Density lab

2

Density

Mass – Length – Volume – Density

Learning Outcomes

1. Calculate volume from length, width and height and convert to different units.

2. Understand the concept of density and calculate the density of objects.

3. Practice using correct significant figures in calculations.

Introduction

This lab is designed to introduce the student to the laboratory setting and begin the process of observation, instrument usage and data recording. In the laboratory environment, one will come across several different types of instruments. A balance will be used to measure the mass of an object (weight is the effect of gravity on mass). A metric ruler or meter-stick will be used to measure distance that may be length, width, or height. A graduated cylinder will be used to measure volume.

First let us examine the International System of Units, known as the SI system (Table 1). This system is used in the scientific community and is accepted worldwide, which prevents having to convert from one system to another. Think of how time consuming it would be every time a breakfast cereal was examined, if a conversion of grains to grams to ounces had to be made, (1 ounce = 28.34952 grams and 1 gram = 15.43236 grain). The following are the accepted SI base units.

In the laboratory a measurement can be made of a very small or a very large amount, as in very much less than a gram or very much more than a gram. To simplify notation there are certain prefixes that are used to increase or decrease each of the base units. In Table 2 are some of the more common prefixes, the decimal equivalents, the fractional equivalents, and the orders of magnitude expressed as the power of 10. A megagram would be one million times the size of a gram while a milligram is one thousandth the size of a gram. It is sometimes easier to discuss 2.57 milligrams than 0.00257 gram or 2.57 x 10-3 gram.

Using a Calibrated Instrument

A calibrated instrument often has calibration marks or lines on the device. Each line or division is a unit of measure and these divisions may have subdivisions, to determine the measured value more precisely and accurately. The finer the subdivisions the more precise and typically the more expensive is the instrument. When taking a reading of a graduated instrument, the user should be able to estimate one decimal place past the smallest calibration.

Refer to Figure 1 below. Using the first meter stick calibrated from 0 to 1 meter and measuring the box above the line, it can be seen that the box certainly is not ZERO nor is it ONE meter in length. An estimated measurement of 0.2 or 0.3 m might be made, where the uncertainty is ±0.1 in the last digit recorded. The next meter-stick is calibrated to the nearest 1/10th of a meter, or 0.1 m. The box may now be estimated to the nearest hundredth of a meter as 0.25 m or 0.26 m, again with uncertainty in the last digit, this time ±0.01. And finally using the last meter-stick calibrated to the nearest hundredth of a meter the box may be estimated to the nearest 1/1000th of a meter, also called a millimeter. An estimate of the length of the box would likely be 0.270 m or 0.275 m, with uncertainty of ± 0.005 in the last digit. Note that because of the resolution of the naked eye, the last calibration can be estimated only in halves or a whole, i.e. 0.000 or 0.005 m.

Percent error:

Percent error tell you how big our errors are when we measure something. Small percent errors mean that you are close to the accepted (or true value). Large percent errors mean that you are far from the accepted value. Errors in measurement are unavoidable. The materials may not be precise, our instruments may have a limited capacity to estimate exactly, and there human factors as well, poor lab technique, incorrect reading of instrument, shaking hands, etc.

Percent error is the difference between a measured value and an accepted value. It can be calculated as follows:

· Never a negative value

Procedure

(this procedure was followed for you and the data is presented below).

Cylinder #1 was acrylic.

Cylinder #2 was polyethylene.

Cylinder #3 was aluminum.

Part One: Density by Measurement

1. Record the mass of cylinder #1 on the balance.

2. Using a ruler, measure the diameter and height of your cylinder (record to the correct number of sig figs).

3. Calculate the radius of the cylinder (Diameter divided by 2). Record on data sheet.

4. Calculate the volume (volume = r2h). Approximate value of Record on data sheet.

5. Calculate the density of the cylinder. (Density = mass/volume).

6. Repeat steps 1-4 for the other two cylinders.

Part Two: Density by Displacement

1. Put enough water to cover the cylinder into a large, graduated cylinder and record the volume. (Record volume to the correct sig figs.)

2. Carefully slide the cylinder down the side of the graduated cylinder into the water. Tossing it in can break the bottom of the graduated cylinder.

3. With the cylinder completely submerged, record the new volume reading.

4. Determine the volume of the cylinder.

5. Determine the density of the cylinder.

6. Repeat steps 1-5 for the other two cylinders.

Data

Use these pictures as your data for the lab.

Fill in the lab report (pages 9-12) and turn in by 11:59 PM on 6/15.

Masses (in grams):

Cylinder #1 Cylinder #2 Cylinder #3

Cylinder #1

Measurements (in cm):

Diameter: Height:

Volume (in mL):

Initial Volume: Final Volume:

Cylinder #2

Measurements (in cm):

Diameter: Height:

Volume (in mL):

Initial Volume: Final Volume

Cylinder #3

Measurements (in cm):

Diameter: Height:

Volume (in mL):

Initial Volume: Final Volume

Density

Name _______________________ Date __________

Part One: Density by Measurement (24 points):

(one point per blank, calculations are 2 points each)

Cylinder #1

Mass: _________________

Diameter: _________________

Radius (diameter/2): _________________

Height: _________________

Calculated volume of cylinder (show your work)

Calculated density of cylinder (show your work):

Cylinder #2 _________________

Mass: _________________

Diameter: _________________

Radius (diameter/2): _________________

Height: _________________

Calculated volume of cylinder (show your work):

Calculated density of cylinder (show your work):

Cylinder #3

Mass: _________________

Diameter: _________________

Radius (diameter/2): _________________

Height: _________________

Calculated volume of cylinder (show your work):

Calculated density of cylinder (show your work):

Part Two: Density By Displacement (24 points):

(one point per blank, calculations are 2 points each)

Cylinder #1

Mass from part one: ________

Initial volume: _________________

Final volume (with cylinder in graduated cylinder): _________________

Volume displaced by cylinder: _________________ (show work below)

Calculate the density of the cylinder by displacement. (show your work):

Cylinder #2

Mass from part one: ________

Initial volume: _________________

Final volume (with cylinder in graduated cylinder): _________________

Volume displaced by cylinder: _________________ (show work below)

Calculate the density of the cylinder by displacement. (show your work):

Cylinder #3

Mass from part one: ________

Initial volume: _________________

Final volume (with cylinder in graduated cylinder): _________________

Volume displaced by cylinder: _________________ (show work below)

Calculate the density of the cylinder by displacement. (show your work):

Calculate the percent error for all three cylinders (5 points).

Use your calculated density by displacement as the experimental value. Use the density given in the chart below as the accepted value. Show your work. Percent error formula was given above.

Substance	Density (g/cm3)
Aluminum	2.7
Acrylic	1.2
Polyethylene	0.9

What sources of error could cause the differences (2 points)?