Lab Topic 1

The Metric System

Measurements and Laboratory Equipment

Introduction

One requirement of the scientific method is that results be repeatable. As numerical results are more precise than purely written descriptions, scientific observations are usually made as measurements. Of course, sometimes a written description without numbers is the most appropriate way to describe a result.

 

The Metric System

Logically, units in the ideal system of measurement should be easy to convert from one to another (for example, inches to feet or centimeters to meters) and from one related measurement to another (length to area, and area to volume). The metric system meets these requirements and is used by the majority of citizens and countries in the world. Universally, science educators and researchers prefer it. In most non-metric countries, governments have launched programs to hasten the conversion to metrics. In fact, the U.S. Department of Defense adopted the metric system in 1957, and all cars made in the United States have metric components. As expected there has been some reluctance on the part of many Americans to change over – some reasons are economic (having to retool factories and households); normal resistance to change and probably some feeling that the metric system is foreign in more ways than one.

It is interesting to take some historical notice of how the metric system came into existence. Prior to the French revolution there was little international agreement on standard weights and measures. Each country had its own standards based on some transient things like the length of the king’s foot or middle knuckle. Just before the French revolution the French Academy of Sciences decided to work on a system of measures based on universal, scientific principles. They decided that the system should be based on a unit of length that was one ten millionth of the distance from the North Pole to the equator. That unit was called the meter. The revolutionists, when they came into power, agreed with the change because it represented a further repudiation of the old ways and another step towards “reason”. Napoleon gave several awards to the scientists and mathematicians who helped devise the new system (including one to Joseph Lagrange who was lucky not to be beheaded in the revolution due to his association with the monarchy). The advantage of metric measurements was quickly appreciated by scientists and others (including merchants, mechanics etc.) from other countries and it spread from France and was eventually adopted almost everywhere. In 1819 an English physicist and chemist, William Wollaston, argued against Britain’s adopting the system and as a result Britain and the commonwealth countries declined to convert to its use. Unfortunately, the United States followed Britain’s lead and also declined – we have been saddled with the irrational English system of weights and measures ever since (ironically the British and the other commonwealth countries have since converted but, alas, we are taking an inordinate amount of time to do so).

The metric reference units are the meter for length, the liter for volume, the gram for mass, and the degree Celsius for temperature. Regardless of the type of measurement, the same prefixes are used to designate the relationship of a unit to the reference unit. Table 1.1 lists the prefixes we will use in this and subsequent exercises. The metric system is a decimal system of measurement (based on ten (deci)). Metric units are 10, 100, 1000, and sometimes 1,000,000 or more times larger or smaller than the reference unit. Thus, it's relatively easy to convert from one measurement to another either by multiplying or dividing by 10 or a multiple of 10.

 

 

TABLE 1.1 Prefixes for Metric System Units     

 

Prefix of Unit (Symbol)	Part of Reference Unit
nano (n)	1/1,000,000,000 = 0.000000001 = 10-9
micro (?)	1/1,000,000 = 0.000001 = 10-6
milli (m)	1/1000 = 0.001 = 10-3
centi (c)	1/100   = 0.01 = 10-2
kilo (k)	1000 = 103

 

There are additional prefixes, but these will suffice for now for our work in Biology. A prefix in front of a unit tells you how many of that unit you have. For example:

1. cm                   =          centimeters     (hundredths of a meter)
2. kg                    =          kilograms        (thousands of grams)
3. ml                    =          milliliters        (thousandths of a liter)

 

In this set of exercises, we examine the metric system and compare it to the American Standard system of measurement (feet, quarts, pounds, and so on).

 

MATERIALS

Per lab room:
? source of distilled water (dH20)	?	hot plate
? metric bathroom scale	?	boiling chips
? ice	?	thermometer on holder

Per student group of two-four.

 

? 30-cm ruler with metric and American              (English) Standard units on opposite edges	1-pound brick of coffee  ceramic coffee mug
? 250-ml beaker made of heat-proof glass	? 1-gallon milk or water bottle
? 250-ml Erlenmeyer flask	? metric tape measure
? 3 graduated cylinders:10-ml, 25-ml, 100-ml	? 1-l measuring cup
? l-quart jar or bottle marked with a fill line	? non-mercury thermometer(s) with
? one-piece plastic dropping pipette (not       graduated) or Pasteur pipette and bulb	Celsius (oC) and Fahrenheit (oF)       scales  (about 220-110 oC)
? graduated pipette and safety bulb or filling	? a triple beam balance

device 

 

PROCEDURES

A. Length ( 15 min.)

Length is the measurement of a real or imaginary line extending from one point to another. The standard unit is the meter, and the most commonly used related units of length are

 

1000 millimeters (mm) = 1 meter (m)

100 centimeters (cm) = 1 m

1 kilometer (km) = 1000 m

 

For orientation purposes, the yolk of a chicken egg is about 3 cm in diameter. Since the difference between metric units is based on multiples of 10, it's fairly easy to convert a measurement in one unit to another.  Before we do that, let’s review a few simple rule from mathematics:  (note: “N” means any number).

 

Rule 1:	Any number multiplied by one equals the original number and doesn’t change its  value.  That is:    N x 1 = N
	For example:  6 x 1 = 6
	153 x 1 = 153
	½ x 1 = ½
Rule 2:	Any number divided by itself equals one, or      N/N = 1
	For example:  7/7 =1
	½ / ½ = 1
	x/x =1
Rule 3:	When multiplying units expressed as fractions, units cancel like numbers.
	For example:  kg        x          cg        x          mg
	1                     kg                    cg
	Here, the kg and cg cancel and we are left with mg, as follows:                         kg        x          cg        x          mg       =          mg
	1                     kg                    cg                      l

 

Now we are ready to perform metric conversions.  We will do this by multiplying the given value by one or more conversion factors to get the value in the desired units.  Doing an example best shows this:

 

1a. Convert 8 km into m:

We know that 1 km = 1000 m.  By dividing this equation by 1000 m, we get:        

 

	1 km	=          1000 m
	1000 m	1000 m
	or,
	1 km	=          1
	1000 m
	This can also be written:	1000 m            =	1

                                                             1 km

 

Recall, multiplying by “1” does not change the value of the original number.  Therefore, we can write:

 

            8 km x             1000 m            =          8 km   x           1000  m =          8000 m             

                                      1 km                                                     1 km

 

(Why did we use 1000m/1 km and not 1 km/1000m for our conversion factor?)

 

1b. Convert 6 cm into m:

            We know that 1 m = 100 cm.  By using the form of one, 100 cm / 1 m, we can multiply as follows:

6 cm      x        1  m               =               6  m                                                100 cm                 100   Try the following:	=          0.06 m
a)  5 mm = ______m              b)  5.5 m = ______ µm	c)  9 km = _______nm

 

(Hint: the last example requires two conversion factors.)

 

 

2. Measure the length of this page in centimeters to the nearest tenth of a centimeter with the metric  edge of a ruler. Note that nine lines divide the space between each centimeter into 10 millimeters. 

The page is _______________ cm long. 

Calculate the length of this page in millimeters, meters   and kilometers.

 

       ________________mm            ______________m    _____________ km

       Now repeat the above measurement using the English side of the ruler. Measure the         length of this page in inches. 

 

        ______________in.    Convert your answer to feet and then yards. 

 

       _________________ ft           _____________ yds

 

Explain why it is much easier to convert units of length in the metric system than in the English

System   _____________________________________________________________________

____________________________________________________________________________________

____________________________________________________________________________________

____________________________________________________________________________________

B. Volume (20 min.)

Volume is a measure of the space an object occupies. The metric standard unit of volume is the liter (l), and the most commonly used subunit, the milliliter (ml).  There are 1000 ml in 1 liter. A chicken egg has a volume of about 60 ml.

            The volume of a box is the length (l)  x  the width (w)  x  the height (h) (Figure A – 1). 

The amount of water contained in a cube with sides 1 cm each in length is 1 cubic centimeter (cc) 

Figure A

-

2

Relationship between the units of length,

volume, and mass in the metric system.

(1

cm x 1 cm x 1 cm) which for all practical

purposes equals 1 ml (Fig A

-

2

).

1.

How many milliliters are there in 1.7 l?

___________________ml

How many liters are there in 1.7 ml?

____________________l

V = l  x  w  x  h

F

igure A

-

1

Determining the volume

of  a box

.

 

 

2. Use Figure A - 3 to recognize graduated cylinders, beakers, Erlenmeyer flasks, and the different types of pipettes. Some of these objects are made of glass; some plastic. Some will be calibrated in milliliters and liters; others will not. (“Graduated” means the container is marked with volume increments.)

 

 

   Figure A - 3 Apparati commonly used    to measure volume: (a) pipette filling    device, (b) pipette safety bulb,

1. 1. 3. Pasteur pipette and bulb,
      4. Erlenmeyer flask,
      5. glass graduated cylinder,
      6. plastic graduated cylinder,   
      7. plastic dropping pipette,   
      8. beaker, (i-k) graduated pipettes. 

  (Photo by D. Morton and J. W. Perry.)

 

 

Figure A - 4. Draw a meniscus in this plain cylinder.

3. Pour some water into a 100-ml graduated cylinder and observe the boundary between fluid and air, the meniscus. Surface tension makes the meniscus curved, not flat. The high surface tension of water is due to its cohesive and adhesive or "sticky" properties.  Draw the meniscus in the plain cylinder outlined in Figure A-4.  The correct reading of the volume is at the lowest point of the meniscus.  

 

           

 

 

 

4. Using the 100-ml graduated cylinder, pour water into a 1-quart jar or bottle.  About how many milliliters of water are needed to fill the vessel up to the line?  __________________ml.

 

 

5. Pipettes are used to transfer small volumes from one vessel to another. Some pipettes are not graduated (for example, Pasteur pipettes and most one-piece plastic dropping pipettes); others are graduated.
   1. Fill a 250-ml Erlenmeyer flask with distilled water.
   2. Use a plastic dropping pipette or Pasteur pipette with a bulb to withdraw some water.
   3. Count the number of drops needed to fill a 10-ml graduated cylinder to the 1-ml mark. Record this number in Table A-2.
   4. Repeat steps b and c two more times and calculate the average for your results in Table A-2. (remember, to find an average, add all the results together, and divide by the number of results).
   5. Explain why the average of three trials is more accurate than if you only do the procedure once.

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

 

TABLE A-2           Estimate of the Number of  Drops in 1 ml                  

Trial		Drops/ml
1
2
3
	Total
	Average

 

C. Mass (25 min.)

Mass is the quantity of matter in a given object. The standard unit of mass is the kilogram (kg), and other commonly used units are the milligram (mg) and gram (g). There are 1,000,000 mg in 1 kg and 1000 g in 1 kg. A chicken egg has a mass of about 60 g. Note that the following discussion avoids the term weight. Mass is a constant (scalem). Your mass on the Earth is the same as your mass on the Moon. However, since gravity on the Moon is 1/6 of that on Earth, your weight on the Moon would be less. For example, a 60 lb. person on earth would weight 10 lbs. on the Moon, but that person would have the same mass. However for our purposes, we will use mass and weight interchangeably.

1. How many milligrams are there in 1 g?

 

_______________________mg

Convert 1.7 g to milligrams and kilograms.

 

_______________________mg     _________________ kg

 

2. A 1-cc cube, if filled with 1 ml of water, has a mass of 1 g (Figure A-1). The mass of other materials depends on their density (water is defined as having a density of 1). The density of any substance is its mass divided by its volume.

Approximately how many liters are present in 1 cubic meter (m³) of water? Since each of the sides of a cubic meter ( m³) is 100 cm in length, it's easy to calculate the number of cubic centimeters (that is, 100 cm X 100 cm X 100 cm = 1,000,000 cc). Now just change cubic centimeters to milliliters and convert 1,000,000 ml to liters.

                                      1,000,000 ml   =  _________ l 

 

What is its mass in kilograms?______________________ kg.

 

 

3. Determine the mass of an unknown volume of water (1).   Mass may be measured with a triple beam balance, which gets its name from its three beams (Figure A-5). In this device a movable mass hangs from each beam.

1. Figure A

   -

   5

   Triple Beam Balance

   movable masses

   10

   -

   g graduations

   on the three beams

   100

   -

   g graduations

   0

   . 1

   -

   g and 1

   -

   g

   pan                                                     graduations

   zero adjust knob

   balance  marks

   Slide all of the movable masses to the         left to zero. Note that the middle and back masses each click into the leftmost notch.
2. Clear the pan of all objects and make sure it is clean.
3. The balance marks should line up, indicating that the beam is level and that the pan is empty. If the balance marks don't line up, rotate the zero adjust knob until they do.
4. Place a 250-ml beaker on the pan. The right side of the beam should rise. Slide the mass on the middle beam until it clicks into the notch at the 100-g mark. If the right end of the beam tilts down below the stationary balance mark, you have added too much mass. Move the mass back a notch. If the right end remains tilted up, additional mass is needed. Add  increments until the beam tilts down; then move the mass back one notch.  Repeat this procedure on the back beam, adding 10 g at a time until the beam tilts down, and then backing up one notch. Next, slide the front movable mass until the balance marks line up.
5. The sum of the masses indicated on the three beams gives the mass of the beaker. Unnumbered lines divide the space between the numbered gram markings on the front beam into 10 sections, each representing 0.1 g.  Record the mass of the beaker to the nearest tenth of a gram in Table A-3.
6. Add an unknown amount of water and repeat the above procedure. Record the mass of the beaker and water in Table A-3.
7. Calculate the mass of the water alone by subtracting the mass of the beaker from that of the combined beaker and water. Record it in Table A-3.

 

TABLE A-3   Weighing an Unknown Quantity of Water with a          

                     Triple Beam Balance

Objects        Masses (g)

Beaker and water

Beaker

Water

 

8. Now measure the volume of the water in milliliters with a graduated cylinder.

 

What is the volume?__________________ ml

 

4.  Using the triple beam balance, determine the mass (that is, weight) of a brick of coffee in grams.

 

_______________________g

 

 (1) Modified from C M Wynn and G. A. Joppich, Laboratory Experiments for Chemistry, A Basic Introduction, 3^rd ed. Wadsworth, 1984.  

 

 

D. Estimating Length, Volume, and Mass (10 min.)

Now that you have experience using metric units, let's try estimating the measurements of some everyday items. 

 

1. Estimate the length of your index finger in centimeters. ___________ cm
2. Estimate your lab partner's height in meters.______________m
3. How many milliliters will it take to fill a ceramic coffee mug?______________ml 
4. How many liters will it take to fill a gallon plastic bottle?_______________l
5. Estimate the weight of some small personal item (for example, loose change) in grams.

____________g

6. Estimate your or your lab partner's weight in kilograms. ______________________kg
7. Record your estimates in Table A-4.
8. Now, check your results using either a ruler, metric tape measure, 100-ml, graduated cylinder, 1-l measuring cup, triple beam balance, or metric bathroom scale, recording your measurements in Table A-4. Complete Table A-4 by calculating the difference between each estimate and measurement.

 

TABLE A-4  Differences Between Estimates and Measurements  

 

Number                    Estimate           Measurement             Estimate - Measurement

1          cm        cm      cm

2          m          m        m

3          ml        ml        ml

4          l            l          l

5          g           g         g

6          kg        kg        kg

(How good are you at estimating?)

 

E. Temperature (About 20 min.)

The degree of hot or cold of an object is termed temperature. More specifically, it is the average kinetic energy of molecules. Heat always flows from high to low temperatures. This is why hot objects left at room temperature always cool to the surrounding or ambient temperature, while cold objects warm up. Consequently, to keep a heater hot and the inside of a refrigerator cold requires energy. Thermometers are instruments used to measure temperature. 

 

ENGLISH SYSTEM

 We in the United States are accustomed to the Fahrenheit scale to measure temperature.  When you realize that Fahrenheit, over 200 years ago, created the lowest temperature he could (by mixing equal parts snow and salt) and called that temperature zero, it is easy to see why this scale is so far out of date.  Water on Fahrenheit's scale freezes at 32? and boils at 212?-- advanced for his time, antiquated and almost silly for ours.  This discourse is not a “put down” of Fahrenheit; to the contrary he was a very bright man who pioneered the use of mercury in thermometers because of its constant rate of expansion over temperature ranges.  We are merely saying that our clinging to a cumbersome, irrational system based on 200 year old technology is unfortunate.

 

METRIC SYSTEM

Celsius took pure water at sea level and said it freezes at 0? and boils at 100? and he put 100 divisions between.

 The Fahrenheit scale has 180 divisions between the freezing and boiling points of water (212 – 32) whereas Celsius has 100. Therefore, the Celsius degrees are almost twice as big as those of Fahrenheit.   180F to 100C = 1.8 to 1 = 9 to 5.

1. Using a thermometer with both Celsius (^oC) and Fahrenheit (^oF) scales, measure room temperature and the temperature of cold and hot running tap water. Record these temperatures in Table A-5.
2. Fill a 250-ml, beaker with ice about three-fourths full and add cold tap water to just below the ice. Wait for 3 minutes, measure the temperature, and record it in Table A-5. Remove the thermometer and discard the ice water into the sink.
3. Observe as the instructor fills a beaker with warm tap water to about three-fourths full and adds three boiling chips. A thermometer holder will be used to clip a thermometer onto the rim of the beaker so that the bulb of the thermometer is halfway into the water. The instructor will boil the water in the beaker by placing it on a hot plate. After the water boils, record its temperature in Table A-5.

 

CAUTION:  Do not touch the hot beaker, the boiling water, or the edges of the hot plate.  

 

4. To convert Celsius degrees to Fahrenheit degrees, multiply by 9/5 and add 32.       Is 4^oC the temperature of a hot or cool day?

            What temperature is 4^oC in degrees Fahrenheit?  ________________^oF

 

5. To convert Fahrenheit degrees to Celsius degrees, subtract 32 and multiply by 5/9.

             

     What is body temperature, 98.6 ^oF, in degrees Celsius?  ___________________^oC

 

6. In summary, the formulas for these temperature conversions are:

 

^oF     =     9/5 (^oC) + 32                                                   ^oC     =    5/9 (^oF - 32)

 

            ^oF         ^oC         water freezes                             32                                                              0 refrigerator temperature            41                                                              5 room temperature                     68                                                             20 body temperature                     98.6                                                          37 water boils                             212                                                            100

 

 

Table A-5    Comparison of Celsius and Fahrenheit Temperatures

Location                                                                  oC                                                             o F

Room

Cold running tap water

Hot running tap water

Ice water

Boiling water