1Introduction

Matter and Measurement

OutlinesThe Study of ChemistryClassification of MatterProperties of MatterUnits of MeasurementsUncertainty in MeasurementsDimensional Analysis

The Study of ChemistryChemistry is the study of matter and the changes that matter undergoes. Matter is made up of almost infinitesimally small building blocks called atoms. Atoms can combine together to form molecules. Molecules of a few familiar substances are represented here. In later chapters you will learn more about how atoms combine to form molecules, and how molecules have the shapes and properties that they do.

The Study of Chemistry

Classification of MatterMatter can exist in one of three states of matter: a gas, a liquid, or a solid. A gas is highly compressible and will assume both the shape and the volume of its container. A liquid is not compressible and will assume the shape but not the volume of its container. A solid also is not compressible, and it has a fixed volume and shape of its own.

Classification of MatterMatter can also be classified according to its composition.Most of the matter that we encounter exists in mixtures, which are combinations of two or more substances. Mixtures can be homogeneous or heterogeneous. Mixtures can be separated into pure substances, and pure substances can be either compounds or elements.

Classification of MatterA familiar example of a mixture is salt water. A sample of salt water has the same composition throughout. It can be separated into pure substanceswater and ordinary table saltby a physical process, such as distillation.

Classification of MatterPure water is collected in the flask on the right.When all of the water has been distilled from the mixture, pure saltNaClwill remain in the flask on the left. Both water and salt are pure substances. They cannot be further separated into simpler substances by any physical process. Each, however, can be decomposed into other substances by a chemical process, namely electrolysis. electrolysis

Classification of MatterThe substances produced by the electrolysis of water cannot be further separated by any physical or chemical means. Oxygen and hydrogen are elements. When water is separated into its constituent elements, the relative amounts of those elements are always the same. Water is 11 percent hydrogen and 89 percent oxygen by mass.

Classification of MatterThis is an example of the law of constant composition, also known as the law of definite proportions. Salt can also be separated into its constituent elements, sodium and chlorine, by electrolysis. Sodium chloride also has a constant composition, as do all pure substances. It is 39 percent sodium and 61 percent chlorine by mass.

Matter Classification Scheme

Matter

Is it uniform throughout?

Heterogeneous mixture

Homogeneous

Can it be separated by physical means?

Homogeneous mixt. (solutn)

Pure substance

Can it be decomposed into other substances by chemical processes?

Element

Compound

YES

YES

YES

NO

NO

NO

Properties of MatterDifferent types of matter have different distinguishing characteristics that we can use to tell them apart. These characteristics are called physical properties and chemical properties. Physical and chemical properties may be intensive or extensive.

Properties of MatterIntensive properties such as density, color, and boiling point do not depend on the size of the sample of matter and can be used to identify substances. Extensive properties such as mass and volume do depend on the quantity of the sample.

Properties of MatterPhysical properties are those that we can determine without changing the identity of the substance we are studying. For instance, we can observe or measure the physical properties of sodium metal. It is a soft, lustrous, silver-colored metal with a relatively low melting point and low density.

Properties of MatterHardness, color, melting point and density are all physical properties. Figure 7.15 shows a chunk of metallic sodium, which is soft enough to be cut with a knife.

Properties of MatterFigure 7.15

Properties of MatterChemical properties describe the way a substance can change or react to form other substances. These properties, then, must be determined using a process that changes the identity of the substance of interest.

Properties of MatterOne of the chemical properties of alkali metals such as sodium and potassium is that they react with water. To determine this, though, we would have to combine an alkali metal with water and observe what happens.

Properties of MatterSodium and Potassium in Water

Properties of MatterSodium metal (Na) reacts rather vigorously with water to produce sodium hydroxide (NaOH) and hydrogen gas (H2).After the reaction has occurred, although we now have evidence of one of sodium metal's chemical properties, we no longer have sodium metal.

Properties of MatterPotassium reacts even more vigorously with water to produce potassium hydroxide (KOH) and hydrogen gas. As with sodium, once we have determined a chemical property of potassium metal, we no longer have potassium metal. To determine the chemical properties of a substance, it is necessary to change the substance's chemical identity.

Properties of MatterThe changes undergone by sodium and potassium when they react with water are chemical changes, also known as chemical reactions. Matter can also undergo physical changes in which the chemical identity of the matter does not change.

Properties of MatterOne example of a physical change is the melting of a solid. When ice melts, it changes from a solid state to a liquid state, but its chemical identity (H2O) is unchanged. All changes of state are physical changes.

Units of MeasurementsThe scientific community uses SI units for measurement of such properties as mass, length, and temperature. There are seven SI base units from which all other necessary units are derived.

Units of Measurements

Units of MeasurementsAlthough the meter is the base SI unit used for length, it may not be convenient to report the length of an extremely small object or an extremely large object in units of meters. Decimal prefixes allow us to choose a unit that is appropriate to the quantity being measured. Thus, a very small object might best be measured in millimeters (1 millimeter = 0.001 meters), while a large distance might best be measured in kilometers (1 kilometer = 1000 meters).

Units of Measurements

Units of MeasurementsThe SI unit of temperature is the kelvin, although the Celsius scale is also commonly used. The Kelvin scale is known as the absolute temperature scale, with 0 K being the lowest theoretically attainable temperature. K = C + 273.15Figure 1.18 shows a comparison of the Kelvin, Celsius, and Fahrenheit scales.

Units of Measurements

Units of MeasurementsNote that there are no units of volume in Table 1.4. For measurements of volume, density, and other properties, we must derive the desired units from SI base units. In the case of volume, which has units of length cubed, (length)3, the basic SI unit for volume is the cubic meter (m3).

Units of MeasurementsThis is an extremely large volume, though, and more often you will see volumes reported in liters, L (1 cubic decimeter, or 1 dm3), or milliliters, mL (which are the same as cubic centimeters: 1 mL = 1 cm3).Density has units of mass per unit volume and is often reported as grams per cubic centimeter, g/cm3.

Uncertainty in MeasurementsEven the most carefully taken measurements are always inexact. This can be a consequence of inaccurately calibrated instruments, human error, or any number of other factors.

Uncertainty in MeasurementsTwo terms are used to describe the quality of measurements: precision and accuracy. Precision is a measure of how closely individual measurements agree with one another. Accuracy refers to how closely individually measured numbers agree with the correct or "true" value.

Uncertainty in Measurements

Uncertainty in MeasurementsWhatever the source, all measurements contain error. Thus, all measured numbers contain uncertainty. It is important that these numbers be reported in such a way as to convey the magnitude of this uncertainty.

Uncertainty in MeasurementsConsider a fourth-grade student who, when asked by his teacher how old the Earth is, replies "Four billion and three years old." (The student had been told by a first-grade teacher three years earlier that the Earth was four billion years old.) Obviously, we don't know the age of Earth to the year, so it is not appropriate to report a number that suggests we do.

Uncertainty in MeasurementsIn order to convey the appropriate uncertainty in a reported number, we must report it to the correct number of significant figures. The number 83.4 has three digits. All three digits are significant. The 8 and the 3 are "certain digits" while the 4 is the "uncertain digit."

Uncertainty in MeasurementsAs written, this number implies uncertainty of plus or minus 0.1, or error of 1 part in 834. Thus, measured quantities are generally reported in such a way that only the last digit is uncertain. All digits, including the uncertain one, are called significant figures.

Uncertainty in MeasurementsGuidelinesNonzero digits are always significant457 cm (3 significant figures); 2.5 g (2 significant figures). Zeros between nonzero digits are always significant1005 kg (4 significant figures); 1.03 cm (3 significant figures). Zeros at the beginning of a number are never significant; they merely indicate the position of the decimal point0.02 g (one significant figure); 0.0026 cm (2 significant figures).

Uncertainty in MeasurementsZeros that fall at the end of a number or after the decimal point are always significant0.0200 g (3 significant figures); 3.0 cm (2 significant figures). When a number ends in zeros but contains no decimal point, the zeros may or may not be significant130 cm (2 or 3 significant figures); 10,300 g (3, 4, or 5 significant figures).

Uncertainty in MeasurementsTo avoid ambiguity with regard to the number of significant figures in a number with tailing zeros but no decimal point, such as 700, we use scientific (or exponential) notation to express the number. If we are reporting the number 700 to three significant figures, we can leave it written as it is, or we can express it as 7.00 x 102. There is no ambiguity in the latter regarding the number of significant figures, because zeros after a decimal point are always significant.

Uncertainty in MeasurementsHowever, if there really should be only two significant figures, we can express this number as 7.0 x 102. Likewise, if there should be only one significant figure, we can write 7 x 102. Scientific notation is convenient for expressing the appropriate number of significant figures.

Uncertainty in MeasurementsIt is also useful to report extremely large and extremely small numbers. It would be most inconvenient for us to have to write all of the zeros in the number 1.91 x 10-24 (0.00000000000000000000000191).

Uncertainty in MeasurementsWhen measured numbers are used in a calculation, the final answer cannot have any greater certainty than the measured numbers that went into the calculation. In other words, the precision of the result is limited by the precision of the measurements used to obtain that result. For example: If we measure the length of one side of a cube and find it to be 1.35 cm; and we then calculate the volume of the cube using this measured length, we get an answer of 2.460375 cm3.

Uncertainty in MeasurementsOur original measurement had three significant figures. The implied uncertainty in 1.35 is 1 part in 135. If we report the volume of the cube to seven significant figures, we are implying an uncertainty of 1 part in over two million! We can't do that. In order to report results of calculations so as to imply a realistic degree of uncertainty, we must follow the following rules.

Uncertainty in MeasurementsWhen multiplying or dividing measured numbers, the answer must have the same number of significant figures as the measured number with the fewest significant figures. When adding or subtracting, the answer can have only as many places to the right of the decimal point as the measured number with the smallest number of places to the right of the decimal point.

Uncertainty in MeasurementsUsing these rules, we would report the volume of the cube in the example above as 2.46 cm3. Use the Significant Figures activity to practice reporting calculated numbers to the appropriate number of significant figures.

Uncertainty in MeasurementsCentralScienceLive\Chapter01\CH01_1.5_Main.html

Uncertainty in MeasurementsNot all numbers are measured numbers. There are some numbers that arise as a result of counting or as a result of a definition. If there are three birds in a cage, there is no uncertainty in the number of birds.

Uncertainty in MeasurementsLikewise, there is no uncertainty in the number of items in a dozen. These are exact numbers, and they are taken to have an infinite number of significant figures (exact numbers should never limit the number of significant figures you report in a calculated answer).

Dimensional AnalysisSolving problems in chemistry requires careful manipulation of numbers and their associated units, a method known as dimensional analysis. For example: What is the volume of a 5.25-gram sample of a liquid with density 1.23 g/mL? The density of the liquid can be used as a conversion factor.

Dimensional AnalysisFor the liquid in the example, 1.23 grams are equal to 1 milliliter (1 mL). When the numerator and denominator of a fraction are equal, the fraction has a value of 1, meaning that we can multiply by it for the purpose of changing units. The density conversion factor can be expressed in either of the following two ways.

Dimensional Analysis

Dimensional AnalysisThe one we choose to multiply by depends on what units we want in our result. In this case we want an answer in units of milliliters. So we choose the fraction on the right and multiply it by the mass given in the problem.Note that if we had chosen the other version of the density conversion factor, we would have ended up with a different number and also nonsensical units.

Dimensional Analysis

Dimensional AnalysisThis illustrates the importance of carrying units through a calculation. One way to check your work is to carefully cancel units to make sure that you arrive at an answer with the appropriate units. When you end up with units that don't seem to have any reasonable physical meaning, such as grams squared per milliliter, you will realize that you must have made some sort of mistake. Go back and check your work.