Introductory Chemistry: A Foundation  Zumdahl S.S., DeCoste D.J. 2019
Measurements and Calculations
Measurements of Length, Volume, and Mass
Objective
· To understand the metric system for measuring length, volume, and mass.
The fundamental SI unit of length is the meter , which is a little longer than a yard . In the metric system, fractions of a meter or multiples of a meter can be expressed by powers of , as summarized in Table 2.3.
Table 2.3. The Metric System for Measuring Length
Unit 
Symbol 
Meter Equivalent 
kilometer 
km 
m or m 
meter 
m 
m 
decimeter 
dm 
m or m 
centimeter 
cm 
m or m 
millimeter 
mm 
m or m 
micrometer 
m or m 

nanometer 
nm 
m or m 
The English and metric systems are compared on the ruler shown in Fig. 2.1. Note that
Figure 2.1.
Comparison of English and metric units for length on a ruler.
Other English—metric equivalencies are given in Section 2.6.
Volume is the amount of threedimensional space occupied by a substance. The fundamental unit of volume in the SI system is based on the volume of a cube that measures meter in each of the three directions. That is, each edge of the cube is meter in length. The volume of this cube is
or, in words, cubic meter.
In Fig. 2.2 this cube is divided into smaller cubes. Each of these small cubes represents a volume of , which is commonly called the liter (rhymes with “meter” and is slightly larger than a quart) and abbreviated L.
Figure 2.2.
The largest drawing represents a cube that has sides m in length and a volume of . The middlesize cube has sides dm in length and a volume of , or L. The smallest cube has sides cm in length and a volume of , or mL.
Chemistry in Focus Measurement: Past, Present, and Future
Measurement lies at the heart of doing science. We obtain the data for formulating laws and testing theories by doing measurements. Measurements also have very practical importance; they tell us if our drinking water is safe, whether we are anemic, and the exact amount of gasoline we put in our cars at the filling station.
Although the fundamental measuring devices we consider in this chapter are still widely used, new measuring techniques are being developed every day to meet the challenges of our increasingly sophisticated world. For example, engines in modern automobiles have oxygen sensors that analyze the oxygen content in the exhaust gases. This information is sent to the computer that controls the engine functions so that instantaneous adjustments can be made in spark timing and air—fuel mixtures to provide efficient power with minimum air pollution.
A recent area of research involves the development of paperbased measuring devices. For example, the nonprofit organization Diagnostics for All (DFA) based in Cambridge, Massachusetts, has invented a paperbased device to detect proper liver function. In this test, a drop of the patient’s blood is placed on the paper, and the resulting color that develops can be used to determine whether the person’s liver function is normal, worrisome, or requires immediate action. Other types of paperbased measuring devices include one used to detect counterfeit pharmaceuticals and another used to detect whether someone has been immunized against a specific disease. Because these paperbased devices are cheap, disposable, and easily transportable, they are especially useful in developing countries.
Scientists are also examining the natural world to find supersensitive detectors because many organisms are sensitive to tiny amounts of chemicals in their environments—recall, for example, the sensitive noses of bloodhounds. One of these natural measuring devices uses the sensory hairs from Hawaiian red swimming crabs, which are connected to electrical analyzers and used to detect hormones down to levels of g/L. Likewise, tissues from pineapple cores can be used to detect tiny amounts of hydrogen peroxide.
These types of advances in measuring devices have led to an unexpected problem: detecting all kinds of substances in our food and drinking water scares us. Although these substances were always there, we didn’t worry so much when we couldn’t detect them. Now that we know they are present, what should we do about them? How can we assess whether these trace substances are harmful or benign? Risk assessment has become much more complicated as our sophistication in taking measurements has increased.
See Problems 2.157 and 2.158
The cube with a volume of ( liter) can in turn be broken into smaller cubes, each representing a volume of . This means that each liter contains . One cubic centimeter is called a milliliter (abbreviated mL), a unit of volume used very commonly in chemistry. This relationship is summarized in Table 2.4.
Table 2.4. The Relationship of the Liter and Milliliter
Unit 
Symbol 
Equivalence 
liter 
L 

milliliter 
mL 
The graduated cylinder (Fig. 2.3), commonly used in chemical laboratories for measuring the volume of liquids, is marked off in convenient units of volume (usually milliliters). The graduated cylinder is filled to the desired volume with the liquid, which then can be poured out.
Figure 2.3.
A mL graduated cylinder.
Another important measurable quantity is mass , which can be defined as the quantity of matter present in an object. The fundamental SI unit of mass is the kilogram .
Because the metric system, which existed before the SI system, used the gram as the fundamental unit, the prefixes for the various mass units are based on the gram , as shown in Table 2.5.
Table 2.5. The Most Commonly Used Metric Units for Mass
Unit 
Symbol 
Gram Equivalent 
kilogram 
kg 

gram 
g 
g 
milligram 
mg 
In the laboratory we determine the mass of an object by using a balance. A balance compares the mass of the object to a set of standard masses (“weights”). For example, the mass of an object can be determined by using a singlepan balance (Fig. 2.4).
Figure 2.4.
METTLER TOLEDO
An electronic analytical balance used in chemistry labs.
To help you get a feeling for the common units of length, volume, and mass, some familiar objects are described in Table 2.6.
Table 2.6. Some Examples of Commonly Used Units
length 
A dime is mm thick. A quarter is cm in diameter. The average height of an adult man is m. 
mass 
A nickel has a mass of about g. A lb woman has a mass of about kg. 
volume 
A oz can of soda has a volume of about mL. A half gallon of milk is equal to about L of milk. 