

13 x 1. 13 x 1. 3| 1. 44mm3| d= 5. 37g/1.

44mm3| 3. 73x103g/cm3| Cube 2 | 5. 42g| 1. 19 x 1. 19 x 1.

19| 1. 69mm3| d= 5. 42g/1. 69mm3| 3. 21x103g/cm3| Sphere 1| 2.

82g| 4/3 pi (. 575)3 *| 0. 80mm3| d= 2. 82g/. 796mm3| 3. 54x103g/cm3| Sphere 2| 2.

59g| 4/3 pi (. 62)3 **| 1. 0mm3| d= 2. 59g/1. 0mm3| 2. 6x103g/cm3| *, ** Values for radius were obtained by using diameter measurement divided by two.

Stage 2 – Density of Irregularly Shaped Objects Object| Mass| Vol. H2O Measured/Calculation| Vol. H2O Displaced| Density Formula| Density| Rock A| 2. 55g| 65. 3ml – 64. 5ml| .

8ml| d = 2. 55g/. 8ml| 3. g/ml| Rock B| 5. 26g| 67. 2ml – 65.

3ml| 1. 9ml| d = 5. 26g/1. 9ml| 2. 8g/ml| Stage 3 – Density of a Liquid Sample Number| 50ml Beaker Mass Empty| H2O Temp.

| Mass Beaker w/ 10ml H2O| Mass of 10ml H2O| DensityFormula| Density| 1| 27. 76g| 24. 2? C| 37. 69g| 9. 93g| d = 9.

93g/10ml| . 99g/ml| 2| 27. 77g| 24. 1? C| 37. 71g| 9. 94g| d = 9.

94g/10ml| . 99g/ml| Densities of water @ various temps taken From CRC Handbook, 8th Ed. ?C| Density(g/ml)| 20. 0| 0. 9982063| 20.

5| 0. 9981019| 21. 0| 0. 9979948| 21. 5| 0. 9978852| 22.

0| 0. 9977730| 22. 5| 0. 9976584| 23. 0| 0. 9975412| 23.

5| 0. 974215| 24. 0| 0. 9972994| 24. 5| 0.

9971749| Stage 4 – Determining Density of a Gas Flask &amp; Balloon Mass| Flask, Balloon &amp; Dry Ice Mass| Mass of Dry Ice| Circ. Of Balloon| Volume Formula| Volume| Density Formula| Density| 130. 04g| 133. 00g| 2. 96g| 43.

5cm*| 4/3 ? (6. 92)3| 1. 388L| d=2. 96g/1. 388L| 2.

13g/L| * Circumference was used to establish radius using (?? (circumference))? 2 = Diameter Stage 5a – Determining Densities of Given Liquids Given Liquid| Empty Grad. Cyl. Mass| Mass Cyl. w/10ml Liquid| Mass of 10ml Liquid| Density Formula| Density| Distilled Water| *| *| *| *| . 9g/ml| Coke| 116.

70g| 127. 03g| 116. 70g-127. 03g = 10. 33g| 10.

33g ? 10ml| 1. 033g/ml| Diet Coke| 116. 70g| 126. 55g| 126. 55g-116. 70g = 9.

85g| 9. 85g ? 10ml| . 985g/ml| * Density figure for distilled water imported from Stage 3 of experiment. Stage 5b – Comparison of Given Liquid’s Density to Water to Determine Specific Gravity Given Liquid| Density of Liquid| Density of Water| Specific Gravity of Given Liquid| Distilled Water| . 99g/ml (@ 24. 2? C)| 1.

00g/ml @ 4? C| ;lt; water| Coke| 1. 033g/ml| 1. 00g/ml @ 4? C| ;gt; water| Diet Coke| . 985g/ml| 1. 00 g/ml @ 4?C| ;lt; water| Results and Discussion With a couple small exceptions, results of the experiment were within expectations.

One exception was the result of the distilled water versus known density of water. Upon further investigation, the reason that the density of the distilled water was . 99g/ml and not 1. 00g/ml as known was because of the difference in temperature. When compared to the excerpt from the CRC Handbook it becomes clear that as temperature of the water increases, the density decreases. This sufficiently explains the difference and the reason for these two figures.

This is also in keeping with the Kinetic-molecular theory and the physical properties of a liquid that as a fluid heats up, the atoms move faster and thus the space between them is increased, causing the density to be lower (“Kinetic-molecular theory of gases”)(“liquids”). The other substances measured were within expectations as Coke contains more sugar in solute than water thus increasing the density. Proposed theories for the lower density of Diet Coke would be that it lacks the sugar of Coke and also contains carbonation which may contribute to the lower density (“specific gravity”).A future experiment to test this theory might include allowing the Diet Coke to become ‘flat’ as it were, and see if results differ. Another unexpected result was that the density of the seemingly plastic spheres was so close to that of the metallic cubes and rectangle.

Also that the density between the two varied by a significant amount when they were seemingly made of the same material. Possible reasoning for this apparent lack of precision besides differing materials could be attributed to the inaccurate measuring method of using a straight ruler to measure the diameter of such a small sphere.Calipers with a greater amount of significant digits would give a far more reliable reading. Also, the fact that the first ball had a small ‘dent’ would render the volume slightly inaccurate since the formula assumes a perfect sphere. The ‘dent’ would remove some mass from the volume of said perfect sphere.

The irregularly shaped object experiment provided interesting results as well. Both of the rocks were seemingly identical in composition. However, their densities varied by four tenths of a gram per milliliter. This again ould be due to the relatively small samples which would in turn cause any inaccuracies in measurement to have a larger effect on the outcome. Then again, enclosed pockets of air within the rocks that water did not fill would also cause inaccuracies.

Perhaps for greater accuracy, the rocks could be scanned in some way to detect any voids. In measuring the density of carbon dioxide created by the subliming dry ice, it was noted that there were no redundancies in this experiment. Also, since temperature was not noted, it is not possible to compare the findings to known densities of carbon dioxide.In future experiments, temperature readings should be included and/or redundant experiments performed to provide a basis for comparison. Conclusion As a whole, these experiments validate many of the formulae they were based upon and yielded results relatively within expectations. The Kinetic-molecular theory as well as the physical behavior of liquids was verified in different ways in these experiments.

These experiments provide solid information that can be used to calculate densities of several different types of matter which is of great importance in many aspects of everyday life for many different applications.Works Cited Hampton, David. Chemistry Laboratory Notebook: Gwinnett Technical College. 2011. Print. C.

J. Shepherd, et al. “THE DYNAMIC BEHAVIOUR OF BALLISTIC GELATIN. ” AIP Conference Proceedings 1195. 1 (2009): 1399-1402. Academic Search Complete.

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