DETERMINATION OF DENSITY
Objectives:
1. Determine the density of a solid or liquid
2. Graph data
3. Use the factor-label method for density calculations.
Matter is defined as anything that has mass * and takes up space. Density is a number that relates th e mass of an object to the space it takes up. Some types of matter are more tightly packed than others, and therefore have higher densities. All forms of matter; solids, liquids and gases have densities. And density is a useful physical property for identifying and classifying materials.
mass .
Mathematically, density is defined as volume Density is the bridge or connecting link between mass and volume. Obviously, 1 mL of mercury would weigh much more than 1 mL of water, and density puts a num erical value on this concept. To calculate the density of an object, or a definite amount of liquid, you need only divide the mass by the volume, and round off the answer to the appropriate number of significant figures. For an example of a SOLID , a cube of wood 2.0 cm on a side and weighing 6.95g, would have a volume of 8.0 cm 3 and a density of 6.95g/8.0 cm 3 , 0.86875 g/cm 3 (round to 0.87 g/cm 3 ) . A LIQUID must be poured into a graduated cylinder to obtain its volume (and the mass of the liquid calcu lated from the mass of the cylinder with and without the liquid in it). You will learn about GAS densities later in the course.
A. Determination of Density of Water.
Weigh a dry, empty 10mL graduated cylinder. Remove the cylinder from the balance pan and add water to the 10mL mark (use eyedropper to adjust). Weigh and record. Calculate the density of water.
Calculations:
Wt. of cylinder + 10.0 mL of water ________g
Wt. of empty cylinder ________g
Wt. of water ________g
Density of water ________g/mL
Mass is the amount of matter in an object. One of its properties is inertia, the resistance to being put in motion and the tendency to remain in motion once it is set in motion.
Isaac Newton's Second Law of Motion tells us that the acceleration of an object is proportional to the force exerted on it divided by the mass. This is how force is normally defined, by the formula usually stated as F = k·m·a. (The units can be chosen so that k = 1 and the formula then becomes F = m·a in that system of units.)
How we experience these things
I'm going to develop some kind of discussion or tables listing some examples where the differences in these concepts show up. Perhaps something showing how gravitational force (one kind of weight) is what makes it difficult to lift objects up, and mass is what makes it difficult to move objects sideways (complicated by friction). Also how buoyancy in air or liquids affects our ideas of both mass and gravitational force. It might also include other forces besides gravitational force, such as the thrust of a rocket or the force necessary to draw a bow in archery (another force commonly called weight).
Common Fallacies
MYTH: The metric system measures mass; the English system measures weight (meaning force)
This is a fairly common misconception, epitomized by World Book Encyclopedia, 1995 ed., vol. 21 p. 187, "Weights and Measures"
The inch-pound system measures the weight of various materials. Avoirdupois weight measures ordinary materials. Apothecaries' weight once measured drugs and medicines. Troy weight measures precious metals and gems. The metric system measures mass (amount of material something contains). An object's mass doesn't change, but its weight decreases with altitude. Mass and weight are equal at sea level, and the comparisons in this table are based on that location.
Both the metric system and the customary system are quite usable for either mass or force. In the International System of Units (SI), force can be measured in newtons. All the various customary systems of mechanical units have units of mass as well as units of force. In one foot-pound-second system, the units of both mass and force are called pounds, and various formulas need to be adjusted with an acceleration of gravity factor. In another foot-pound-second system, pounds are the units of mass, and poundals the units of force. In another, pounds are the units of force and slugs the units of mass.
The final paragraph in the paragraph above is objectionable under several other grounds. Mass and force (called weight there) are never equal; they are different physical quantities. The magnitudes of the measurements of mass and force may be the same, within the limits of the precision of the measurement, at some places on earth if the mass is measured in pounds mass and the force is measured in pounds force, for example. But the magnitudes are never the same on Earth if the mass is in kilograms and the force in newtons, or the mass in pounds and the force in poundals, etc. In addition, the statement that they are equal "at sea level" is incorrect even under the pound force/pound mass situation. The acceleration of gravity at sea level on Earth varies with latitude (the earth isn't a sphere, but is flattened out so the poles are closer to the center of the earth than the equator). The acceleration of gravity varies from 9.780 m/s2 at the Equator to 9.832 m/s2 at the poles.
Units of "weight" in some of the various systems
SI ft lbm lbf s ft lbm pdl s ft slug lbf s cgs
mass kilogram pound pound slug gram
force newton pound poundal pound dyne
There are also other systems using inches and slinches, or tons (megagrams) and sthenes, or the obsolete grams force, for example. The systems above also have variants depending on whether the units and formulas are rationalized or not, or with various options for other quantities such as the cgs electrostatic units or electromagnetic units or Gaussian units (a combination of esu and emu). Some fps "systems" might include units such as horsepower or various gallons, in which case the units are not all "coherent" in the technical sense used in metrology. (Calories and British thermal units, Btu, are other units which do not fit into any of the coherent systems of mechanical units)
Before you dismiss World Book Encyclopedia out of hand as something no serious researcher would use, consider how pervasive this encyclopedia is in our school systems. The World Book is likely to be the first place students go to look for information. This misinformation will be a big hindrance to their future education.
It isn't just World Book either. Other U.S. encyclopedias and dictionaries have similar problems with these concepts. Follow this link for more examples, from Encyclopædia Britannica, The Universal Almanac.
Despite the statement quoted above, World Book in its tables of conversion factors does not include any conversion of pounds and other customary "weight" units as units of force. These units are always converted to kilograms (SI mass units) in the tables, and never to newtons (SI force units).
MYTH: Pounds are units of force, and not units of mass.
I've run into this statement several times in various newsgroup threads. It seems to pop up at least once a month on one newsgroup or another. On one newsgroup, after I had pointed out that as a farmer I know that as they are used today, bushels are usually units of mass (differing amounts for different commodities) rather than units of volume, someone responded:
And as an engineer, I feel impelled to point out that the pound is a unit of weight, not mass. :)
The pound mass is the older definition of the pound. It is also the primary definition of the pound.
Back in 1893, the United States abandoned its independent standards for pounds and yards and defined them as fractions of the kilogram and the meter.
In 1959, the directors of the national standards laboratories of the United States, Canada, the United Kingdom, Australia, New Zealand, and the Union of South Africa got together to agree on common definitions of the customary length and mass units. They defined the pound avoirdupois as 0.453 592 37 kg, and the yard as 0.914 4 m, exactly. These metrologists were quite aware of the difference between force and mass, and they defined the pound as a unit of mass.
Before the redefinition of the pounds as fractions of a kilogram, they were defined as the mass of independently maintained artifacts.
The modern practice is to use pounds and ounces, etc., for the mass units with the symbols lb, oz, etc. If the force units of the same name are used, they should be identified as such (pounds force, ounces force, short tons force, long tons force). The symbol for the pound force is lbf, and the symbol for the ounce force is ozf. The old engineering practice of using lbm for pounds mass is obsolete. See, for example, the list of units and conversion factors in NIST Special Publication 811.
MYTH: Weight is the force due to the attraction of gravity.
Don't get me wrong. Weight does have this meaning. It may even be good idea to limit "weight" to this definition in any technical context.
However, that is not the only meaning of "weight": it also means "mass." (There are a number of other definitions of weight as well, but let's stick to the two most relevant to this topic.)
The problem comes in when someone has had a little bit of training in physics or some subject, and then assumes that whenever "weight" or "weigh" or similar terms are used, that is what is meant (or that is what is supposed to be meant by this use of these words, which isn't necessarily the same thing).
Definitions from the United States, Sweden, and Canada.
Metrologists are likely to know how the word "weight" has always been used. It is mostly some engineers and physicists who ignore history and try to insist that "weight" never means "mass."
Consider for example, the out-of-print NBS Special Publication 447, Weights and Measures Standards of the United States: a brief history, by Lewis V. Judson (originally issued Oct 1963, updated Mar 1976). This publication discusses only two kinds of standards, those for length and those for mass (i.e., yards, meters, pounds troy and avoirdupois, and kilograms). But look at the word in the title--it isn't "mass." Throughout the publication, weight and mass are used pretty much interchangeably, and the various documents quoted use one or the other or both. "Weight" is used many times in the publication, but it is never used to mean a force of any kind.
In more general terms, whenever systems of weights and measures, or systems of troy weight and things like this are discussed, the intended meaning of weight is mass.
For another example, see, NIST Special Publication 811 (1995 ed.), _Guide for the Use of the International System of Units (SI)_ by Barry N. Taylor (NIST is the National Institute of Standards and Technology, the successor agency to the National Bureau of Standards):
In commercial and everyday use, and especially in common parlance, weight is usually used as a synonym for mass. Thus the SI unit of the quantity weight used in this sense is the kilogram (kg) and the verb "to weigh" means "to determine the mass of" or "to have a mass of".
Examples: the child's weight is 23 kg the briefcase weighs 6 kg Net wt. 227 g
There's more to the explanation in section 8.3, including a good discussion of the force definition of weight often used in physics and engineering. I recommend this publication for anyone interested in the subject. You can download all 80-odd pages in .pdf format at http://physics.nist.gov/P ubs/SP811/sp811.html
This section concludes with the excellent advice that "whenever the word 'weight' is used, it should be made clear which meaning is intended."
The various official interpretations published in the Federal Register by the Secretary of Commerce in accordance with U.S. law, which set out the guidelines for use of the metric system, include in their tables of the base units a footnote for the word mass, saying
"Weight" is the commonly used term for "mass."
The quantity measured with the newton is called 'force' with no mention of 'weight.' [One was FR Doc. 75-15798, filed 18 June 1975. The most recent one should be available from the NIST web pages, try http://physics.nist.gov/cuu/index.html?/]
For a viewpoint from outside the United States, consider this from SP -- Swedish National Testing and Research Institute.
Mass is a measure of the amount of matter in a body. The term "weight" is sometimes used as a synonym for mass. However, this term has also several other meanings and should therefore be avoided.
The National Standard of Canada, CAN/CSA-Z234.1-89 Canadian Metric Practice Guide, January 1989, says something similar:
5.7.3 Considerable confusion exists in the use of the term "weight." In commercial and everyday use, the term "weight" nearly always means mass. In science and technology, "weight" has primarily meant a force due to gravity. In scientific and technical work, the term "weight" should be replaced by the term "mass" or "force," depending on the application.
5.7.4 The use of the verb "to weigh" meaning "to determine the mass of," e.g., "I weighed this object and determined its mass to be 5 kg," is correct.
Scales, and what they measure
Weight is an old concept. Archaeologists have found weights that are 6000 years old or more.
Throughout prehistory and well into the historical period, whenever people wanted to weigh something, they compared the two objects on a balance scale.
Balances (weight = mass)
What does a balance measure? It measures mass, not force. The normal gravitational balances require some force to work; but they cannot measure the magnitude of that force. They compare the mass of an unknown object to a standard mass. If two objects balance on Earth (in a vacuum, to avoid consideration of the differences in the buoyancy of the two objects in air), they will also balance on the Moon, or on an accelerating rocket for that matter.
The balance will tell you an object 'weighs' the same on the Moon as it does on Earth. That is a property of mass, not of force. It will not "measure" the sixfold difference in the force which that object exerts due to the local acceleration of gravity. The same object will exert much less force on the Moon.
A balance will, of course, be affected by forces such as the proverbial butcher's thumb on the scale, and it can even be rigged up to measure other forces (in terms of mass units).
Spring scales and load cells (weight = force)
Spring scales do measure force. But spring scales were never used before the 1600s. It wasn't until 1678 that Robert Hooke expressed his Law that the distance a spring stretches is proportional to the force exerted on it. It wasn't until 1687 that Isaac Newton published his Principia Mathematica setting forth his Laws of Motion.
Original meaning of "weight"
Not only did ancient peoples measure mass (using balances to determine weight), but if they'd had a clear understanding of the differences between mass and force, mass is the one they most often would have wanted to measure. Today when we do know the difference, it is still mass which we use in the grocery store or the jewelry store. If spring scales are used in commerce, a government inspector will test them not for their accuracy in measuring force, but rather for their accuracy in measuring mass in the particular location in which they are used.
And thy meat which thou shalt eat shall be by weight, twenty shekels a day; from time to time shalt thou eat it.
Ezekiel 4:10 (KJV)
Consider a few questions about this passage from the Bible.
1. Did anyone in Ezekiel's time have any way of "weighing" these 20 shekels of meat (actually a multigrain bread, in an obsolete meaning of meat), other than with a balance? (Ezekiel was exiled to Babylon in 597 B.C., and called to prophecy in a vision in about 592 B.C.) No, they measured its mass with a balance.
2. Did any of King James's scholars who translated this passage into English as "weight" in 1611 have any way of "weighing" things other than by a balance? No, they still always measured mass when they wanted to weigh something. By that time they had better balances, with knife edges. They also had steelyards in addition to the classic double pan balances. But they were still balances which measure mass, not force.
3. This passage in the New American Bible (1971) is rendered as "The food you eat shall be twenty shekels a day by weight; each day the same." Is there any reason that this should not still be translated as "weight" in today's world? Of course not. We still use the term "net weight" all the time in the grocery store or the butcher shop, and this "weight" is still mass, as it always has been. In America where labels are often in dual units, the labels such as "net wt. 1 lb (454 g)" or "400 g (14.1 oz)" are correct. It would be incorrect to use "net wt. 1 lb (4.45 N)" or "4.0 N (14.4 oz)" because the quantity we are interested in is mass, not force.
History of the word "weight" from Oxford English Dictionary
Jim Carr has posted information on the newsgroups giving more details of the history of the word "weight" from the Oxford English Dictionary (OED). He found that all the older definitions were for a measurement of mass with a balance; the first force definition of weight doesn't appear until the 1700s.
When discussing metrology and science, you must be careful about definitions. The meaning of "weight" as mass is much older than the meaning of "weight" as the force of gravity. More than seven centuries older. The older meanings are those preserved in the Weights and Measures name -- mass and distance|duration.
I cannot even begin to summarize the three pages of entries in the OED for "weigh" and the three others for "weight", plus the half page or so on "wey" which leads to both of these. In fact, it is almost pointless to type in something from 800 or 1000 since the 'English' is pretty much incomprehensible now.
The earliest reference (805-810) is to a standard of dry-goods weight. That is for 'wey'. Of course, what is meant by 'weight' requires a reference to the other words. We find (c1000) to compare quantities by means of weighing, and, at the same time, we find that this comparison was made with a balance. All of the definitions of "weight" send us back to the verb -- which should make us as scientists happy. The measurement process is the key part.
So let us note well the first meaning under 'weigh' of type II (type I being of the sense to carry or bear): to balance in the scales; to ascertain the weight of; to consider or compare in this respect. 7. trans. To ascertain the exact heaviness of (an object or substance) by balancing it in a pair of scales, or on a steelyard, against a counterpoise of known amount. This is clear: "weight" originally meant what we today call "mass", the quantity of matter determined by comparison on a pan balance. There are many other old (middle ages or before) references to this usage -- consistent with all that Nygaard has written here.
Later, under "weight", we find d. In scientific use (see quots.). 1721 KEILL Maupertius' Diss. (1734) 3 A secret Force, we call Weight or Gravity, attracts, urges or impels Bodies towards the Center of the Earth. This is the meaning used in much common parlance and intro physics books.
Used with permission of James A. Carr (visit his web page) In another message, Jim discussed the origins of the word "slug" as chronicled in the OED (link to this may be posted later).
The online version of Merriam-Webster's Tenth Collegiate Dictionary, WWWester Dictionary, also contains some dates of first use of words in English, but without the detailed examples found in the OED. It just lists "before 12th century" for the word "weight."
* Technically, mass and weight are different. The mass of an object refers to the amount of matter it contains; its weight is a measure of the pull of gravity on that mass. Astronauts may become weightless in space flight, but if they becomes massless , they are in trouble! We can be somewhat careless in our use of these terms because lab is earthbound.
B. Determination of the Density of an Organic Liquid.
Sign out an unknown liquid from the stockroom Unknown No. ______
Weigh a clean , dry, 10mL graduated cylinder. Remove the cylinder from the balance, and put exactly 2.0 mL of the liquid in the cylinder (use dropper as before). Weigh. Again, remove the cylinder from the balance, and put another 2.0 mL of the liquid in the cylinder (reading should now be 4.0 mL). Weigh. Repeat for total volumes of 6.0 mL, 8.0 mL, and 10.0 mL. NEVER ADD LIQUID WHEN THE CYLINDER IS ON THE BALANCE PAN ! Pour the liquid back in the original container and return it to the stockroom. Fill in the table below as you take your data. Make a graph with mL liquid on the x-axis (horizontal) and grams liquid on the y-axis (vertical). The mL of liquid have been marked for you. Write the grams of liquid on the y-axis. Draw the best straight line through the points (use a ruler). See your instructor if you have problems with graphing.
Ave. density: __________ g/mL
C. Density of a Solid Object.
Sign out an unknown solid from the stockroom. Unknown Letter ______
Weigh and record. Determine the volume by water displacement as follows: Carefully measure 25.0 mL of water into a 100mL graduated cylinder. Tilt the cylinder and gently slide the solid into the water. If the solid is dropped into the water, the cylinder may break. Record the new level of w ater to the nearest 0.1 mL. Draw diagrams to show your measurements. Calculate the density of the solid.
Calculations:
Wt. of unknown solid g.
Water level with solid mL
Water level without solid 25.0 mL
Volume of solid mL
Density of solid g/mL
Problems. Show method clearly; include correct units in answers. Note that density can be used as a conversion factor. If the density of a liquid is 1.23 g/mL, then the factors are:
1.23 g or 1 ml
1 mL 1.23 g
1. Use your graph in B. to read the weight of 5.8 mL of your unknown.
___________ g
2. A piece of metal weighs 44.867 g. When the metal is lowered into 25.0 mL of water in a graduated cylinder, the level rises to 28.5 mL. Calculate the density.
___________ g/mL
Which measurement, the weight or the volume, would be most likely to be inaccurate, giving error in the calculated density? Explain.
3. A solid cube, 2.2 cm on an edge weighed 6.488 grams. Will it sink or float in water? Explain.
4. An oil has a density of 1.44 g/mL. How many mL are needed for 22.036 grams?
___________ mL
5. How easy is it to toss around a brick of solid gold as they do in the movies? Calculate the weight in grams and pounds (454 g = 1 lb) of a gold brick 35.0 cm long with a square cross-section 9.5 cm by 9.5 cm. The density of Au is 19.3 g/cc.
___________ g
___________ lb
Expt. 3 Name: Section:
S IGNIFICANT F IGURES : When you use numbers in calculation (multiplication and/or division) your final answer must show the accuracy with which the measurements were made. Suppose you want to calc ulate the volume of a box which you measure with a small ruler and record the length, width, and height as 4.4 cm by 5.8 cm by 6.2 cm. Write the math expression for the calculation of volume, and record all of the numbers in the answer on your calculator.
Your calculator should show 158.224 cm 3 . However, if your write down this number, you indicate that each measurement you made is reliable to six significant figures. Look at the measurements you made with your ruler. How many significant figures are in each measurement? ______
Therefore you answer should also have the same number of significant figures. Write the volume as it should be recorded __________. When you do multiplication or division, your answer should have the same number of significant figures as there are in the measured value with the smallest number significant figures.
Practical application: Density measurement of a liquid. You will do all weighings using the balance which weighs accurately to 0.001 grams. This is the measu rement with the largest number of significant figures. You will measure volume two different ways. Record the density in each calculation to show correct number of significant figures.
Use a clean, dry graduated 50mL beaker to measure 20 mL of a liquid as accurately as you can. This volume is recorded for you and has 2 significant figures. Weigh a clean dry 25mL graduated cylinder. Pour the liquid from the beaker into the graduate and record the volume to the nearest 0.1 mL. (How many significant fi gures? _________) Calculate the density using the weight of the liquid, and the 2 different volume measurements, rounding off to the correct number of significant figures in each case. Record your values on next page. Show calculations.
DETERMINATION OF DENSITY:
Vol. of liquid using the 50mL beaker: 20 mL
Vol. of liquid using a 25mL graduated cylinder mL
Wt. of cylinder plus liquid g
Wt. of empty cylinder g
Wt. of liquid g
Density values, calculated:
using volume in beaker g/mL
using volume in graduated cylinder g/mL