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5.1: Measurement Systems

  • Page ID
    49890
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    Skills to Develop

    • State the different measurement systems used in chemistry.
    • Describe how prefixes are used in the metric system and identify how the prefixes milli-, centi-, and kilo- compare to the base unit.
    • Explain the difference between mass and weight.
    • Identify SI units of mass, distance (length), volume, temperature, and time.
    • Describe absolute zero.

    Even in ancient times, humans needed measurement systems for commerce. Land ownership required measurements of length and the sale of food and other commodities required measurements of mass. Mankind's first elementary efforts in measurement required convenient objects to be used as standards and the human body was certainly convenient. The names of several measurement units reflect these early efforts. Inch and foot are examples of measurement units that are based on parts of the human body. The inch is based on the width of a man's thumb, and the foot speaks for itself.

    It should be apparent that measurements of a foot by two people could differ by a few inches. To achieve more consistency, everyone could use the king's foot as the standard. The length of the king's foot could be marked on pieces of wood and everyone who needed to measure a length could have a copy. Of course, this standard would change when a new king was crowned. What was needed were objects that could be safely stored so they didn't change over time. Copies would be made of these objects and distributed so that everyone was using exactly the same units of measure. The requirements of science in the 1600's, 1700's, and 1800's necessitated even more accurate, reproducible measurements.

    The Metric System

    The metric system is an international decimal-based system of measurement. Because the metric system is a decimal system, making conversions between different units of the metric system are always done with factors of ten. Let's consider the English system - that is, the one that is in everyday use in the US - to explain why the metric system is so much easier to manipulate. For instance, if you need to know how many inches are in a foot, you only need to remember what you at one time memorized: 12 inches \(=\) 1 foot. But now you need to know how many feet are in a mile. What happens if you never memorized this fact? Of course you can look it up online or elsewhere, but the point is that this fact must be given to you, as there is no way for you to derive it our yourself. This is true about all parts of the English system: you have to memorize all the facts that are needed for different measurements.

    Metric Prefixes and Equivalents

    The metric system uses a number of prefixes along with the base units. A base unit is one that cannot be expressed in terms of other units. The base unit of mass is the gram (\(\text{g}\)), that of length is the meter (\(\text{m}\)), and that of volume is the liter (\(\text{L}\)). Each base unit can be combined with different prefixes to define smaller and larger quantities. When the prefix centi- is placed in front of gram, as in centigram, the measure is now \(\frac{1}{100}\) of a gram. When milli- is placed in front of meter, as in millimeter, the measure is now \(\frac{1}{1000}\) of a meter.

    Common prefixes are shown in the table:

    CK12 Screenshot 5-1-1.png

    ​​These prefixes are used for all metric units of measurement, including units for volume, time, distance, etc. Common metric units, symbols, and relationships to a base unit are shown below.

    \[\begin{array}{rcccl} 1 \: \text{micrometer} & = & 1 \: \mu \text{m} & = & 1 \times 10^{-6} \: \text{m} \\ 1 \: \text{microliter} & = & 1 \: \mu \text{L} & = & 1 \times 10^{-6} \: \text{L} \\ 1 \: \text{kilometer} & = & 1 \: \text{km} & = & 1 \times 10^3 \: \text{m} \\ 1 \: \text{kilogram} & = & 1 \: \text{kg} & = & 1 \times 10^3 \: \text{g} \end{array}\]

    SI Units

    The International System of Units, abbreviated SI from the French Le Systeme International d'Unites, is the main system of measurement units used in science. Since the 1960's, the International System of Units has been internationally agreed upon as the standard metric system. The SI base units are based on physical standards. The definitions of the SI base units have been and continue to be modified and new base units added as advancements in science are made. Each SI base unit except the kilogram is describe by stable properties of the universe.

    MassCK12 Screenshot 5-1-2.png

    Mass and weight are not the same thing. Although we often use the terms mass and weight interchangeably, each one has a specific definition and usage. The mass of an object is a measure of the amount of matter in it. The mass (amount of matter) of an object remains the same regardless of where the object is placed. For example, moving a brick to the moon does not cause any matter in it to disappear or be removed.

    The weight of an object is the force of attraction between the object and the earth (or whatever large body it is resting on). We call this force of attraction the force of gravity. Since the force of gravity is not the same at every point on the earth's surface, the weight of an object is with respect to the Earth or other gravity-producing object. For example, a man who weighs 180 pounds on Earth would weigh only 45 pounds if he were in a stationary position 4,000 miles above the Earth's surface. This same man would weigh only 30 pounds on the moon because theCK12 Screenshot 5-1-3.png moon's gravity is only one-sixth that of Earth. The mass of this man, however, would be the same in each situation because the amount of matter in him is constant. Consistency requires that scientists use mass and not weight in its measurements of the amount of matter.

    The basic unit of mass in the International System of Units is the kilogram. A kilogram is equal to 1000 grams. A gram is a relatively small amount of mass and so larger masses are often expressed in kilograms. When very tiny units of matter are measured, we often use milligrams, which are equal to 0.001 grams. There are numerous larger, smaller, and intermediate mass units that may also be appropriate.

    At the end of the 18\(^\text{th}\) century, a kilogram was the mass of a liter of water. In 1889, a new international prototype of the kilogram was made of a platinum-iridium alloy. The kilogram is equal to the mass of this international prototype, which is held in Paris, France.

    Length

    Length is the measurement of anything from end to end. In science, length usually refers to how long an object is. There are many units and sets of standards used in the world for measuring length. The ones familiar to you are probably inches, feet, yards, and CK12 Screenshot 5-1-4.pngmiles. Most of the world, however, measures distances in meters and kilometers for longer distances, and centimeters and millimeters for shorter distances. For consistency and ease of communication, scientists around the world have agreed to use the SI system of standards regardless of the length standards used by the general public.

    The SI unit of length is the meter. In 1889, the definition of the meter was a bar of platinum-iridium alloy stored under conditions specified by the International Bureau of Standards. In 1960, this definition of the standard meter was replaced by a definition based on a wavelength of krypton-86 radiation. In 1983, that definition was replaced by the following: the meter is the length of the path traveled by light in a vacuum during a time interval of \(\frac{1}{299,792,458}\) of a second.

    VolumeCK12 Screenshot 5-1-5.png

    The volume of an object is the amount of space it takes up. In the SI system, volume is a derived unit, that is, it is based on another SI unit. In the case of volume, a cube is created with each side of the cube measuring 1.00 meter. The volume of this cube is \(1.0 \: \text{m} \cdot 1.0 \: \text{m} \cdot 1.0 \: \text{m} = 1.0 \: \text{m}^3\) or one cubic meter. The cubic meter is the SI unit of volume. The cubic meter is a very large unit and is not very convenient for most measurements in chemistry. A more common unit is the liter (\(\text{L}\)) which is \(\frac{1}{1000}\) of a cubic meter. Another commonly used volume measurement is the milliliter, which is equal to \(\frac{1}{1000}\) of a liter.

    Temperature

    When used in a scientific context, the words heat and temperature do NOT mean the same thing. Temperature represents the average kinetic energy of the particles that make up a material. Increasing the temperature of a material increases its thermal energy. Thermal energy is the sum of the kinetic and potential energy in the particles that make up a material. Objects to not "contain" heat; rather they contain thermal energy. Heat is the movement of thermal energy from a warmer object to a cooler object. When thermal energy moves from one object to another, the temperature of both objects change.

    A thermometer is a device that measures temperature. The name is made up of "thermo" which means heat and "meter" which means to measure. The temperature of a substance is directly proportional to the average kinetic energy it contains. In order for the average kinetic energy and temperature of a substance to be directly proportional, it is necessary that when the temperature is zero, the average kinetic energy must also be zero. This is not true with either Fahrenheit or Celsius temperature scales. Most of us are familiar with temperatures that are below the freezing point of water. It should be apparent that even though the air temperature may be \(-5^\text{o} \text{C}\), the molecules of air are still moving. Substances like oxygen gas and nitrogen gas have already melted and boiled to vapor at temperatures below \(-150^\text{o} \text{C}\).

    It was necessary for use in calculations in science for a third temperature scale in which zero degrees corresponds with zero kinetic energy, that is, the point where molecules cease to move. This temperature scale was designed by Lord Kelvin. Lord Kelvin stated that there is no upper limit of how hot things can get, but there is a limit as to how cold things can get. Kelvin developed the idea of Absolute Zero, which is the temperature at which molecules stop moving and therefore, have zero kinetic energy. The Kelvin temperature scale has its zero at absolute zero (determined to be \(-273.15^\text{o} \text{C}\)), and uses the same size degree as the Celsius scale. Therefore, the mathematical relationship between the Celsius scale and the Kelvin scale is \(\text{K} \: = \: ^\text{o} \text{C} + 273\). In the case of the Kelvin scale, the degree sign is not used. Temperatures are expressed, for example, simply as \(450 \: \text{K}\).

    Time

    The SI unit for time is the second. The second was originally defined as a tiny fraction of the time required for Earth to orbit the Sun. It has since been redefined several times. The definition of a second (established in 1967 and reaffirmed in 1997) is: the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium-133 atom.

    Summary

    • The metric system is an international decimal-based system of measurement.
    • The metric system uses a number of prefixes along with the base units.
    • The prefixes in the metric system are multiples of 10.
    • The International System of Units, abbreviated SI from the French Le Systeme International d'Unites is, since the 1960's, internationally agreed upon as the standard metric system.
    • The mass of an object remains the same regardless of where the object is placed.
    • The basic unit of mass in the International System of Units is the kilogram.
    • The SI unit of length is the meter.
    • Temperature represents the average kinetic energy of the particles that make up a material.
    • Absolute Zero is the temperature at which molecules stop moving and therefore, have zero kinetic energy.
    • The Kelvin temperature scale has its zero at absolute zero (determined to be \(-273.15^\text{o} \text{C}\)), and uses the same size degree as the Celsius scale.
    • The mathematical relationship between the Celsius scale and the Kelvin scale is \(\text{K} \: = \: ^\text{o} \text{C} + 273\).
    • The SI unit for time is the second.

    Vocabulary

    • Metric system: An international decimal-based system of measurement.
    • International System of Units (Le Systeme International d'Unites): The internationally agreed upon standard metric system.
    • Mass: A measure of the amount of matter in an object.
    • Weight: The force of attraction between an object and the earth (or whatever large body it is resting one).
    • Temperature: The average kinetic energy of the particles that make up a material.
    • Absolute Zero: The temperature at which molecules stop moving and therefore, have zero kinetic energy.

    Contributors


    5.1: Measurement Systems is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by LibreTexts.

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