## Contents

## Lesson ObjectivesEdit

- Define qualitative and quantitative observations.
- Distinguish between qualitative and quantitative observations.
- Use quantitative observations in measurements.
- State the different measurement systems used in chemistry.
- State the different prefixes used in the metric system.
- Do unit conversions.
- Use scientific notation and significant figures.
- Use basic calculations and dimensional analysis.
- Use mathematical equations in chemistry.

## Qualitative and Quantitative ObservationsEdit

One of the steps in the scientific method is observation. Observation involves recording data about the phenomenon we wish to investigate. There are two different types of observations which are called qualitative and quantitative. Qualitative observations are those involving words only while quantitative observations are those involving both words and numbers. Although all the observations we can make on a phenomenon are valuable, quantitative observations are more helpful than qualitative. Qualitative observations are somewhat more vague in nature because they involve comparative terms.

A qualitative observation would be "The attendance clerk is a small woman". If the observer was 6 feet 4 inches tall, he/she might refer to a woman who is 5 feet 8 inches tall as "small". But if the observer reported this observation to a person who was 5 feet 2 inches tall, the listener would not acquire a good idea of the height of the attendance clerk because they would not think that a woman who is 5 feet 8 inches tall was small (Figure 2.1).

The description "a small woman" could refer to any woman whose height was between 2 feet and 6 feet tall depending on who did the observing. Similarly, "a small car" could refer to anything from a compact car to a child's toy car. The word small is a comparative term. The same is true of words like tall, fast, slow, hot, and cold. These words do not have exact meanings.

Quantitative observations on the other hand, have numbers and units associated with them and are, therefore, more exact (Table 2.1). Even if the number is only an estimate, it is more valuable than no number at all.

Qualitative (words only) | Quantitative (words and numbers) |
---|---|

The girl has very little money. | The girl has 85 cents. |

The man was short. | The man was 5 feet 2 inches tall. |

Use a small test tube. | Use a test tube less than 12 cm long. |

It is a short walk to my house. | It is about 1 mile to my house. |

You can see that even if the number is an estimate, a quantitative observation contains more information because of the number associated with the observation. (Some people might not think that a walk of one mile was short even though the speaker in the above case did. If an actual measuring instrument is not available, the observer should always try to estimate a measurement so the observation will have a number associated with it.

While estimated measurements may not be accurate, they are valuable because they establish an approximate size for observations. The observation, "The car is small", provides us with certain information. We know that the object is some kind of automobile (perhaps real, perhaps a toy) and we know that it is probably smaller than a limousine because almost no one would describe a limousine as “small”. Suppose instead, the observation had been, "The car is about 3 feet tall, 3 feet long, and 2 feet wide". While these estimated measurements cannot be considered to be accurate, we now know that we are not dealing with a compact automobile nor are we dealing with a toy car like Hot Wheels. With these estimated measurements, we know we are dealing with a car that is about the size of a tricycle. If we discover later that the car was actually 2 feet high instead of 3 feet high, it is not a problem because we knew the original observation was an estimate since it contained the word "about". Estimates are excellent observations if we do not have the ability to actually measure the object. Estimated measurements qualify as quantitative observations.

Here is some information you may find helpful in making estimated observations. The distance from the top of your index finger to the first knuckle is about one inch. The entire index finger is about three inches long. Your foot is probably between eight and twelve inches long. Your height is probably between five and six feet. The distance from your wrist to your elbow is about one foot. A twenty-five cent coin is about one inch across and dollar bills are about 2.5 inches wide and about six inches long (Figure 2.2).

In science, accurate quantitative observations are a great deal more useful than qualitative observations. When we speak about accurate quantitative measurements, we are essentially referring to measurements. Accurate measurements are vital to science. There are many measurement systems used in the world but only one that is used consistently in science. That system is called the International System of Units and is abbreviated as SI units. You are probably already familiar with part of the SI system because part of the SI system is called the Metric System.

## Mass and Its SI UnitEdit

When you step on a bathroom scale, you are most likely thinking that about determining your *weight*, right? You probably aren't wondering if you have gained mass. Is it okay then to use either term?

Although we often use mass and weight interchangeably, each one has a specific definition and usage. The *mass* of an object does not change; whether the object is on the earth's equator, on top of Mt. Everest, or in outer space, the mass will always be the same. Because mass measures how much matter the object contains, it has to be a constant value.

Weight, on the other hand, is a measure of the *force* with which an object is attracted to the earth or body upon which it is situated. Since the force of gravity is not the same at every point on the earth's surface, the weight of an object is not constant. For example, an object weighing 1.00000 lb in Panama weighs 1.00412 lb in Iceland. For large objects this difference may not be significant. However, since we will often be working with extremely tiny pieces of matter – atoms, molecules, etc. – we need to use mass and not weight.

The basic unit of mass in the International System of Units (SI comes from the French name, *Systeme Internationale*) is the gram. A gram is a relatively small measurement compared to, for instance, one pound. 454 grams equals one pound. While pounds are helpful in measuring the mass of a package that needs to be mailed, grams are much more useful in science.

One gram is equal to 1, 000 milligrams or 0.001 kilogram; there are numerous intermediate measurements between each of these mass units as well as ones that are even larger and smaller that may be appropriate to the application at hand. These will be discussed in more detail in a later section.

## Length and its SI UnitEdit

When the four minute mile was achieved on May 6, 1954 by Roger Bannister, it was an international sensation. Today, many runners have broken that record. Only a few countries measure length or distance using miles, feet, or inches. For instance, if you live in the US, you probably know your height in feet and inches, right? Or, if there is a mountain or even a hill near where you live, you probably know its height in feet. And when you discuss how far school is from your home, you probably try to figure out the distance in miles.

However, most of the world measures distances in meters and kilometers; for shorter lengths, millimeters and centimeters will be used. For a student in Germany, she will state how many kilometers her school is from home, and the height of the mountain she is thinking of climbing will be given in meters (Figure 2.3).

## Volume: A Derived UnitEdit

Volume is used to measure how much space an object takes up. It is a derived unit, meaning it is based on another basic SI unit—in this case, the meter (length) was used to measure the sides of a cube, designating a certain volume. This volume was determined to be a cubic meter, m^{3}, which is used as the standard SI unit of volume. This is a very large unit, and it is not very useful for most measurements in chemistry. A more common unit is the liter (L), which is equal to 1/1000 of a cubic meter. Another commonly used volume measurement is the milliliter; 1000 mL = 1 L.

One liter is the volume of the soda bottle that you might have recently purchased and have sitting in the refrigerator at home. You might also have a quart of milk in your refrigerator. Even though the size of the liter container and the milk carton may not appear to be the same, they are, in fact, almost exactly the same volume. A quart is just slightly smaller in volume than a liter (1 L = 1.057 quarts). It's only the packaging that is different!

## Measuring TemperatureEdit

In order to discuss temperature scales, let's briefly compare the concepts of *heat* and *temperature*. Heat is a measurement of the total amount of kinetic energy while temperature describes the intensity of the heat, or what is often referred to as the average kinetic energy of the material. When we are measuring the temperature of an object we are measuring its average kinetic energy. For that, we use the Celsius and Kelvin scales. Scientists do not usually use the Fahrenheit scale. The size of a degree in kelvin (the unit is not capitalized) is the same as 1 degree Celsius. The difference is that the Kelvin scale begins with an absolute zero, the temperature at which all motion stops. To convert between the two scales you can use: K = °C + 273. Therefore, on the Kelvin scale, water freezes at 273 K and boils at 373 K.

You might want to make note of the following: while most mathematical calculations in chemistry require you to convert Celsius temperatures into kelvin, when you are given a *difference in temperature*, ΔT , you do *not* need to convert it to kelvin! A difference in temperature is the same whether it is in Celsius or kelvin.

## Lesson SummaryEdit

- The International System unit for mass if the gram.
- The International System unit for length is the meter.
- The unit for volume is derived from a cube that is 1.00 meter on each side; therefore the volume unit is cubic meters. A more common unit is the liter which is of a cubic meter.
- The SI uses both degrees Celcius (°C) and absolute temperature in kelvin (K) for temperature units. K = °C + 273.

## Review QuestionsEdit

- What are the basic units of measurement in the metric system for length and mass?
- What unit is used to measure volume? How is this unit related to the measurement of length?
- Explain the difference between weight and mass.
- Give both the Celsius and kelvin values for the boiling and freezing points of water.
- How do you convert from Celsius to kelvin? How does one degree Celsius compare with one kelvin?
- If someone told you that a swimming pool's temperature was 275 K, would it be safe for you to go for a swim?
- Determine which metric measurement you would use for each of the following:
- (a) The distance to the moon.
- (b) The mass of a doughnut.
- (c) The volume of a drinking glass.
- (d) The length of your little finger.

## VocabularyEdit

- International System of Units, SI
- The SI system of units is the modern form of the metric system and is generally a system devised around the convenience of multiples of 10.
- Kelvin temperature scale
- The kelvin is unit of increment of temperature and is one of the seven SI basic units. The Kelvin scale is thermodynamic absolute temperature scale where absolute zero is the absence of all thermal zero. At K = 0, there is no molecular motion. The kelvin is not referred to as a "degree", it is written simply as K, not °K.

This material was adapted from the original CK-12 book that can be found here. This work is licensed under the Creative Commons Attribution-Share Alike 3.0 United States License