Understanding Density: Definition, Formula, And Applications

1. Now Use your graph you plotted to find the mass of 40 mL of water. What is the density of this volume of water?
2. The equation of this best-fit line will have the familiar form y = mx + b, where m represents the slope of the line, and b represents the y-intercept. This is illustrated in
the figure above

3. Use the graph to find the density of water by finding the slope using the formula below?

Definition of Density

Density is one of the characteristic properties of any substance. All the forms of matter including solids, liquids, gases and aqueous exhibit this properties that is determined by the mass and the volume of the substance (Holzbecher 266). Matter is any substance that occupies space and has mass while density is defined as the mass per unit volume of a substance or matter. Mass refers to the amount of matter that is present in an object. Mass is measured in various units with the scientific standard unit being grams (g). Other units of measurement of mass include kilograms (kg). volume refers to the amount of space occupied by an object and is measured in various dimensions among them liters (l), milliliters (ml), cubic meters (m³), gallons among other units.

Mass is constant for a given object or substance. Mass and volume change from one object to another for example volume is determined by the size of an object. Picking an example of two pieces of plastic substances that may be derived from the same initial material. One of the pieces may be bigger while the other is smaller. The bigger piece of plastic will be found to have a higher volume than the smaller piece (Shamos 415). The bigger piece of plastic will automatically be occupying a bigger space and thus translates to a larger volume in comparison with the smaller piece. Still, the bigger piece will be expected to be heavier than the smaller piece. This is because the bigger piece has more amount of matter than the smaller piece. Assuming the two pieces of plastic are derived from the same material, that one is twice as big as the other is, then the ration of their masses, and volumes will be the same and thus the same ration in their densities.

The density of any substance is determined from the formula density=M/V where m is the mass while v is the volume of the substance that density is to be determined (Baue 321). In most cases density of expressed in grams per cubic centimeter. Gram is the SI unit for mass while cubic centimeter is the SI unit for volume. An example is the density of water, which is normally 1 gram per cubic centimeter, and the density of the earth, which is 5.51 grams per cubic centimeter. Still, density can be expressed in other units among them kilograms per cubic meter as for the example of air whose density is 1.2 kilograms per cubic meter (Trigg 175). Through the calculations involving density, it is possible and convenient to determine masses of substances and objects from their volumes as well as the volumes of such objects from their masses as long as the any of the two variables is known in the equation. To determine the mass of a substance from given density and volume values, the equation mass=volume*density is applicable while volume is determined from the equation volume=mass/density.

Formula for Calculating Density

Density is a physical property that finds it use in day-to-day applications in chemistry and related fields. It is in most cases used in the classification of chemical substances that are in fluid states making it possible to conduct Quality Monitoring and Process Control. A solid object dropped in water may either sink or float on the water surface. A solid which sinks in the water means that it has a density higher than that of water while that, which floats on the water surface, translates to a lower density than the density of water. In the case of liquids, which do not mix, the least dense liquid rises to the top while the one with the highest density sinks to the bottom (Baue 158). The same case is applicable for gases even though this is a bit of a challenge to observe as most gases freely mix. For the case of objects with regular shapes, it is  not possible to determine the volumes using the most commonly applicable formulae hence uses other mechanisms among them the eureka can to establish the volume which is then calculated against the mass in order to determine their volumes.

Materials used

The experiment was divided into three parts, each part taking a specific aspect of density to be measured. Each of the three parts had its own materials. The materials included:

Experiment 1

• Graduated cylinder
• Water
• Balance that measure in grams and can measure beyond 100 g
• Density meter

Experiment 2

• Balance
• Ruler

Experiment 3

• Water
• Graduated cylinder, 100 ml
• Balance taking measurements and measure beyond 100g 

Experiment 1: Test for liquid density

1. Find the mass of an empty graduated cylinder and record the mass in grams (m1=mass of empty cylinder)
2. Pour 100mL of water into the graduated cylinder taking caution to be as accurate as possible by taking note that the meniscus is at the mL mark. Use a dropper to add or remove amount of water(Mireles 216)
3. Weigh the graduated cylinder with the water in it and record the mass in grams (m2=mass of water + cylinder)
4. Find the mass of only the water by subtracting the mass of the empty cylinder (mass of water=m2-m1)
5. Use the mass and volume of the water to find the density. Record the density in g/cm³in the table by dividing mass/volume
6. Pour off water until you have 50mL of water in the graduated cylinder. Add water until you can as close as you can to 50mL in case your pour out too much
7. Find the mas of 50mL of water. Record the mass in the activity sheet. Calculate and record the density
8. Pour off water until you have 25mL water left in the graduated cylinder.
9. Find the mass of 25mL of water and record it in the table. Calculate and record the density(Mireles 166).
10. Measure the density using the density meter and compare obtained results with the density of 100mL 

Experiment 2: Test procedure for regular solids

1. Obtain a set of objects (spheres, pyramids) made from the same material
2. Measure the mass of the samples using the provided balance and record it in the table
3. Calculate the volume based on the provided shape and its formula

Measure the mass using balance and record its results in the table

Standard equations and formulae are used in the determination of the volumes of regular shapes. The equations for the commonly used regular shapes are as shown below: 

Experiment 3: Test procedure for irregular objects

• Measure the mass of the irregular object using an analytical balance and record the mass in grams(Leavitt 219)
• Add 50mL of water in a measuring cylinder (volume=v1)
• Submerge the object in the measuring cylinder and measure its volume in mL (volume=v2)
• Find the difference in the two volumes (Volume of object=v2-v1)
• Record your data in the table and calculate the density of the irregular object by dividing its mass with the volume(Fukuyama 109)
• Repeat the procedure above for another sample of an irregular solid object. 

Results and Calculations

Experiment 1

1 mL of water=1cm³=1 cc

Using this expression the density of the water can be calculated as follows:

14.65/100=0.1465

19.9/50=0.398

24.7/25=0.988

Graph of mass against volume is as illustrated below 

From the graph, it can be observed that as the volume of water increases, the mass of water increases proportionately. A line of best fit is thus obtained when the mass of water is plotted against the volume (Lebedev 230). The equation of the line can be found using the formula y=mx+c where m is the gradient and c the co-efficient of the y-axis.

The gradient of the line is found by

Applications of Density in Day-to-day Life

From calculation bases on the graph, the equation y=mx+c has been determined to be y=0.06x + 0.001. This means the density of the liquid is 0.06,

where the theoretical value refers to the actual, known or true value 

Experiment 2

Experiment 3

Using another sample of an irregular object made from the same material, comparison can be made and thus a conclusion arrived at demonstrating whether the densities of the objects will be the same. Being that the objects are from the same material, is expected from the experimental results that the determined densities will be very close to each other (Kyrala 155). Due to the possible sources of error in the experiment that include errors in taking the various measurements of mass and volumes, it is not possible for the experimental results to be the same as the theoretical values. From the calculated density, it is assumed that calculations and experimental data using the same material would yield the same density since the mass and volume would be proportionate depending on the size of the irregular object.

Summary and Conclusion

This lab report purposed to determine the density a liquid, regular shape and an irregular shape. Density is a derivative of the quantity of matter present in a given unit of volume. Density is a physical and intensive property that does not dependent on the amount of material present in a substance (National Research Council 298). The formula for determination of density is given by density=mass/volume. In the lab experiments above, measurements of the mass were done in grams while volume was measured in cm³

The type of material whose density is to be determined determines the procedure to be used in determining its density and thus the procedure is a factor of the given material. Geometrical formula and equation are used in the determination of the density of regular shaped objects. Each solid object of a regular shape has a corresponding geometric formula and equation that is deployed in the determination of its density and the formula does not change with changes in the dimensions of the shape. In this lab experiment, the regular shaped objects that were used were a sphere and a prism (Slowinski 168). The geometric formulae that were thus used in the calculation of the density was , for the case of the spherical shape and 

The density of a liquid is determined through direct measurement. Through the use of direct measurement, the experimental density of water as the liquid used in this experiment was found to be 0.06 g/cm³ and a percentage error of 94% found in the final results. The high percentage error illustrates the level of mistakes and errors that were performed in taking the direct measurements.

Experiment 1: Test for Liquid Density

Displacement of volume is used in the estimation of the volume of irregular shaped objects. The various measurements involving the irregular shaped object in this experiment were taken and the measurements used in the formulation of the final density of the object as per the experiment (Cook 215). The irregular shaped object only identified as sample was found to have a density of 1 g/cm³. Calculations and considerations were not made as far as the percentage error in the determination of the theoretical density of the sample was concerned. This could be attributed to the fact that the theoretical density of the sample was not included as part of the information about the experiment (Slowinski 188). The size of the sample considered was significant and this ensured more meaningful results were obtained from the experiment. The use of a very small sized sample would lead not to significant data collected thereby making the experiment fail to achieve its objectives. The measuring cylinder used was to one decimal place. Such marking of units do not provide a high level of precision of the results when it comes to recording the difference in the levels of water. Still, chances are that the graduated cylinder may fill beyond the measured are and this would lead to variations in the results of the density of the sample.

The objective of this density laboratory that aimed at calculating the density of water, irregular shapes and regular shapes has been met. It was also possible to determine the percentage error in the estimation of the density of water, which was done upon collection of data. Balances were used in the determination of the masses of each of the substances that was to be used in the experiment (Lebedev 278). The volume of the graduated cylinders had as well to be measured including the mass when both empty and containing substances. The volume of water in the graduated cylinder was measured, an irregular shaped object dropped inside the cylinder and the measurement of the new volume taken. The variation between the two volumes became the volume of the irregular shaped object.

The theoretical density of water from the density lab was found to be 0.06 g/cm³ while the densities of the regular objects were 0.0906 g/cm³, 0.987 g/cm³ and 0.335 g/cm³ for the shapes 1, 2 and 3 respectively (Holzbecher 177). The objectives of the lab were met in the determination of the density of the substances in the experiment. The density of the each of the substances was determined by dividing the mass by the volume of each of the substances. An error of 94% was established in the calculation of the density of water using the experimental values found.

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