Density and Measurements

 

Goals

Measure and record length, volume and mass accurately.

Write the measurement to the correct number of significant figures.

Use significant figures correctly in calculations.

 

Making Measurements

Scientists and medical professionals carry out experiments and laboratory procedures regularly.  They need to make measurements and be able to report results accurately and precisely.  Correct measurement and reporting is critical to achieving successful experiments. You need to learn how to measure accurately and how to report your result with the correct precision (significant figures).

 

Metric Units of Length

We will be using a ruler to measure length.  The standard unit of length in the metric system is the meter (m). A meter is divided into 100 centimeters (cm).  Each centimeter is divided into 10 millimeters (mm).

 

Metric Units of Volume

We will be using a ruler and graduated cylinders to measure volume.  Volume is a measure of the space a substance occupies.  A cube that measures 1 meter in length, height and width has a volume of (1m)3 = 1m3.  Volume is a derived unit based on length.  The unit of volume most commonly used in the lab is the liter (L).  1 liter is equal to 1 cubic decimeter (dm)3.  1 liter = (1dm)3.  There are 10 decimeters in 1 meter.

            1 liter = (1dm)3 = (10 cm)3 = 1000 cm3

So 1 liter contains 1000 cubic centimeters (cm3 or cc) or 1000 milliliters.

 

Metric Units of Mass

We will use a balance to measure mass.  Mass is the measure of the amount of material or matter.  This is different than weight, which is the measure of the pull of gravity on a specific mass.  Mass remains constant for a particular amount of matter while the weight can change if you change gravity.   For example, you have the same amount of mass on the moon as on the earth but on the moon you weigh less because the moon has less gravity than the earth.  The metric unit for mass is the gram (g).

 

Significant Figures in Measurements

When using any measuring device, the measurement should be reported as precisely as possible.  The number of significant figures in the number reported will depend on the measuring device used.  For example, when you use a 50mL graduated cylinder, the smallest lines marked on the cylinder represent 1mL.  The last digit of the number is estimated.  If a liquid has a volume halfway between 35 and 36mL, its volume would be reported as 35.5mL. If the volume lies exactly on the 35mL line then the volume would be reported as 35.0mL.  The number of digits in the reported result tells us how well we know the volume.  35.0 or 35.5 has three significant figures.  Only three significant figures can be obtained using a 50mL graduated cylinder.  Make sure that you keep all of the significant figures that you obtain in a measurement.  Never round off any number obtained from a measurement. 

 

Materials Needed

1 metal block

 

Ruler

 

Graduated cylinders

 

Top loading balances

 

Deionized water (in larger white containers on the lab benches)

Laboratory Activities

A.  Measuring mass

 1.  Find a metal block, record its number or letter and measure its mass by using a top-loading balance.  Report the mass using all of the possible significant figures and remember to use the correct units.  Example:  25.0789 g.  You will notice the last digit displayed on the electronic balances fluctuates.  Don’t wait for this value to stabilize, try to estimate an average value for this digit.

 

B.  Measuring Length.

1.     Obtain a ruler and measure the length (l), width (w) and height (h) of your metal block in cm.  Calculate the volume (cm3) of the metal block.  Make sure to determine the correct significant figures for your calculated value based on the significant figures of your measurement.

V = l• wh.

 

C.   Measuring Volume.

1.     Pour at least 8 mL of deionized water in a 10mL graduated cylinder and record the volume to the correct number of significant figures.

2.     Pour the water from the 10 mL graduated cylinder into a 50 mL cylinder.  Record the Volume to the correct number of significant figures.

3.     Pour the water from the 50 mL graduated cylinder into a 250 mL cylinder.  Record the Volume to the correct number of significant figures.

4.     What trend do you see as the relative fullness in the cylinders goes down?

 

D.   Density                          

1.  Using the mass and volume of the metal block in parts A and B, calculate the

     density of the block to the correct number of significant figures.

2.  Obtain a relatively dry 10 or 25 mL graduated cylinder.  Weigh the cylinder  

      and record the mass to the correct number of sig figs.  Fill the cylinder about 

      75% full with deionized water, record the volume and reweigh.  Use this

      information to calculate the density of water to the correct number of sig figs.

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