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# Use of Different Methods to Define Density: Analytical Essay

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## Abstract

Have you ever wonder why ice cubes floats when mixed with water? or when oil stays at the top of the water instead of mixing together? This goes back to 250 B.C when a Greek mathematician named Archimedes discovered density. Density explains the correlation of mass and volume and also when the object is supposed to rise, sink, or suspend an example is when oil stays at the top of the water that is because the oil is less dense than water that’s why the oil rises when put together with water and we can also say the same for the ice cube and the water. There are three methods to solve for the density of an object/s and these are the Caliper Method, the Liquid Displacement Method, and the Suspension Method but we need to weigh in the shape of the object given. The purpose of this paper is to identify which is the most accurate method for the known shape and unknown shape of an object although all have the same difficulty level the most accurate results that I found most accurate is by using the caliper method for the known density and by using the suspension method for the unknown object.

Keywords: Density, Caliper Method, Liquid Displacement, Suspension Method

## Introduction

Density has been around since 250 B.C and is discovered by a Greek mathematician named Archimedes. What is exactly density? Density is to see how much of a substance can occupy a certain volume. One of the important key point of density is that with an established temperature and pressure, the volume of a substance is directly correlating with the amount of the substance as shown in Equation 1.1. It also correlates to whether a substance is supposed to sink, rise or suspend. Less dense objects are more likely to rise than more dense materials.

### Equation 1.1

The focus of the lab experiment is the importance of accuracy of measurements, computations and understanding when it comes to determining the density of an object and how it differ when it comes to known and unknown shape of the substance. There are three methods to identify the density of a certain object or substance these are Caliper Method, the Liquid Displacement Method, and the Suspension Method but these methods are not both applicable for known shapes and unknown shapes.

## Materials and Methods

This experiment is equipped with cylinder flask, pipet, scale, caliper, Diethyelene Glycol, DI water, Methanol, and cube. The cubes on your bench are identical and have a density of 0.946 g/cm.

Observe the behavior of the cube in each of the liquids. Transfer approximately 3-5mL of a liquid into a clean graduated cylinder and add cube to the liquid. Then place the used graduated cylinder and its contents into the wash container.

Determine the mass of cube. Select a new cube, weigh it on the balance, and record its mass. Caliper Method. Using the calipers, measure its edge length and then calculate its volume.

Liquid Displacement Method. Use a liquid with a lesser density than the cube. Use the pipet to fill the graduated cylinder with approximately 3-5 mL of liquid. Record the exact volume. Add the cube to the same graduated cylinder. Record the new volume and calculate the volume of the cube.

Suspension Method. Create a liquid mixture that will suspend the cube. Add 1 mL of the liquid that has a lesser density than the object. Then select and add a liquid with a higher density than the object. Stir the mixture and record the liquid volumes. Add the cube and record your observations. Prepare different combinations of the object is suspended in the mixture. Calculate the density for each method and record these values.

## Results and Discussion

The experiment wants us to determine the difference in solving for the density between known object and unknown object for the cubes are given an identical density which is and there is no given for the unknown objects since is unknown

DI water

Methanol

Diethylene glycol

Cube

Float

Sink

Float

• Table 1.1. Cube behavior in liquids of the known objects

DI water

Methanol

1,2- Dichloroethane

10 Objects

Float

Sink

Float

• Table 1.2. Cube behavior in liquids of the unknown objects

As shown in the table (Table1.1.) the behavior of the cube when put into the DI water results for the cube to float, showing that the density of the cube is lesser than the density of the DI water which is and this also applies with the behavior of the cube with Diethylene Glycol with a density of , meanwhile the behavior of the Methanol shows otherwise that because have Methanol have a density that is and for the Table 1.2 since the density is not given for the unknown object we’ll use the behavior of the object as a guide for the density. The results have shown that since the objects float when put into the DI water its safe to assume that the objects have lesser density than water and same goes for the 1,2 Dichloroethane but for the Methanol I observed that the objects sink now I know that the objects have greater density than the liquid.

Edge(cm)

Calculated Vol (

Cube

1.001

1.003

• Table 1.3. Caliper Method

Mass(g)

10 Objects

1.55

• Table 1.4. Mass of the cube

Mass(g)

Cube

0.95

• Table 1.5. Mass of the unknown objects

The Table 1.2. and Table 1.3. shows the caliper method as a form of computing the density of a certain substance which is the cube. The first step is finding the mass of the cube using the balance which is , second is finding the volume of the cube by getting the measurement of the sides using the caliper which is then I followed the formula of the volume of the cube ( ) to find the calculated volume that’ll be . We can’t use the caliper method since the shape of the object is unknown, we can’t measure the sides but we can measure the mass (Table 1.5.) to identify the density in other methods

Volume of liquid (mL)

Volume of liquid and cube (mL)

Volume of cube (mL)

Cube

3

4.5

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1.5

• Table 1.6. Liquid Displacement Method known objects

Volume of liquid (mL)

Volume of liquid and cube (mL)

Volume of cube (mL)

10 objects

3

4.9

1.9

• Table 1.7. Liquid Displacement Method unknown objects

The table (Table 1.6. and Table 1.7.) shows the method of liquid displacement of the experiment wherein we’ll need to find the correlation of the measured mass to its displaced volume. To get the liquid displacement is first I measured the volume of the liquid on the cylinder flask by itself, after that I put the object/s into the cylinder and record the new volume of the liquid with the cube. To find the volume of the cube I computed the change in volume, to find this I needed to subtract the volume of liquid and object/s (final volume) to the volume of liquid (initial volume). The formula can be seen below Equation 1.2

Equation 1.2

Liquid 1

Liquid 2

Cube Behavior

Diethylene glycol

Methanol

1 mL

1 mL

Suspended

• Table 1.8. Suspension Method of the known subjects

Liquid 1

Liquid 2

Cube Behavior

1,2- Dichloroethane

Methanol

1 mL

1 mL

Suspended

• Table 1.9. Suspension Method of the unknown subjects

As stated on the table (Table 1.8. and Table 1.9.) that is the suspension method. The essence of the method is the submersion in the investigated medium of two liquid, to perform and find the results for the suspension method is first as stated in the materials and method we need to add a 1mL of a less dense liquid in the cylinder flask then add the more dense liquid. Stir the solution for it to combine after that we can observe the behavior of the object/s in which the suspends. It suspends because the amount of density of each variables are equal.

• Table 1.10. Density of the cube

Caliper Method

Liquid Displacement Method

Suspension Method

Density

Of Cube

0.947

0.633

0.95

Liquid Displacement Method

Suspension Method

Density

Of the objects

0.816

0.775

• Table 1.11. Density of unknown object

The table shows (Table 1.8. and Table 1.9.) the comparison between the three methods that can be used to calculate the density of a certain object and we need to discuss which have more accurate results. The caliper method is the most accurate method for the cube we can observe that in doing this experiment it can explain that maybe it’s because the variables that are taken didn’t have any correlation with substance other than itself. We can also observe that the suspension method is also close for the both objects we can explain that by saying that in the suspension method it’s needed for the objects to have the same density for it to suspend. While in the liquid displacement method it’s not fairly accurate because of the inconsistent change in volume.

## Conclusion

The factors that can affect the density of the variables are the shapes of the object because there’s a different formula for both situation and that can be a great factor on finding the density. Second is the ability to follow the rules to find the density it’s one of the great factors also because it can affect the results of your experiment and not following the proper formula or the instructions can lead to a great change on the results.

Density can be found using three methods and these are Caliper Method, Liquid Displacement, Suspension Method but we need to weigh in the shape of the object because as we said before it has a great factor because not all methods are applicable to both situations. An object with an unknown shape’s density can only be found by using two method these are caliper method and liquid displacement since caliper method recquires you to get the volume of the object and this is only applicable for the known shapes because only these objects have a formula for the volume.

## References

1. Adamov, G.A. Measurement of density and specific weight of suspensions, boiling layers, liquids and gases in ascending flow. Meas Tech 1, 426–433 (1958). https://doi.org/10.1007/BF01006178
2. Callahan, R. (2019, March 02). Ways to Determine Density. Retrieved September 20, 2020, from https://sciencing.com/ways-determine-density-2508.html

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