Experiment #: Measurements, Metric System & Density of Irregular Object

Objective
The purpose of this experiment is to become familiar with the metric system by taking measurements with metric units. A second purpose of this experiment is learn how to handle data collection and then and the proper use of significant figures, proper unit usage and the application of dimensional analysis.

Equipment and Materials (Total Time 90 - 120 min.)
 Your Kit Contains: Alcohol Thermometer 100 mL beaker 250 mL beaker 10 mL grad cylinder 25 mL grad cylinder 100 ml grad cylinder metric ruler Lab Supplies: marble You supply: rand new #2 pencil string pennies course textbook empty 2-L bottle w/ cap

Discussion
Observations are very important in chemistry experiments. Two types of observations are qualitative and quantitative. Qualitative observations are description of an observable property such as the color, odor, or texture. Quantitative observations are numerical measurements and require a number and a unit in order to be complete. For example, if your height is six feet, then the number is "six", and the unit is "feet". In scientific work, quantitative measurements are almost always recorded in the units of the metric system.

In laboratory work, the basic metric units of mass, length, and volume used are the gram (g), the meter (m), and the liter (L), respectively.  Also commonly used in the laboratory, is the degree Celsius (°C), which is the metric unit of temperature measurement.

For convenience and consistency, metric units are subdivided by either multiplication or division by some power of ten.  The prefixes deci-, centi-, and milli-, mean 1/10, 1/100, and 1/1000 of the original unit, respectively.  The prefix kilo- and mega-, means 1000 and 1,000,000 times the original unit. Refer to some tables (textbook, website …) containing the commonly used units and their conversions.)

It is very important to realize that whenever any measurement is made, some part of the measurement is an estimation.  Therefore, any measurement always has some degree of uncertainty.  For example, in measuring the outside diameter of a test tube, as shown in Figure 1, you would record the diameter as 1.52 cm.  The first two digits, one and five, would be the same regardless of who made the measurement; that is, they are certain.  The third digit, two, however, was determined by a visual estimate.  This digit would depend on who made the measurement; that is, it is uncertain.  Each number which is recorded, including all the certain numbers, and the first uncertain number, are called significant figures.  The number of significant figures obtained in a measurement will always be determined by the scale of the measuring device used.

Figure 1
Suppose that you are measuring the outside diameter of a coin shown under the centimeter scale.  The diameter is recorded as 1.52 cm, the first two digits, 1.5, being read with certainty, and the third digit, 2, being doubtful or estimated with an uncertainty of perhaps 1 in that digit or + 0.01 cm overall.  Only three digits are recorded because any more digits to the right would not be valid significant figures.

 Dimensional analysis is a technique used when converting measurements from one unit to another.  For example, one might wish to convert a measurement from units of centimeters to meters, or liters to milliliters.  This is accomplished by using a conversion factor.  A conversion factor is a ratio that relates the two units.  A conversion factor is given by an equivalence statement, which defines the relationship between the unit from which you are converting and the unit to which you are converting. In the example above the conversion factor relates inches and centimeters. What is the diameter of the above test tube in inches?  This problem may be expressed as: 1.52 cm = ? in. The question mark stands for the number we would like to find.  The relationship between centimeters and inches is set up using the equivalence statement: 2.54 cm = 1 in. This equivalence statement can lead to two possible conversion factors:  2.54 cm     or             1 in      1 in                       2.54 cm We choose the conversion factor that upon multiplication with the given measurement, will cancel the unit we want to convert from (cm), and leave behind the unit we want to convert to (inches).  1.52 cm     •      1 in      =   0.598          2.54 cm Two important facts about this conversion are: 1. When the units changed from centimeters to inches, notice that the numerical value also changed (from 1.52 to 0.598)  That is, 1.52 cm is exactly the same value (i.e. same length) as 0.598 in. 2. Notice that although your calculator will display more than three decimal places in the final answer, the final answer is reported to three significant figures.  All answers should be rounded to the correct number of significant figures using the rules for rounding and significant figures.  Sometimes, measurements may be combined to express a relationship between them (e.g. miles/gallon).  One important property of a substance, density, is defined as the relationship of mass (g) and volume (ml): Density  =    mass  (g)               volume (ml) The density of a substance is a characteristic property of that substance and can help identify the material.   There are two ways to determine the volume of a regularly shaped object when calculating its density.  One is direct measurement, the other is volume by displacement.  In the direct measurement method, the appropriate dimensions of the object  are measured using either a metric ruler or a meter stick and then the dimensions are placed in the formula for the proper geometrical shape to calculate the volume.  In the volume by displacement method, the object is submerged in water contained in a graduated cylinder.  Submerging of this object under water will cause the water level to rise.  The difference in the water level before and after the object is submerged is due to the volume of the object.  (See Figures  .3 & .4.)

Procedure

1.  Measuring Temperature

Fill a 250ml beaker 3/4 full with tap water and allow it to come to room temperature (about 30 minutes).  You may proceed with steps 2 - 4 while you wait.  After 30 minutes, using an alcohol thermometer, measure the temperature of the water to the correct number of significant figures as determined by your thermometer and record it in your worksheet, see Fig 2.
 Figure 2 Note that the thermometer is calibrated to the nearest 0.5°C and that the end of the alcohol column lies between 21.0°C and 21.5°C.  Thus, there is no doubt about the first two digits, 21.  Our only remaining task is to estimate the distance between 21.0 and 21.5 and to record one doubtful or estimated digit.  The estimated digit is probably 4, and the temperature is recorded as 21.4°C.  This conveys to a reader that the uncertainty in the temperature is at least + 0.1°C.  Obviously, it would be foolish to record the temperature to the hundredth place i.e., 21.45°C, because this digit, in this case the digit 5, has no significance.
2. Measuring Mass
Measure the mass of the following solid objects using the laboratory balance and record your data in your data sheet with the correct number of significant figures and units.  Note that all the numbers in the digital reading are significant.
a.   brand new #2 pencil

b.   coffee mug or 100 ml beaker

c.  2-L soda bottle empty with cap.

d.   Now estimate the mass of your textbook and record the estimate in your notebook.  DO NOT WEIGH THE OBJECT on the scale !!

3. Measuring Length

Measure the following lengths (in centimeters), using a meter stick, and record the data in your notebook with the correct number of significant figures and units.  Record the measurement as precise as the instrument allows.

c. circumference of the 2-L soda bottle.

d. Now estimate the length (in centimeters) of this lab book and record this estimate in your data sheet. DO NOT MEASURE THE LENGTH !

4. Measuring Volume

Fill a 100 mL, 25 mL and 10 mL graduated cylinder half-way up with water. Read the volume (in milliliters) of each of the three graduated cylinders at your laboratory table and record the data in your notebook.  (See Figure 3 for instructions in reading the volume of a fluid in a graduated cylinder.)

 Figure 3 When reading a graduated cylinder, read the bottom of the meniscus while holding the meniscus at eye level.  The volume reads 54.0 ml.

d. Now click on the link and estimate the volume (in milliliters) of the liquid in the test tube provided by your instructor and  record  the estimate in your data sheet and lab notebook. Link to volume estimation

5. Determination of Density

a.  Take the glass marble that was issued to you.  Determine the density using the method of direct measurement (geometry) and by volume displacement.  In the direct method, measure the mass using the digital pocket scale and the volume by using the dimensions of the sphere (volume = 4/3 x p x r3), where p is 3.14 and r is radius of the sphere or the diameter ÷ 2.  For example if a sphere has a diameter of 2.6 cm, then the volume is calculated to be 4/3 x 3.14 x (1.3)3 = 9.20 cm3.  Record your work and data in your data sheet.

b. Using the same solid, determine the volume by water displacement (see Figure 3). Using the mass from part 5a, calculate the density. Record your work and data in your data sheet. (density by displacement)

c. How do the two values for density compare?  Explain why they might differ.

 Figure 4 The density of a solid with a irregular shaped can be found by first determining the mass of a sample and then placing the sample in a graduated cylinder partly filled with water (or some liquid in which the solid does not float). The solid will displace a volume of liquid equal to its value.  Thus, by noting the position of the meniscus before and after the addition of the solid, the volume of the solid can be determine.
Write the conversion factor on the heading of each table for this section.
6. Mass Conversions
Convert the masses recorded in Step 2 (a-c) from grams to milligrams, kilograms and pounds.  Record your work and data in your notebook.

7. Length Conversions

Convert the lengths recorded in Step 3 (a-c) from centimeters to millimeters, meters and inches.  Record your work and data in your notebook.

8. Volume Conversions

Convert the volumes recorded in Step 4 (a-c) from milliliters to liters and gallons.  Record your work and data in your notebook.

 Experiment # Measurements and the Metric System Name ______________________________________ Partner _____________________________________ Lab Section: Day _________  Time _______

1. Measuring Temperature of water in 250 ml beaker (use correct number of significant figures and correct units).

Temperature of water   _________________

2. Measuring Mass (use correct number of significant figures and correct units).

a. Brand new #2 pencil    __________________

b. coffee mug or 100 ml beaker  __________________

c. 2-L soda bottle empty with cap __________________

d. textbook (estimate) _______________
(to be filled by instructor)

3. Measuring Length (use correct number of significant figures and correct units).

c. circumference of 2-L bottle  __________________

d. length of course textbook (estimate) _______________
(to be filled by instructor)

4. Measuring Volume (use correct number of significant figures and correct units).

a. 100 ml graduated cylinder  __________________

b. 25 ml graduated cylinder  __________________

c. 10 ml graduated cylinder  __________________

d. test tube (estimate) _______________ actual ______________
(to be filled by instructor)

5. Determination of  Density

a. Density by geometry:

 mass ______________________   dimension: length  _____________ width  _____________________ height  _____________________   volume of marble  ______________   density _____________________ Show your work for part  5a.

b. Density by displacement

 mass ____________________     volume initial _________ volume final  ______________   Volume solid ______________ density __________________ Show your work for part  5b.

c.  Explain why the two values above may be different

6. Mass Conversions
Using your data from procedure 2 above, show a sample calculation for one of each type of conversion. (Be sure to write the conversion factor you will use above each column.)
 Conversion factor: ____ mg  =   ____g Conversion factor: _____g  =   _____ kg Conversion factor: _____ lb  =   _____g measurement from 2 milligrams kilograms pounds a _________ a a a b _________ b b b c _________ c c c

7. Length Conversions:

 Conversion factor: ____ mm =   ____cm Conversion factor: _____m  =   ____cm Conversion factor: ____ in  =   ____ cm measurement from 3 millimeters meters inches a _________ a a a b _________ b b b c _________ c c c