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Matter
Dr. K. Shahzad Baig
MUN-Canada
Petrucci, et al. 2011. General Chemistry: Principles and Modern Applications. Pearson Canada Inc., Toronto, Ontario.
Tro, N.J. 2010. Principles of Chemistry. : A molecular approach. Pearson Education, Inc.
The Scientific Method
The scientific method is a set of procedures used to develop explanations of natural
phenomena and possibly to predict additional phenomena.
The four basic stages of the scientific method are
1. gathering data through observations and experiments;
2. reducing the data to simple verbal or mathematical expressions known as natural laws;
3. offering a plausible explanation of the data through a hypothesis;
4. testing the hypothesis to make a theory that explains the hypothesis
Matter
Matter is defined as anything that occupies mass, and display space, possesses
inertia.
Composition refers to the component parts of a sample of matter and their
relative proportions.
Atom is the basic building blocks of matter
Element
Matter that is composed of a collection of a single type of atom is known as an element.
Compound
Matter composed of two or more elements is known as a compound
Molecule is the smallest entity of a compound having the same proportions of the
constituent atoms as does the compound as a whole
Extensive properties depend on the amount of matter in a sample e.g. mass , volume
Intensive property is independent of the amount of matter sampled, e.g. density
In making a series of measurements,
the degree to which the measurements agree with one another is known as
the precision of the measurement
the degree to which the measurement agrees with the actual value is referred
to as the accuracy of the measurement.
The significant figures of a number are the digits that contribute to its measurement
resolution. This includes all digits except: All leading zeros
SI Base Quantities
Physical quantity Unim
Length meter
Mass kilogram
Time second
Temperature kelvin
Amount of
substance
mole
Electric current ampere
Luminous intensity candela
Density and Percent Composition:
Density is the ratio of mass to volume.
๐ท๐‘’๐‘›๐‘ ๐‘–๐‘ก๐‘ฆ ๐‘‘ =
๐‘€๐‘Ž๐‘ ๐‘  (๐‘š)
๐‘‰๐‘œ๐‘™๐‘ข๐‘š๐‘’ (๐‘ฃ)
=
๐‘”
๐‘๐‘š3
Density is a function of temperature because volume varies with temperature, whereas
mass remains constant
The mass of 1.000 L of water at 4 ยฐC = 1.000 kg.
The density of water at 4 ยฐC = 1000 g/1000 mL = 1.0 g/mL
The density of water at 20 ยฐC = ? g/ ? mL = 0.9982 g/mL
the average temperature of seawater increases, the seawater will become less dense, its
volume will increase, and sea level will rise even if no continental ice melts.
Example
A cube of osmium 1.000 cm on edge weighs 22.59 g. The density of osmium (the densest
of the elements) is 22.59 g/m3. What would be the mass of a cube of osmium that is 1.25
in. on edge ( 1 in = 2.54 cm)
๐‘€๐‘Ž๐‘ ๐‘  ๐‘œ๐‘“ ๐‘‚๐‘ ๐‘š๐‘–๐‘ข๐‘š ๐‘ ๐‘Ž๐‘š๐‘๐‘™๐‘’ = ๐‘” = 1.25 ๐‘–๐‘› ๐‘ฅ
2.54 ๐‘๐‘š
1 ๐‘–๐‘›
3
๐‘ฅ
22.59 ๐‘” ๐‘œ๐‘ ๐‘ ๐‘š๐‘–๐‘ข๐‘š
1๐‘๐‘š3
=
= 723 g ossmium
๐‘€๐‘Ž๐‘ ๐‘  = ๐‘‰๐‘œ๐‘™๐‘ข๐‘š๐‘’ ๐‘ฅ ๐ท๐‘’๐‘›๐‘ ๐‘–๐‘ก๐‘ฆ
๐ท๐‘’๐‘›๐‘ ๐‘–๐‘ก๐‘ฆ ๐‘‘ =
๐‘€๐‘Ž๐‘ ๐‘  (๐‘š)
๐‘‰๐‘œ๐‘™๐‘ข๐‘š๐‘’ (๐‘ฃ)
=
๐‘”
๐‘๐‘š3
Example
๐ท๐‘’๐‘›๐‘ ๐‘–๐‘ก๐‘ฆ ๐‘‘ =
๐‘€๐‘Ž๐‘ ๐‘  (๐‘š)
๐‘‰๐‘œ๐‘™๐‘ข๐‘š๐‘’ (๐‘ฃ)
=
๐‘”
๐‘๐‘š3
At 25 ยฐC the density of mercury, the only metal that is liquid at this temperature, is 13.5
g/cm 3. What is the volume, in mL, of 1.000 kg of mercury at 25 ยฐC.
๐‘‰๐‘œ๐‘™๐‘ข๐‘š๐‘’ ๐‘ฃ = ๐‘€๐‘Ž๐‘ ๐‘  ๐‘š ๐‘ฅ
1
๐ท๐‘’๐‘›๐‘ ๐‘–๐‘ก๐‘ฆ (๐‘‘)
= ? ๐‘š๐ฟ
๐‘š๐ฟ, ๐ป๐‘” = 1.000 ๐‘˜๐‘” ๐‘ฅ
1000 ๐‘”
1 ๐‘˜๐‘”
๐‘ฅ
1 ๐‘š๐ฟ ๐ป๐‘”
13.5 ๐‘”
= 74.1 ๐‘š๐ฟ ๐ป๐‘”
Example 1-2 Relating Mass, Volume, and Density
The stainless steel in the solid cylindrical rod pictured below has a density of 7.75 g/cm3. If
we want a 1.00 kg mass of this rod, how long a section must we cut off?
๐‘‘ =
(๐‘š)
(๐‘ฃ)
๐‘ฃ = ๐‘š ๐‘ฅ
1
๐‘‘
๐‘ฃ = 1.00 ๐‘˜๐‘” ๐‘ฅ
1000 ๐‘”
1 ๐‘˜๐‘”
๐‘ฅ
1 ๐‘๐‘š3
7.75 ๐‘”
= ? ๐‘๐‘š3
๐‘ฃ = ๐œ‹ ๐‘Ÿ2 ๐ฟ
๐ฟ =
๐‘ฃ
๐œ‹๐‘Ÿ2
๐ฟ =
129 ๐‘๐‘š3
3.1416 ๐‘ฅ 0.500 ๐‘–๐‘› ๐‘ฅ
2.54 ๐‘๐‘š
1 ๐‘–๐‘›
2
= 25.5 ๐‘๐‘š3
PRACTICE EXAMPLE A:
To determine the density of trichloroethylene, a liquid used to degrease electronic
components, a flask is first weighed empty (108.6 g). It is then filled with 125 mL of the
trichloroethylene to give a total mass of 291.4 g. What is the density of trichloroethylene
in grams per milliliter?
PRACTICE EXAMPLE B:
Suppose that instead of using the cylindrical rod of Example 1-2 to prepare a 1.000 kg
mass we were to use a solid spherical ball of copper (d = 8.96 g/cm3). What must be the
radius of this ball?
Example 1-3
Determining the Density of an Irregularly Shaped Solid
A chunk of coal is weighed twice while suspended from a spring scale. When the coal is
suspended in air, the scale registers 156 g; when the coal is suspended underwater at 20 ยฐC,
the scale registers 59 g. What is the density of the coal? The density of water at 20 ยฐC is
0.9982 g cm3
.
If we use mwater to denote the mass of displaced water, then the volume of the displaced
water is calculated as follows:
๐‘ฃ =
๐‘š๐‘Ž๐‘ ๐‘  ๐‘ค๐‘Ž๐‘ก๐‘’๐‘Ÿ
๐‘‘
= ? ๐‘๐‘š3
=
156 ๐‘” โˆ’ 59 ๐‘”
0.9982 ๐‘”
๐‘๐‘š3
= 97 ๐‘๐‘š3
The volume of the chunk of coal is the same as the volume of displaced water.
๐‘‘ =
156 ๐‘”
97 ๐‘๐‘š3
= ? = 1.6 g / cm 3
Alternate way to solve
๐‘ฃ =
๐‘š๐‘Ž๐‘ ๐‘  ๐‘ค๐‘Ž๐‘ก๐‘’๐‘Ÿ
๐‘‘
= ? ๐‘๐‘š3
๐‘‘ =
๐‘€๐‘Ž๐‘ ๐‘  ๐‘”
๐‘‰๐‘œ๐‘™๐‘ข๐‘š๐‘’ ๐‘๐‘š3
= ?
๐ท๐‘’๐‘›๐‘ ๐‘–๐‘ก๐‘ฆ ๐‘œ๐‘“ ๐‘‚๐‘๐‘—๐‘’๐‘๐‘ก
๐ท๐‘’๐‘›๐‘ ๐‘–๐‘ก๐‘ฆ ๐‘œ๐‘“ ๐‘ค๐‘Ž๐‘ก๐‘’๐‘Ÿ
=
๐‘Š๐‘’๐‘–๐‘”โ„Ž๐‘ก ๐‘–๐‘› ๐‘ค๐‘Ž๐‘ก๐‘’๐‘Ÿ
๐‘Š๐‘’๐‘–๐‘”โ„Ž๐‘ก ๐‘–๐‘› ๐‘Ž๐‘–๐‘Ÿ โˆ’ ๐‘Š๐‘’๐‘–๐‘”โ„Ž๐‘ก ๐‘–๐‘› ๐‘ค๐‘Ž๐‘ก๐‘’๐‘Ÿ
PRACTICE EXAMPLE A:
A graduated cylinder contains 33.8 mL of water. A stone with a mass of 28.4 g is
placed in the cylinder and the water level rises to 44.1 mL. What is the density of the
stone?
EXAMPLE 1-4
Using Percent Composition as a Conversion Factor
A 75 g sample of sodium chloride (table salt) is to be produced by evaporating to
dryness a quantity of seawater containing 3.5% sodium chloride by mass. What volume
of seawater, in liters, must be taken for this purpose? Assume a density of 1.03 g/mL for
seawater
๐ท๐‘’๐‘›๐‘ ๐‘–๐‘ก๐‘ฆ ๐‘‘ =
๐‘€๐‘Ž๐‘ ๐‘  (๐‘š)
๐‘‰๐‘œ๐‘™๐‘ข๐‘š๐‘’ (๐‘ฃ)
=
๐‘”
๐‘๐‘š3
๐‘‰๐‘œ๐‘™๐‘ข๐‘š๐‘’ ๐‘ฃ = [๐‘€๐‘Ž๐‘ ๐‘  ๐‘š ] ๐‘ฅ
1
[๐ท๐‘’๐‘›๐‘ ๐‘–๐‘ก๐‘ฆ ๐‘‘ ]
= ? ๐‘š๐‘™
๐ฟ ๐‘†๐‘’๐‘Ž๐‘ค๐‘Ž๐‘ก๐‘’๐‘Ÿ ๐‘ฃ = 75 ๐‘” ๐‘๐‘Ž๐ถ๐‘™
100 ๐‘” ๐‘†๐‘’๐‘Ž๐‘ค๐‘Ž๐‘ก๐‘’๐‘Ÿ
3.5 ๐‘” ๐‘๐‘Ž๐ถ๐‘™
๐‘ฅ
1 ๐‘š๐ฟ ๐‘†๐‘’๐‘Ž๐‘ค๐‘Ž๐‘ก๐‘’๐‘Ÿ
1.03 ๐‘” ๐‘†๐‘’๐‘Ž๐‘ค๐‘Ž๐‘ก๐‘’๐‘Ÿ
๐‘ฅ
1 ๐ฟ ๐‘†๐‘’๐‘Ž๐‘ค๐‘Ž๐‘ก๐‘’๐‘Ÿ
1000 ๐‘š๐ฟ ๐‘†๐‘’๐‘Ž๐‘ค๐‘Ž๐‘ก๐‘’๐‘Ÿ
= 2.1 ๐ฟ ๐‘†๐‘’๐‘Ž๐‘ค๐‘Ž๐‘ก๐‘’๐‘Ÿ
PRACTICE EXAMPLE A:
How many kilograms of ethanol are present in 25 L of a gasohol solution that is 90%
gasoline to 10% ethanol by mass? The density of gasohol is 0.71 g/mL
PRACTICE EXAMPLE B:
Common rubbing alcohol is a solution of 70.0% isopropyl alcohol by mass in water. If a
25.0 mL sample of rubbing alcohol contains 15.0 g of isopropyl alcohol, what is the
density of the rubbing alcohol?
The Scientific Methods

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The Scientific Methods

  • 1. Matter Dr. K. Shahzad Baig MUN-Canada Petrucci, et al. 2011. General Chemistry: Principles and Modern Applications. Pearson Canada Inc., Toronto, Ontario. Tro, N.J. 2010. Principles of Chemistry. : A molecular approach. Pearson Education, Inc.
  • 2. The Scientific Method The scientific method is a set of procedures used to develop explanations of natural phenomena and possibly to predict additional phenomena. The four basic stages of the scientific method are 1. gathering data through observations and experiments; 2. reducing the data to simple verbal or mathematical expressions known as natural laws; 3. offering a plausible explanation of the data through a hypothesis; 4. testing the hypothesis to make a theory that explains the hypothesis
  • 3. Matter Matter is defined as anything that occupies mass, and display space, possesses inertia. Composition refers to the component parts of a sample of matter and their relative proportions. Atom is the basic building blocks of matter Element Matter that is composed of a collection of a single type of atom is known as an element. Compound Matter composed of two or more elements is known as a compound Molecule is the smallest entity of a compound having the same proportions of the constituent atoms as does the compound as a whole
  • 4. Extensive properties depend on the amount of matter in a sample e.g. mass , volume Intensive property is independent of the amount of matter sampled, e.g. density In making a series of measurements, the degree to which the measurements agree with one another is known as the precision of the measurement the degree to which the measurement agrees with the actual value is referred to as the accuracy of the measurement. The significant figures of a number are the digits that contribute to its measurement resolution. This includes all digits except: All leading zeros
  • 5. SI Base Quantities Physical quantity Unim Length meter Mass kilogram Time second Temperature kelvin Amount of substance mole Electric current ampere Luminous intensity candela
  • 6.
  • 7. Density and Percent Composition: Density is the ratio of mass to volume. ๐ท๐‘’๐‘›๐‘ ๐‘–๐‘ก๐‘ฆ ๐‘‘ = ๐‘€๐‘Ž๐‘ ๐‘  (๐‘š) ๐‘‰๐‘œ๐‘™๐‘ข๐‘š๐‘’ (๐‘ฃ) = ๐‘” ๐‘๐‘š3 Density is a function of temperature because volume varies with temperature, whereas mass remains constant The mass of 1.000 L of water at 4 ยฐC = 1.000 kg. The density of water at 4 ยฐC = 1000 g/1000 mL = 1.0 g/mL The density of water at 20 ยฐC = ? g/ ? mL = 0.9982 g/mL the average temperature of seawater increases, the seawater will become less dense, its volume will increase, and sea level will rise even if no continental ice melts.
  • 8. Example A cube of osmium 1.000 cm on edge weighs 22.59 g. The density of osmium (the densest of the elements) is 22.59 g/m3. What would be the mass of a cube of osmium that is 1.25 in. on edge ( 1 in = 2.54 cm) ๐‘€๐‘Ž๐‘ ๐‘  ๐‘œ๐‘“ ๐‘‚๐‘ ๐‘š๐‘–๐‘ข๐‘š ๐‘ ๐‘Ž๐‘š๐‘๐‘™๐‘’ = ๐‘” = 1.25 ๐‘–๐‘› ๐‘ฅ 2.54 ๐‘๐‘š 1 ๐‘–๐‘› 3 ๐‘ฅ 22.59 ๐‘” ๐‘œ๐‘ ๐‘ ๐‘š๐‘–๐‘ข๐‘š 1๐‘๐‘š3 = = 723 g ossmium ๐‘€๐‘Ž๐‘ ๐‘  = ๐‘‰๐‘œ๐‘™๐‘ข๐‘š๐‘’ ๐‘ฅ ๐ท๐‘’๐‘›๐‘ ๐‘–๐‘ก๐‘ฆ ๐ท๐‘’๐‘›๐‘ ๐‘–๐‘ก๐‘ฆ ๐‘‘ = ๐‘€๐‘Ž๐‘ ๐‘  (๐‘š) ๐‘‰๐‘œ๐‘™๐‘ข๐‘š๐‘’ (๐‘ฃ) = ๐‘” ๐‘๐‘š3
  • 9. Example ๐ท๐‘’๐‘›๐‘ ๐‘–๐‘ก๐‘ฆ ๐‘‘ = ๐‘€๐‘Ž๐‘ ๐‘  (๐‘š) ๐‘‰๐‘œ๐‘™๐‘ข๐‘š๐‘’ (๐‘ฃ) = ๐‘” ๐‘๐‘š3 At 25 ยฐC the density of mercury, the only metal that is liquid at this temperature, is 13.5 g/cm 3. What is the volume, in mL, of 1.000 kg of mercury at 25 ยฐC. ๐‘‰๐‘œ๐‘™๐‘ข๐‘š๐‘’ ๐‘ฃ = ๐‘€๐‘Ž๐‘ ๐‘  ๐‘š ๐‘ฅ 1 ๐ท๐‘’๐‘›๐‘ ๐‘–๐‘ก๐‘ฆ (๐‘‘) = ? ๐‘š๐ฟ ๐‘š๐ฟ, ๐ป๐‘” = 1.000 ๐‘˜๐‘” ๐‘ฅ 1000 ๐‘” 1 ๐‘˜๐‘” ๐‘ฅ 1 ๐‘š๐ฟ ๐ป๐‘” 13.5 ๐‘” = 74.1 ๐‘š๐ฟ ๐ป๐‘”
  • 10. Example 1-2 Relating Mass, Volume, and Density The stainless steel in the solid cylindrical rod pictured below has a density of 7.75 g/cm3. If we want a 1.00 kg mass of this rod, how long a section must we cut off? ๐‘‘ = (๐‘š) (๐‘ฃ) ๐‘ฃ = ๐‘š ๐‘ฅ 1 ๐‘‘ ๐‘ฃ = 1.00 ๐‘˜๐‘” ๐‘ฅ 1000 ๐‘” 1 ๐‘˜๐‘” ๐‘ฅ 1 ๐‘๐‘š3 7.75 ๐‘” = ? ๐‘๐‘š3 ๐‘ฃ = ๐œ‹ ๐‘Ÿ2 ๐ฟ ๐ฟ = ๐‘ฃ ๐œ‹๐‘Ÿ2 ๐ฟ = 129 ๐‘๐‘š3 3.1416 ๐‘ฅ 0.500 ๐‘–๐‘› ๐‘ฅ 2.54 ๐‘๐‘š 1 ๐‘–๐‘› 2 = 25.5 ๐‘๐‘š3
  • 11. PRACTICE EXAMPLE A: To determine the density of trichloroethylene, a liquid used to degrease electronic components, a flask is first weighed empty (108.6 g). It is then filled with 125 mL of the trichloroethylene to give a total mass of 291.4 g. What is the density of trichloroethylene in grams per milliliter? PRACTICE EXAMPLE B: Suppose that instead of using the cylindrical rod of Example 1-2 to prepare a 1.000 kg mass we were to use a solid spherical ball of copper (d = 8.96 g/cm3). What must be the radius of this ball?
  • 12. Example 1-3 Determining the Density of an Irregularly Shaped Solid A chunk of coal is weighed twice while suspended from a spring scale. When the coal is suspended in air, the scale registers 156 g; when the coal is suspended underwater at 20 ยฐC, the scale registers 59 g. What is the density of the coal? The density of water at 20 ยฐC is 0.9982 g cm3 . If we use mwater to denote the mass of displaced water, then the volume of the displaced water is calculated as follows: ๐‘ฃ = ๐‘š๐‘Ž๐‘ ๐‘  ๐‘ค๐‘Ž๐‘ก๐‘’๐‘Ÿ ๐‘‘ = ? ๐‘๐‘š3 = 156 ๐‘” โˆ’ 59 ๐‘” 0.9982 ๐‘” ๐‘๐‘š3 = 97 ๐‘๐‘š3 The volume of the chunk of coal is the same as the volume of displaced water. ๐‘‘ = 156 ๐‘” 97 ๐‘๐‘š3 = ? = 1.6 g / cm 3
  • 13. Alternate way to solve ๐‘ฃ = ๐‘š๐‘Ž๐‘ ๐‘  ๐‘ค๐‘Ž๐‘ก๐‘’๐‘Ÿ ๐‘‘ = ? ๐‘๐‘š3 ๐‘‘ = ๐‘€๐‘Ž๐‘ ๐‘  ๐‘” ๐‘‰๐‘œ๐‘™๐‘ข๐‘š๐‘’ ๐‘๐‘š3 = ? ๐ท๐‘’๐‘›๐‘ ๐‘–๐‘ก๐‘ฆ ๐‘œ๐‘“ ๐‘‚๐‘๐‘—๐‘’๐‘๐‘ก ๐ท๐‘’๐‘›๐‘ ๐‘–๐‘ก๐‘ฆ ๐‘œ๐‘“ ๐‘ค๐‘Ž๐‘ก๐‘’๐‘Ÿ = ๐‘Š๐‘’๐‘–๐‘”โ„Ž๐‘ก ๐‘–๐‘› ๐‘ค๐‘Ž๐‘ก๐‘’๐‘Ÿ ๐‘Š๐‘’๐‘–๐‘”โ„Ž๐‘ก ๐‘–๐‘› ๐‘Ž๐‘–๐‘Ÿ โˆ’ ๐‘Š๐‘’๐‘–๐‘”โ„Ž๐‘ก ๐‘–๐‘› ๐‘ค๐‘Ž๐‘ก๐‘’๐‘Ÿ
  • 14. PRACTICE EXAMPLE A: A graduated cylinder contains 33.8 mL of water. A stone with a mass of 28.4 g is placed in the cylinder and the water level rises to 44.1 mL. What is the density of the stone?
  • 15. EXAMPLE 1-4 Using Percent Composition as a Conversion Factor A 75 g sample of sodium chloride (table salt) is to be produced by evaporating to dryness a quantity of seawater containing 3.5% sodium chloride by mass. What volume of seawater, in liters, must be taken for this purpose? Assume a density of 1.03 g/mL for seawater ๐ท๐‘’๐‘›๐‘ ๐‘–๐‘ก๐‘ฆ ๐‘‘ = ๐‘€๐‘Ž๐‘ ๐‘  (๐‘š) ๐‘‰๐‘œ๐‘™๐‘ข๐‘š๐‘’ (๐‘ฃ) = ๐‘” ๐‘๐‘š3 ๐‘‰๐‘œ๐‘™๐‘ข๐‘š๐‘’ ๐‘ฃ = [๐‘€๐‘Ž๐‘ ๐‘  ๐‘š ] ๐‘ฅ 1 [๐ท๐‘’๐‘›๐‘ ๐‘–๐‘ก๐‘ฆ ๐‘‘ ] = ? ๐‘š๐‘™ ๐ฟ ๐‘†๐‘’๐‘Ž๐‘ค๐‘Ž๐‘ก๐‘’๐‘Ÿ ๐‘ฃ = 75 ๐‘” ๐‘๐‘Ž๐ถ๐‘™ 100 ๐‘” ๐‘†๐‘’๐‘Ž๐‘ค๐‘Ž๐‘ก๐‘’๐‘Ÿ 3.5 ๐‘” ๐‘๐‘Ž๐ถ๐‘™ ๐‘ฅ 1 ๐‘š๐ฟ ๐‘†๐‘’๐‘Ž๐‘ค๐‘Ž๐‘ก๐‘’๐‘Ÿ 1.03 ๐‘” ๐‘†๐‘’๐‘Ž๐‘ค๐‘Ž๐‘ก๐‘’๐‘Ÿ ๐‘ฅ 1 ๐ฟ ๐‘†๐‘’๐‘Ž๐‘ค๐‘Ž๐‘ก๐‘’๐‘Ÿ 1000 ๐‘š๐ฟ ๐‘†๐‘’๐‘Ž๐‘ค๐‘Ž๐‘ก๐‘’๐‘Ÿ = 2.1 ๐ฟ ๐‘†๐‘’๐‘Ž๐‘ค๐‘Ž๐‘ก๐‘’๐‘Ÿ
  • 16. PRACTICE EXAMPLE A: How many kilograms of ethanol are present in 25 L of a gasohol solution that is 90% gasoline to 10% ethanol by mass? The density of gasohol is 0.71 g/mL PRACTICE EXAMPLE B: Common rubbing alcohol is a solution of 70.0% isopropyl alcohol by mass in water. If a 25.0 mL sample of rubbing alcohol contains 15.0 g of isopropyl alcohol, what is the density of the rubbing alcohol?

Editor's Notes

  1. Newton's law of universal gravitation: F = attraction= G [( m1 m2)/ r2] .
  2. The International System of Units (SI, abbreviated from the French Systรจme international = metric system
  3. if we know the density of an object, we can use density as a conversion factor to determine the object s mass or volume
  4. the radius of the rod = one-half the diameter