Unit, of measurement

An example of the exponential function is in the decay of radioactive isotopes. If A o is the number of atoms of the isotope at time r = 0, the number at any other time, t, is given by 

A certain population is growing exponentially and doubles in size each 30 years. 

A reactant in a first-order chemical reaction without back reaction has a concentration governed by die same formula as radioactive decay, 

The measurement of a length or other variable would be impossible without a standard definition of the unit of measurement. For many years science and commerce were hampered by the lack of accmately defined units of measurement. This problem has been largely overcome by precise measurements and international agreements. The internationally accepted system of units of measurements is called the Systeme International d Unites, abbreviated SI. This is an MKS system, which means that length is measured in meters, mass in kilograms, and time in seconds. In 1960 the international chemical commimity agreed to use SI units. 

SI base units (units with independent definitions) 

The basic unit of mass in the SI system is the kilogram (Table 1-7). The kilogram is defined as the mass of a platinum-iridium cylinder stored in a vault in Sevres, near Paris, France. A 1-lb object has a mass of 0.4536 kg. The basic mass unit in the earlier metric system was the gram. A U.S. five-cent coin (a nickel ) has a mass of about 5 g. 

The meter is the standard nnit of length (distance) in both SI and metric systems. The meter is defined as the distance light travels in a vacuum in 1/299,792,468 second. It is approximately 39.37 inches. In situations in which the English system would use inches, the 

OAtfiple-beam balance used for determining mass to about 0,01 g 

0 A modern eiectronic top-ioading baiance that gives a direct readout ot mass to 0.001 g 

O A modern anaiytical balance that can be used to determine mass to 0.0001 g. Anaiyticai baiances are used when masses must be determined as preciseiy as possibie. 

The unit of measurement for radioactivity in the international system of measurement is the bequerel, defined as 1 decay s , corresponding to 60 decays/min. The previous unit. Curie (Ci), is also still in use to some extent today  

for example, nCi is converted into Bq by multiplying the value of nCi by 37. 

Radio-chemical decay takes place according to statistical laws. It cannot 

A radionuclide decays in a reaction of the first order, whereby the radioactive decay can be described by an exponential function. Of the nuclei 

As criterion for the rate of decay of a radionuclide, the half-life is defined as that time in which half of the radioactive nuclei originally present have decayed 

An older unit of measurement used to express the con-centfation of electrolytes in plasma is the milliequivalent (mEq), which is one thousandth of an equivalent. 

MiUigrams per 100 mL (deciliter) can be converted to mEq per liter using the following formula  

Example If the serum sodium concentration is 322 mg/dL, then the serum contains 3220 mg/L. The equivalent mass of sodium is 23, and the valence is 1 therefore  

The recommended units for sodium concentration in plasma are millimoles per liter (mmol/L). In the previous example, the concentration of sodium is  

In chemical terms, the titer of a solution is the mass of a substance equivalent to a unit volume of the solution. 

IBLG See questions from Uncertainty, Measurement, and Calculations  

Making observations is fundamental to aU science. A quantitative observation, or measurement, always consists of two parts a number and a scale (called a unit). Both parts must be present for the measurement to be meaningful. 

Most scientists in all countries have used the metric system for many years. In I960, an international agreement set up a system of units called the International System (le Systeme International in French), or the SI system. This system is based on the metric system and units derived from the metric system. The fundamental SI units are listed in Table 1.1. We will discuss how to manipulate these units later in this chapter. 

Unless otherwise noted, all arton this page is O Cengage Learning 2014. 

How important are conversions from one unit to another If you ask the National Aeronautics and Space Administration (NASA), very important In 1999, NASA lost a 125 million Mars Climate Orbiter because of a failure to convert from English to metric units. 

Chemistry and measurements are an important part of our everyday lives. Levels of toxic mate rials in the air, soil, and water are discussed in our newspapers. We read about radon gas in our homes, holes in the ozone layer, trans fatty acids, and climate change. Understanding chemistry and measurement helps us make proper choices about our world. 

Think about your day. You probably took some measurements. Perhaps you checked your weight by stepping on a bathroom scale. If you made some rice for dinner, you added two cups of water to one cup of rice. If you did not feel well, you may have taken your temperature. Whenever you take a measurement, you 

Write the names and abbreviations for the metric or SI units used in measurements of length, volume, mass, temperature, and time. 

Scientists and health professionals throughout the world use the metric system of measurement. It is also the common measuring syston in all but a few countries in the worid. The International System of Units (SI), or Systone hitemalional, is the official system of measurement throughout the world except for the United States. In chemistry, we use metric units and SI units for length, volume, mass, tanpeiatuie, and time, as listed in Table 2.1. 

FIGURE 2.1 Length in the metric (SI) system is based on the meter, which is slightly longer than a yard. How many centimeters are in a length of 1 inch  

Many properties of matter are quantitative, that is, associated with numbers. When a number represents a measured quantity, the units of that quantity must be specified. To 

The metric system, developed in France during the late eighteenth century, is used as the system of measurement in most countries. The United States has traditionally used the English system, although use of the metric system has become more common ( 4 FIGURE 1.15). 

In spite of the landmark achievements of Einstein s theory, scientists can never say the theory is proven. A theory that has excellent predictive power today may not work as well in the future as more data and improved scientific equipment are developed. Thus, 

Eventually, we may be able to tie together a great number of observations in a scientific law, which is a concise verbal statement or mathematical equation that summarizes a broad variety of observations and experiences. We tend to think of scientific laws as the basic rules under which nature operates. However, it is not so much that matter obeys these laws, but rather that these laws describe the behavior of matter. As we proceed through this text, we will rarely have 

Formulate and test hypotheses to explain patterns and trends 

The text has employed, as far as possible, the internationally accepted units of the Systeme International d Unites (SI Units). Some of the source material, however, was expressed in other units and has been quoted as such. This appendix shows the connections and lists the standard prefixes of size. 

The effective dose in sievert is the physical dose in gray multiplied by modifying factors, the most important of which is the quality factor expressing the relative biological effectiveness compared to gamma radiation (see Appendix 1). 

Foo-Sun Lau, A Dictionary of Nuclear Power and Waste Management, Research Studies Press (Wiley), 1987. 

Summary of Significant Dates and Timing Relevant to the Chernobyl 

1 Selected events prior to the Chernobyl-4 accident 1948-1952 Harwell/Risley, UK Evaluation work on graphite moderated, carbon dioxide-cooled 

Because the fundamental units are not always convenient (expressing the mass of a pin in kilograms is awkward), prefixes are used to change the size of the unit. These are listed in Table 1.2. Some common objects and their measurements in SI units are listed in Table 1.3. 

One physical quantity that is very important in chemistry is volume, which is not a fundamental SI unit but is derived from length. A cube that measures 1 meter (m) on each edge is represented in Fig. 1.5. This cube has a volume of (1 m) = 1 m Recognizing that there are 10 decimeters (dm) in a meter, the volume of this cube is (1 m) = (10 dm) = 1000 dm A cubic decimeter, that is (1 dm) is commonly called a liter (L), which is a unit of volume slightly larger than a quart. As shown in Fig. 1.5, 1000 liters are contained in a cube with a volume of 1 cubic meter. Similarly, since 1 decimeter equals 10 centimeters (cm), the liter can be divided into 1000 cubes each with a volume of 1 cubic centimeter  

Thus 1 liter contains 1000 cubic centimeters, or 1000 milliliters. 

You probably know your height in feet and inches. Most people outside the United States, however, measure height in meters and centimeters. The system of standard units that includes the meter is called the metric system. Scientists today use a revised form of the metric system called the SystSme Internationale d Unit6s, or SI. 

SI is based on a decimal system. So are the prefixes in Table 2-2, which are used to extend the range of SI units. 

Prefix Symbol Factor Scientific notation Example 

1-g ice cube raises the level of water in a 10-mL graduated cylinder 1.2 mL. What is the density of the ice cube  

To find the ice cube s density, divide its mass by the volume of water it displaced and solve. 

Chemistry and physics are experimental sciences, based on measurements. Our characterization of molecules (and of everything else in the universe) rests on observable physical quantities, expressed in units that ideally would be precise, convenient and reproducible. These three requirements have always produced trade-offs. For example, the English unit of length inch was defined to be the length of three barleycorns laid end to end—a convenient and somewhat reproducible standard for an agricultural society. When the metric system was developed in the 1790s, the meter was defined to be 

000 of the best current estimate of distance from the equator to the North Pole along the Prime Meridian. Unfortunately, this definition was not convenient for calibrating meter sticks. The practical definition was based on the distance between two scratches on a platinum-iridium bar. This bar was termed the primary standard. Copies (secondary standards) were calibrated against the original and then taken to other laboratories. 

The most important modem system of units is the SI system, which is based around seven primary units time (second, abbreviated s), length (meter, m), temperature (Kelvin, K), mass (kilogram, kg), amount of substance (mole, mol), current (Amperes, A) and luminous intensity (candela, cd). The candela is mainly important for characterizing radiation sources such as light bulbs. Physical artifacts such as the platinum-iridium bar mentioned above no longer define most of the primary units. Instead, most of the definitions rely on fundamental physical properties, which are more readily reproduced. For example, the second is defined in terms of the frequency of microwave radiation that causes atoms of the isotope cesium-133 to absorb energy. This frequency is defined to be 9,192,631,770 cycles per second (Hertz) —in other words, an instrument which counts 9,192,631,770 cycles of this wave will have measured exactly one second. Commercially available cesium clocks use this principle, and are accurate to a few parts in 1014. 

In principle, Avogadro s number could be used to eliminate the standard kilogram mass. We could define Avogadro s number to be exactly 6.0221367 x 1023, then define. 012 kg as the mass of one mole of carbon-12. However, we can determine the mass of a metal weight with more accuracy than we can count this large number of atoms. 

All other physical quantities have units that are combinations of the primary units. Some of these secondary units have names of their own. The most important of these for our purposes are listed in Table 1.1. 

Many properties of matter are quantitative, that is, associated with numbers. When a number represents a measured quantity, the units of that quantity must be specified. To say that the length of a pencil is 17.5 is meaningless. Expressing the number with its units, 17.5 centimeters (cm), properly specifies the length. The units used for scientific measurements are those of the metric system. 

Where does scientific knowledge come from How is it acquired How do we know it is reliable How do scientists add to it, or modify it  

As more information is gathered, the initial hypotheses get winnowed down. Eventuahy just one may stand out as most consistent with a body of accumulated evidence. We then begin to caU this 

When nature behaves in a certain way over and over again, under all sorts of different conditions, we can summarize that behavior in a scientific law. For example, it has been repeatedly observed that in a chemical reaction there is no change in the total mass of the materials reacting as compared with the materials that are formed we call this observation the Law of Conservation of Mass. It is important to make a distinction between a theory and a scientific law. The latter simply is a statement of what always 

Collect information via observations of natural phenomena and experiments 

Suppose you get an e-mail from a friend who lives in Canada. Your friend complains that it has been too hot lately to play soccer or ride a hike. The high temperature each day has been about 35. You think that this figure must be wrong because a temperature of 35 is cold, not hot. Actually, 35 can he either hot or cold depending on which temperature units are used. For a measurement to be useful, it must include both a number and a unit. 

For people born in the United States, the mile is a familiar unit. People in most other countries measure distances in kilometers. Kilometers and miles are units of length in different measurement systems. 

The system that includes kilometers is the system used by scientists worldwide. 

How many miles apart are Baker and Barstow Which is longer, a mile or a kilometer  

A star s temperature and size determine its brightness, or luminous intensity. The SI base unit for luminous intensity is the candela. The more massive a star and the hotter its temperature, the brighter the star will be. How bright a star appears from Earth can be misleading because stars are at different distances from Earth. Light spreads out as it travels from its source. Thus, distant stars will appear less bright than stars of equal intensity that are closer to Earth. 

Fraction Prefix Symbol Multiple Prefix Symbol 

The common units of time, texts, the angular degree. such as hour or year, will persist, and also, in appropriate con-  

EXAMPLES OF UNITS CONTRARY TO IS, WITH THEIR EQUIVALENTS  

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The determination of equilibria is done theoretically via the calculation of free energies. In practice, the concept of fugacity is used for which the unit of measurement is the bar. The equation linking the fugacity to the free energy is written as follows >... 

Imagine that you find the following instructions in a laboratory procedure Transfer 1.5 of your sample to a 100 volumetric flask, and dilute to volume. How do you do this Clearly these instructions are incomplete since the units of measurement are not stated. Compare this with a complete instruction Transfer 1.5 g of your sample to a 100-mL volumetric flask, and dilute to volume. This is an instruction that you can easily follow. 

The standard unit of measure for refrigeration capacity is known as the refrigeration ton. It represents the amount of heat that must be removed from a short ton (909 kg) of water to form ice ia 24 h. Its value is 3.51 kWt (12,000 Btu/h(= 12.7 MJ/h)). It is conventional to designate a kilowatt of refrigeration as a thermal kilowatt (kWt) to distiaguish it from the amount of electricity (kWe) required to produce the refrigeration. 

To understand permeabiUty or barrier property values, it is necessary to define the units of measure. These units are compHcated and many different sets of units are ia common use. Furthermore, from time to time the units of permeabiUty are presented ia confused or iacorrect fashion ia the Hterature. 

Select the units of measurement for iaput data and output reports. 

Material costs are conveniently presented in tables that give the following name of material, form and grade, method of dehveiy, unit of measure, cost per unit, source of cost, annual consumption, annual cost, fractional consumption per unit of production, and cost per unit of production. 

To express the quantity of energt available in the lit]iiid entering into the pump, the unit of measure for NPSH is feet of head or elevation in the pump suction. The pump has its NPSHr, or Net Positive Suction Head Required. The system, meaning all pipe, tanks and connections on the suction side of the pump has the NPSHa, or the Net Positive Suction Head Available. There should always be more NPSHa in the system dian the NPSHr of the pump. Let s look at them, beginning with what the pump recgiires ... 

Composition by mol%, volume %, or weight %. To what extent does composition vary Corrosive effects. Limits to discharge temperature, which may cause problems with the gas. Quantity to Be Handled, for Each Stage Stage quantity and unit of measurement. 

Make sure to standardize units of measurement (liters, tons, or kilograms) on a per-day, per-year, or per-batch basis. Finally, summarize the measured values in standard units by referring to your process flow sheets (it may have been necessary to modify your process flow sheets following the in-plant assessment). 

Micrometer a unit of length equal to one millionth of a meter the unit of measure for particle size. 

For the dimensions on the LHS of this expression to satisfy the RHS, the exponents on the principal units of measure must be equal. Thus, we have the following system of three equations (corresponding to the number of values with independent dimensions) ... 

Mathematica alsoprovidesaspecialpackagefortheinterconversionof units of measure. To accessthisfunctionalityofthesoftwareweneedtoloadthepackagenamed Miscellaneous... 

Systematic error, as stated above, can be eliminated— not totally, but usually to a sufficient degree. This elimination process is called calibration. Calibration is simply a procedure where the result of measurement recorded by an instrument is compared with the measurement result of a standard. A standard is a measuring device intended to define, to represent physically, to conserve, or to reproduce the unit of measurement in order to transmit it to other measuring instruments by comparison. There are several categories of standards, but, simplifying a little, a standard is an instrument with a very high accuracy and can for that reason be... 

Rem (Rbntgen equivalent man) The unit of measure of the radiation dose to the internal tissues. 

Establish a specification for the parameter to be controlled which provides limits of acceptability and units of measure. 

Importance also applies to what may appear minor decisions in the planning or design phase. If such decisions are incorrect they could result in major problems downstream. If not detected, getting the decimal place wrong or the units of measure wrong can have severe consequences. Audits should verify that the appropriate controls are in place to detect such errors before it is too late. 

Mess-einheit, /. unit of measurement, -eln-teilung, /. graduation. 

Metric Units of Measiu ement. For the purpose of this Code, metric units of measurement are in accordance with the modernized metric system known as the International System of Units (SI). 

As illustrated in Figure 43.11, the peak-to-peak amplitude (2A, where A is the zero-to-peak) reflects the total amplitude generated by a machine, a group of components, or one of its components. This depends on whether the data gathered is broadband, narrowband, or component. The unit of measurement is useful when the analyst needs to know the total displacement or maximum energy produced by the machine s vibration profile. 

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