 # Chapter 1: Matter, Measurements, and Calculations

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Chapter 1: Matter, Measurements, and Calculations

Part 1: Matter Sections

MATTER MASS Matter is anything that has mass and occupies space.
Mass is a measurement of the amount of matter in an object. Mass is independent of the location of an object. An object on the earth has the same mass as the same object on the moon.

WEIGHT Weight is a measurement of the gravitational force acting on an object. Weight depends on the location of an object. An object weighing 1.0 lb on earth weighs about 0.17 lb on the moon.

PHYSICAL PROPERTIES OF MATTER
Physical properties can be observed or measured without attempting to change the composition of the matter being observed. Examples of physical properties are color, shape and mass. CHEMICAL PROPERTIES OF MATTER Chemical properties can be observed or measured only by attempting to change the composition of the matter being observed. Examples of chemical properties are flammability and the ability to react (e.g. when vinegar and baking soda are mixed).

PHYSICAL CHANGES OF MATTER
Physical changes take place without a change in composition. Examples of physical changes are the freezing, melting, or evaporation of a substance (e.g. water). CHEMICAL CHANGES OF MATTER Chemical changes are always accompanied by a change in composition. Examples of chemical changes are the burning of paper and the fizzing of a mixture of vinegar and baking soda.

ATOMS THE PARTICULATE MODEL OF MATTER MOLECULES
All matter is made up of tiny particles called molecules and atoms. MOLECULES A molecule is the smallest particle of a pure substance that is capable of a stable independent existence. ATOMS Atoms are the particles that make up molecules.

DIATOMIC MOLECULES TRIATOMIC MOLECULES POLYATOMIC MOLECULES
Diatomic molecules contain two atoms. TRIATOMIC MOLECULES Triatomic molecules contain three atoms. POLYATOMIC MOLECULES Polyatomic molecules contain more than three atoms.

HETEROATOMIC MOLECULES
HOMOATOMIC MOLECULES The atoms contained in homoatomic molecules are of the same kind. HETEROATOMIC MOLECULES The atoms contained in heteroatomic molecules are of two or more kinds.

CLASSIFICATION OF MATTER
Matter can be classified into several categories based on chemical and physical properties. PURE SUBSTANCES Pure substances have a constant composition and a fixed set of other physical and chemical properties. An example is pure water that always contains the same proportions of hydrogen and oxygen, and freezes at a specific temperature.

MIXTURES Mixtures can vary in composition and properties.
An example is a mixture of table sugar and water which can have different proportions of sugar and water. A glass of water could contain one, two, three, etc. spoons of sugar. Properties such as sweetness would be different for the mixtures with different proportions.

HETEROGENEOUS MIXTURES
The properties of a sample of a heterogeneous mixture depends on the location from which the sample was taken. A pizza pie is a heterogeneous mixture. A piece of crust has different properties than a piece of pepperoni taken from the same pie.

HOMOGENEOUS MIXTURES Homogeneous mixtures are also called solutions. The properties of a sample of a homogeneous mixture are the same regardless of where the sample was obtained from the mixture. Samples taken from any part of a mixture made up of one spoon of sugar mixed with a glass of water will have the same properties such as the same taste.

ELEMENTS Elements are pure substances that are made up of homoatomic molecules or individual atoms of the same kind. Examples are oxygen gas made up of homoatomic molecules and copper metal made up of individual copper atoms.

COMPOUNDS Compounds are pure substances that are made up of heteroatomic molecules or individual atoms (ions) of two or more different kinds. Examples are pure water made up of heteroatomic molecules and table salt made up of sodium atoms (ions) and chlorine atoms (ions).

MATTER CLASSIFICATION SUMMARY

Part 2: Measurement & Problem Solving
Sections

MEASUREMENTS AND MEASUREMENT UNITS
Measurements consist of two parts, a number and a unit or label such as feet, pounds, or gallons. Measurement units are agreed upon by those making and using the measurements. Measurements are made using measuring devices (e.g. rulers, balances, graduated cylinders, etc.).

THE METRIC SYSTEM OF MEASUREMENT
The metric system is a decimal system in which larger and smaller units are related by factors of 10. TYPES OF METRIC SYSTEM UNITS Basic or defined units [e.g. 1 meter (1 m)] are used to calculate derived units [e.g. 1 square meter (1 m2)].

THE USE OF PREFIXES Prefixes are used to relate basic and derived units. The commonly-used prefixes are given in the following table:

TEMPERATURE SCALES The three most commonly-used temperature scales are the Fahrenheit, Celsius and Kelvin scales. The Celsius and Kelvin scales are used in scientific work.

RELATIONSHIPS BETWEEN THE TEMPERATURE SCALES

CONVERSIONS FROM ONE TEMPERATURE SCALE TO ANOTHER
Readings on one temperature scale can be converted to the readings on the other scales by using mathematical equations. Converting Fahrenheit to Celsius. Converting Celsius to Fahrenheit. Converting Kelvin to Celsius. Converting Celsius to Kelvin

COMMONLY-USED METRIC UNITS

SCIENTIFIC NOTATION Scientific notation provides a convenient way to express very large or very small numbers. Numbers written in scientific notation consist of a product of two parts in the form M x 10n, where M is a number between 1 and 10 (but not equal to 10) and n is a positive or negative whole number. The number M is written with the decimal in the standard position.

STANDARD DECIMAL POSITION
The standard position for the decimal is to the right of the first nonzero digit in the number M. SIGNIFICANCE OF THE EXPONENT n A positive n value indicates the number of places to the right of the standard position that the original decimal position is located. A negative n value indicates the number of places to the left of the standard position that the original decimal position is located.

MULTIPLICATION OF NUMBERS WRITTEN IN SCIENTIFIC NOTATION
Multiply the M values of each number to give a product represented by M'. Add together the n values of each number to give a sum represented by n'. Write the final product as M' x 10n'. Move decimal in M' to the standard position and adjust n' as necessary.

DIVISION OF NUMBERS WRITTEN IN SCIENTIFIC NOTATION
Divide the M values of each number to give a quotient represented by M'. Subtract the denominator (bottom) n value from the numerator (top) n value to give a difference represented by n'. Write the final quotient as M' x 10n'. Move decimal in M' to the standard position and adjust n' as necessary.

COUNTING ZEROS AS SIGNIFICANT FIGURES
Significant figures are the numbers in a measurement that represent the certainty of the measurement, plus one number representing an estimate. COUNTING ZEROS AS SIGNIFICANT FIGURES Leading zeros are never significant figures. Buried zeros are always significant figures. Trailing zeros are generally significant figures.

NUMBER OF SIGNIFICANT FIGURES TO USE IN A PRODUCT OR QUOTIENT OF NUMBERS
The answer obtained by multiplication or division must contain the same number of significant figures (SF) as the quantity with the fewest number of significant figures used in the calculation.

NUMBER OF SIGNIFICANT FIGURES TO USE IN A SUM OR DIFFERENCE OF NUMBERS
The answer obtained by addition or subtraction must contain the same number of places to the right of the decimal (prd) as the quantity in the calculation with the fewest number of places to the right of the decimal.

ROUNDING RULES FOR NUMBERS
If the first of the nonsignificant figures to be dropped from an answer is 5 or greater, all the nonsignificant figures are dropped and the last remaining significant figure is increased by one. If the first of the nonsignificant figures to be dropped from an answer is less than 5, all nonsignificant figures are dropped and the last remaining significant figure is left unchanged.

EXACT NUMBERS A number used as part of a defined relationship between quantities is an exact number (e.g. 100 cm = 1 m). A counting number obtained by counting individual objects is an exact number (e.g. 1 dozen eggs = 12 eggs). A reduced simple fraction is an exact number (e.g. 5/9 in equation to convert ºF to ºC).

USING UNITS IN CALCULATIONS
The factor-unit method for solving numerical problems is a four-step systematic approach to problem solving. Step 1: Write down the known or given quantity. Include both the numerical value and units of the quantity. Step 2: Leave some working space and set the known quantity equal to the units of the unknown quantity. Step 3: Multiply the known quantity by one or more factors, such that the units of the factor cancel the units of the known quantity and generate the units of the unknown quantity.

Step 4: After you generate the desired units of the unknown quantity, do the necessary arithmetic to produce the final numerical answer. Please see Example 1.15 and 1.16 for an example. I also suggest that you try “Learning Check 1.16 on the bottom of page 27 in your textbook. If you have problems, please bring it up on the discussion board.

PERCENTAGE CALCULATIONS
The word percentage means per one hundred. It is the number of items in a group of 100 such items. PERCENTAGE CALCULATIONS Percentages are calculated using the equation: In this equation, part represents the number of specific items included in the total number of items.

EXAMPLE OF A PERCENTAGE CALCULATION
A student counts the money she has left until pay day and finds she has \$ Before payday, she has to pay an outstanding bill of \$ What percentage of her money must be used to pay the bill? Solution: Her total amount of money is \$36.48, and the part is what she has to pay or \$ The percentage of her total is calculated as follows:

DENSITY Density is the ratio of the mass of a sample of matter divided by the volume of the same sample. or

EXAMPLE OF A DENSITY CALCULATION
A mL sample of liquid is put into an empty beaker that had a mass of g. The beaker and contained liquid were weighed and had a mass of g. Calculate the density of the liquid in g/mL. The mass of the liquid is the difference between the mass of the beaker with contained liquid, and the mass of the empty beaker or g g = g. The density of the liquid is calculated as follows: