MASS, DENSITY, and also VOLUME

## CONCEPT

Among the physical properties learned by chemists and also other scientists, mass is one of the many fundamental. All matter, by definition, has actually mass. Mass, in turn, theatre a role in 2 properties essential to the study of chemistry: density and volume. Every one of these—mass, density, and also volume—are simple concepts, however in order to occupational in chemistry or any of the other tough sciences, it is necessary to understand these types of measurement. Measuring density, for instance, aids in identify the ingredient of a offered substance, when volume is a crucial component to utilizing the gas laws.

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## HOW the WORKS

### Fundamental nature in relation to Volume and also Density

Most characteristics of the human being studied by scientists have the right to be measured in regards to one or much more of 4 properties: length, mass, time, and also electric charge. The volume the a cube, for instance, is a unit of size cubed—that is, size multiplied through "width," i beg your pardon is then multiplied by "height."

Width and height space not, for the functions of science, distinctive from length: they are merely versions of it, distinguished by their orientation in space. Length provides one dimension, while width gives a 2nd perpendicular come the third. Height, perpendicular both to length and width, renders the 3rd spatial dimension—yet all of these are just expressions the length distinguished according to direction.

VOLUME and also DENSITY DEFINED.

Volume, then, is measured in regards to length, and can be characterized as the amount of three-dimensional room an object occupies. Volume is generally expressed in cubic devices of length—for example, the milliliter (mL), additionally known together the cubic centimeter (cc), is same to 6.10237 · 10−2 in3. As its surname implies, there are 1,000 milliliters in a liter.

Density is the proportion of mass to volume—or, to placed its meaning in terms of fundamental properties, that mass separated by cubed length. Thickness can likewise be viewed as the lot of matter within a provided area. In the SI system, thickness is typically expressed together grams every cubic centimeter (g/cm3), equivalent to 62.42197 pounds every cubic foot in the English system.

### Mass

MASS DEFINED.

Though length is easy enough to comprehend, mass is much more involved. In his 2nd law of motion, teacher Isaac Newton (1642-1727) characterized mass together the proportion of force to gravity. This, the course, is a statement the belongs come the kingdom of physics; for a chemist, it is an ext useful—and also accurate—to define mass together the quantity of issue that an object contains.

Matter, in turn, deserve to be defined as physical substance that occupies space; is written of atom (or in the situation of subatomic particles, is part of one atom); is convertible into energy—and has mass. The kind or state of issue itself is not important: on earth it is mainly observed as a solid, liquid, or gas, however it can also be found (particularly in various other parts that the universe) in a 4th state, plasma.

The an ext matter an item contains, the an ext mass. Come refer again to the laws of motion, in his very first law, Newton identified inertia: the propensity of objects in motion to continue to be in motion, or that objects at remainder to remain at rest, in a constant velocity uneven they room acted ~ above by some external force. Fixed is a measure of inertia, meaning that the an ext mass other contains, the more difficult it is to placed it into motion, or to avoid it native moving.

MASS VS. WEIGHT.

Most people who space not scientifically trained have tendency to think the mass and weight space the same thing, but this is favor saying the apples and apple pies room the same. That course, an apple is an ingredient in one apple pie, however the pie consists of something else—actually, a variety of other things, such together flour and sugar. In this analogy, mass is tantamount to the apple, and also weight the pie, while the acceleration because of gravity is the "something else" in weight.

It is understandable why civilization confuse mass with weight, since most load scales carry out measurements in both pounds and also kilograms. However, the pound (lb) is a unit of weight in the English system, whereas a kilogram(kg) is a unit of massive in the metric and also SI systems. Despite the 2 are relatively convertible on planet (1 lb = 0.4536 kg; 1 kg = 2.21 lb), they space actually rather different.

Weight is a measure up of force, which Newton"s second law that motion characterized as the product of mass multiplied by acceleration. The acceleration component of load is a an outcome of Earth"s gravitational pull, and also is same to 32 ft (9.8 m) per 2nd squared. Therefore a person"s load varies follow to gravity, and also would be different if measure up on the Moon; mass, ~ above the other hand, is the same throughout the universe. Offered its invariable value, scientists typically speak in regards to mass fairly than weight.

Weight differs as a solution to the gravitational pull of the planet, moon, or other body top top which the is measured. Thus a person weighs less on the Moon, due to the fact that the Moon possesses much less mass 보다 Earth, and, thus, exerts much less gravitational force. Therefore, it would certainly be less complicated on the Moon come lift a human from the ground, but it would be no simpler to relocate that human being from a relaxing position, or to protect against him or she from moving. This is since the person"s mass, and also hence his or her resistance come inertia, has not changed.

## REAL-LIFE APPLICATIONS

### Atomic mass Units

Chemists carry out not constantly deal in big units of mass, such as the fixed of a person body—which, of course, is measure in kilograms. Instead, the chemist"s work is often concerned with dimensions of mass because that the smallest types of matter: molecules, atoms, and other elementary school particles. To measure these even in regards to grams (0.001 kg) is absurd: a single atom that carbon, for instance, has actually a massive of 1.99 · 10−23 g. In various other words, a gram is around 50,000,000,000,000,000,000,000 times bigger than a carbon atom—hardly a usable comparison.

Instead, chemists use an atom mass unit (abbreviated amu), i m sorry is equal to 1.66 · 10−24 g. Even so, is hard to imagine identify the fixed of solitary atoms top top a continuous basis, so chemists make use of figures because that the median atomic mass of a particular element. The median atomic fixed of carbon, because that instance, is 12.01 amu. Together is the instance with any kind of average, this way that some atoms—different isotopes of carbon—may weigh much more or less, yet the figure of 12.01amu is quiet reliable. Some other typical atomic mass figures for different aspects are together follows:

Hydrogen (H): 1.008 amu Helium (He): 4.003 amu Lithium (Li): 6.941 amu Nitrogen (N): 14.01 amu Oxygen (O): 16.00 Aluminum (Al): 26.98 Chlorine (Cl): 35.46 amu yellow (Au): 197.0 amu Hassium (Hs): <265 amu>

The number for hassium, with an atomic variety of 108, is offered in brackets because this number is the mass because that the longest-lived isotope. The average value of mass because that the molecules in a provided compound can also be rendered in regards to atomic massive units: water (H2O) molecules, because that instance, have actually an median mass of 18.0153 amu. Molecule of magnesium oxide (MgO), which deserve to be extract from sea water and also used in do ceramics, have actually an average mass much higher than because that water: 40.304 amu.

These worths are obtained simply by adding those that the atoms had in the molecule: because water has actually two hydrogen atoms and also one oxygen, the median molecular mass is obtained by multiplying the median atomic massive of hydrogen through two, and including it come the mean atomic mass of oxygen. In the instance of magnesium oxide, the oxygen is external inspection to simply one various other atom—but magnesium, v an mean atomic fixed of 24.304, weighs much an ext than hydrogen.

### Molar Mass

It is often essential for a chemist to know precisely how countless atoms are in a provided sample, an especially in the situation of a chemistry reaction in between two or more samples. Obviously, it is impossible to counting atoms or various other elementary particles, but there is a means to determine whether 2 items—regardless of the aspects or compound involved—have the same variety of elementary particles. This an approach makes usage of the numbers for median atomic mass that have been developed for every element.

If the typical atomic massive of the substance is 5 amu, then there should be a very big number of atom (if it is one element) or molecules (if that is a compound) of that substance having actually a complete mass that 5 grams (g). Similarly, if the typical atomic massive of the substance is 7.5 amu, then there must be a very huge number of atoms or molecules of the substance having actually a complete mass that 7.5 g. What is needed, clearly, is a very large number through which elementary particles should bemultiplied in order to productivity a mass whose worth in grams is same to the value, in amu, of its average atomic mass. This is known as Avogadro"s number.

The first scientist to identify a meaningful distinction between atoms and also molecules was Italian physicist Amedeo Avogadro (1776-1856). Avogadro preserved that gases consisted of particles—which he referred to as molecules—that in turn included one or more smaller particles. He further reasoned that one liter of any kind of gas should contain the same number of particles as a liter of one more gas.

In order to discuss the habits of molecules, it was crucial to set a big quantity as a straightforward unit, due to the fact that molecules themselves are an extremely small. This led to the establishment of what is known as Avogadro"s number, equal to 6.022137 × 1023 (more than 600 exchange rate trillion.)

The magnitude of Avogadro"s number is virtually inconceivable. The same number of grains of sand would cover the entire surface of earth at a depth of numerous feet. The same variety of seconds, for instance, is about 800,000 time as long as the age of the universe (20 billion years). Avogadro"s number—named after ~ the guy who introduced the ide of the molecule, however only calculated years after his death—serves a an extremely useful function in computations involving molecules.

THE MOLE.

To compare 2 substances include the same variety of atoms or molecules, researchers use the mole, the SI fundamental unit for "amount of substance." A mole (abbreviated mol) is, generally speaking, Avogadro"s variety of atoms or molecules; however, in the more precise SI definition, a mole is same to the variety of carbon atoms in 12.01 g (0.03 lb) the carbon. Note that, as proclaimed earlier, carbon has actually an average atomic massive of 12.01 amu. This is no coincidence, that course: multiplication of the typical atomic massive by Avogadro"s number yields a number in grams same to the worth of the typical atomic massive in amu.

The term "mole" can be provided in the same means we use the word "dozen." just as "a dozen" deserve to refer come twelve cakes or twelve chickens, so "mole" constantly describes the same variety of molecules. Simply as one liter that water, or one liter the mercury, has a particular mass, a mole of any given substance has its own details mass, express in grams. A mole that helium, because that instance, has a fixed of 4.003 g (0.01 lb), whereas a mole of steel is 55.85 g (0.12 lb) These numbers represent the molar mass for each: the is, the mass of 1 mol that a provided substance.

Once again, the value of molar fixed in grams is the exact same as the of the median atomic massive in amu. Also, it should be clean that, given the fact that helium weighs much less than air—the reason why helium-filled balloons float—a quantity of helium v a massive of 4.003 g have to be a great deal of helium. And indeed, as shown earlier, the quantity of atoms or molecules in a mole is sufficiently an excellent to do a sample the is large, yet still usable because that the objectives of examine or comparison.

### Measuring Volume

Mass, due to the fact that of its basic nature, is sometimes hard to comprehend, and also density calls for an explanation in regards to mass and also volume. Volume, ~ above the other hand, appears to be fairly straightforward—and that is, as soon as one is relenten a heavy of regular shape. In various other situations, however, volume measurement is much more complicated.

As noted earlier, the volume that a cube can be obtained simply by multiplying length by width by height. There are other means for measure the volume of other straight-sided objects, such as a pyramid. Still other formulae, which make use of the constant π (roughly equal to 3.14) are necessary for measure the volume the a cylinder, a sphere, or a cone.

For an item that is rarely often rare in shape, however, one may have to employ calculus—but the most basic technique is merely to immerse the object in water. This procedure entails measuring the volume of the water before and after immersion, and also calculating the difference. The course, the object gift measured cannot be water-soluble; if the is, that volume need to be measure in a non-water-based liquid such as alcohol.

LIQUID and also GAS VOLUME.

Measuring liquid quantities is even much easier than because that solids, given the truth that liquids have no definite shape, and will just take the form of the container in which they room placed. Gases are similar to liquids in the sense that they broaden to fit their container; however, measurement of gas volume is a more involved procedure than that used to measure up either liquids or solids, due to the fact that gases arehighly responsive to transforms in temperature and also pressure.

If the temperature that water is raised from that is freezing suggest to its cook point—from 32°F (0°C) come 212°F (100°C)—its volume will rise by just 2%. If its push is double from 1 atm (defined as normal air push at sea level) to 2 atm, volume will decrease by only 0.01%. Yet if air to be heated indigenous 32° come 212°F, the volume would boost by 37%; if its push were doubled from 1 atm to 2, its volume would decrease by 50%.

Not only do gases respond considerably to alters in temperature and also pressure, yet also, gas molecules have tendency to be non-attractive toward one another—that is, they often tend not to stick together. Hence, the ide of "volume" in relation to a gas is basically meaningless unless its temperature and also pressure are known.

### Comparing Densities

In the discussion of molar fixed above, helium and also iron to be compared, and we experienced that the fixed of a mole of iron was about 14 time as great as the of a mole the helium. This may seem like a relatively small element of difference in between them: after ~ all, helium floats top top air, whereas stole (unless the is arranged in simply the appropriate way, for instance, in a tanker) sinks to the bottom that the ocean. Yet be careful: the comparison of molar massive is only an expression that the massive of a helium atom as contrasted to the fixed of an iron atom. It provides no reference to density, i m sorry is the ratio of mass to volume.

Expressed in regards to the ratio of mass to volume, the difference in between helium and also iron becomes much more pronounced. Suppose, ~ above the one hand, one had actually a gallon jug filled with iron. How many gallons that helium does it take to equal the fixed of the iron? Fourteen? shot again: the takes much more than 43,000 gallons the helium to same the mass of the iron in one gallon jug! Clearly, what this mirrors is that the thickness of stole is much, much better than the of helium.

This, that course, is fixed a surprising revelation; still, that is periodically easy to get confused by comparisons of mass together opposed to comparisons of density. One could even get tricked by the old elementary-school brain-teaser the goes something like this: "Which is heavier, a ton of feather or a ton of cannonballs?" Of course neither is heavier, however the trick facet in the inquiry relates come the reality that the takes a much higher volume of feathers (measured in cubic feet, for instance) 보다 of cannonballs to equal a ton.

One the the interesting things about density, as distinguished from mass and volume, is the it has actually nothing to carry out with the amount of material. A kilogram that iron differs from 10 kg of iron both in mass and volume, but the thickness of both samples is the same. Indeed, as discussed below, the recognized densities that various materials make it possible to identify whether a sample that that material is genuine.

COMPARING DENSITIES.

As provided several times, the densities of many materials are recognized quantities, and can be conveniently compared. Some instances of density, every expressed in regards to grams per cubic centimeter, are provided below. These figures are measured in ~ a temperature the 68°F (20°C), and for hydrogen and also oxygen, the worth was acquired at typical atmospheric pressure (1 atm):

Comparisons the Densities for assorted Substances:

Oxygen: 0.00133 g/cm3 Hydrogen: 0.000084 g/cm3 Ethyl alcohol: 0.79 g/cm3 Ice: 0.920 g/cm3 Water: 1.00 g/cm3 Concrete: 2.3 g/cm3 Iron: 7.87 g/cm3 Lead: 11.34 g/cm3 Gold: 19.32 g/cm3

### Specific Gravity

IS IT yes, really GOLD?

Note the pure water (as protest to sea water, i beg your pardon is 3% an ext dense) has a density of 1.0 g every cubic centimeter. Water is therefore a useful standard because that measuring the certain gravity of various other substances, or the ratio in between the thickness of that substance and the thickness of water. Due to the fact that the particular gravity of water is 1.00—also the thickness of water in g/cm3—the details gravity of any type of substance (a number, fairly than a number an unified with a unit that measure) is the very same as the worth of the own density in g/cm3.

Comparison of densities make it feasible to identify whether a piece of jewel alleged to it is in solid gold is yes, really genuine. To identify the answer, one have to drop the sample in a beaker of water with graduated devices of measure up clearlymarked. Mean the item has actually a mass of 10 g. The density of gold is 19 g/cm3, and because density is same to mass divided by volume, the volume of water displaced need to be same to the mass divided by the density. The latter number is same to 10 g divided by 19 g/cm3, or 0.53 ml. Suppose that instead, the item displaced 0.88 ml the water. Clearly it is not gold, however what is it?

Given the figures for mass and also volume, its thickness is same to 11.34 g/cm3—which wake up to be the density of lead. If, on the various other hand, the amount of water displaced were somewhere between the values for pure gold and also pure lead, one could calculate what section of the item was gold and also which lead. That is possible, the course, that it could contain some various other metal, but given the high particular gravity the lead, and also the reality that its density is reasonably close to the of gold, lead is a favorite gold substitute among jewelry counterfeiters.

SPECIFIC GRAVITY and THE DENSITIES of PLANETS.

Most rocks close to the surface ar of planet have a specific gravity somewhere in between 2 and also 3, if the specific gravity the the earth itself is around 5. Exactly how do scientists know that the density of planet is roughly 5 g/cm3? The computation is fairly simple, given the reality that the mass and also volume of the planet are known. And also given the reality that most of what lies close come Earth"s surface—sea water, soil, rocks—has a specific gravity well below 5, it is clear that Earth"s internal must save on computer high-density materials, such as nickel or iron. In the same way, calculations regarding the thickness of other objects in the Solar System provide a clue as to their interior composition.

This brings the discussion earlier around to a topic raised much earlier in this essay, when comparing the load of a human being on earth versus the person"s weight on the Moon. It so happens the the Moon is smaller sized than Earth, yet that is not the reason it exerts much less gravitational pull: as provided earlier, the gravitational force a planet, moon, or other body exerts is pertained to its mass, not its size.

It therefore happens, too, the Jupiter is much bigger than Earth, and also that it exerts a gravitational pull much better than the of Earth. This is since it has actually a mass numerous times as good as Earth"s. However what about Saturn, the second-largest planet in the Solar System? In size it is only around 17% smaller sized than Jupiter, and both room much, much larger than Earth. However a person would weigh much much less on Saturn than on Jupiter, because Saturn has actually a mass lot smaller than Jupiter"s. Given the close relation in size between the two planets, that is clear the Saturn has actually a lot lower thickness than Jupiter, or in fact also Earth: the great ringed planet has a specific gravity of much less than 1.

### WHERE TO discover MORE

Chahrour, Janet. Flash! Bang! Pop! Fizz!: interesting Science because that Curious Minds. Depicted by Ann Humphrey Williams. Hauppauge, NY: Barron"s, 2000.

"Density and certain Gravity" (Web site). (March 27, 2001).

"Density, Volume, and also Cola" (Web site). (March 27, 2001).

Ebbing, Darrell D.; R. A. D. Wentworth; and James P. Birk. Introductory Chemistry. Boston: houghton Mifflin, 1995.

"The massive Volume density Challenge" (Web site). (March 27, 2001).

"MegaConverter 2" (Web site). (May 7, 2001).

"Metric thickness and certain Gravity" (Web site). (March 27, 2001).

Robson, Pam. Clocks, Scales and Measurements. New York: Gloucester Press, 1993.

"Volume, Mass, and also Density" (Web site). (March 27, 2001).

Zumdahl, Steven S. Introductory Chemistry: A Foundation, fourth ed. Boston: house Mifflin, 2000.

## KEY TERMS

### ATOMIC fixed UNIT:

An SI unit (abbreviated amu), equal to 1.66 · 10−24 g, for measuring the fixed of atoms.

### AVERAGE atom MASS:

A figure used by chemists to clues the mass—in atom mass units—of the typical atom in a big sample. The typical atomic massive of carbon, for instance, is 12.01 amu. If a problem is a compound, the typical atomic massive of every atoms in a molecule of that substance should be added together to yield the median molecular fixed of the substance.

A figure, named after Italian physicist Amedeo Avogadro (1776-1856), same to 6.022137 × +023 . Avogadro"s number indicates the variety of atoms, molecules, or various other elementary corpuscle in a mole.

### DENSITY:

The proportion of mass come volume—in various other words, the lot of issue within a offered area. In the SI system, density is generally expressed as grams every cubic centimeter (g/cm3), equal to 62.42197 pounds per cubic foot in the English system.

### MASS:

The amount of matter things contains.

### MATTER:

Physical substance the occupies space, has mass, is composed of atom (or in the instance of subatomic particles, is component of an atom), and also is convertible come energy.

### MILLILITER:

One of the most generally used devices of volume in the SI mechanism of measures. The milliliter (abbreviated mL), also known together a cubic centimeter (cc), is same to 6.10237 · 10−2 cubic inch in the English system. Together the surname implies, there are 1,000 milliliters in a liter.

### MOLAR MASS:

The mass, in grams, of1 mole the a provided substance. The worth in grams that molar massive is constantly equal to the value, in atomic mass units, of the typical atomic fixed of that substance: thus, carbon has a molar mass of 12.01 g, and also anaverage atomic mass of 12.01 amu.

### MOLE:

The SI basic unit for "amount the substance." A mole is, generally speaking, Avogadro"s number of atoms, molecules, or other elementary particles; however, in the much more precise SI definition, a mole is equal to the number of carbon atom in 12.01 g of carbon.

### SPECIFIC GRAVITY:

The thickness of an object or substance relative to the density of water; or more generally, the ratio in between the densities of two objects or substances. Due to the fact that the specific gravity that water is 1.00—also the density of water ing/cm3—the details gravity of any substance is the very same as the worth of its own thickness in g/cm3. Certain gravity is simply a number, without any unit of measure.

### VOLUME:

The quantity of three-dimensional space an object occupies. Volume is normally expressed in cubic units of length—for instance, the milliliter.

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### WEIGHT:

The product the mass multiplied by the acceleration because of gravity (32 ft or 9.8 m/sec2). A pound is a unit the weight, vice versa, a kilogram is a unit ofmass.