1) Dimensional Analysis

• Dimensional analysis helps ensure that solutions to problems have the correct units.
• A conversion factor is a fraction whose numerator and denominator have equal quantities expressed in different units.
• Example: 1ft = 12in, can be written as 1ft/12in or 12in/1ft.
• A conversion factor is used to convert a quantity from one unit to another.
• Example: 6in x (1ft/12in) = ½ ft, 2ft x (12in/1ft) = 24in.
• Example model: given unit x (desired unit/given unit) = desired unit
• Sometimes two or more conversion factors are needed.
• Example: 2yd x (3ft/1yd) x (12in/1ft) = 72in.
• Some conversions involve altering the measure.
• For example, instead of converting from length to length, some conversions involve converting form volume to mass.
• Example: convert 3.00in³ of gold to grams, density of gold is 19.3g/1cm³.
• Continued: First you must convert the conversion factor, 2.54cm/1in, into volume: (2.54cm)³/(1in)³ = 16.39cm³/1in³.
• Continued: 3.00in³ x (16.39cm³/1in³) x (19.3g/1cm³) = 948g.

1) Ambiguities in Measurement

·         There are two kinds of numbers in scientific work: exact numbers and inexact numbers.

·         Exact numbers have defined values.

·         Inexact numbers are values that have uncertainty; numbers obtained by measurements are always inexact.

·         Precision is a measure of how closely individual measurements agree with one another.

·         Accuracy refers to how closely individual measurements agree with the correct value.

·         Consistent measurements are precise but may be inaccurate due to an error in the instrument used.

·         Measured quantities are displayed in a way that leaves only the last digit uncertain.

·         Significant figures are all digits in a measured quantity, including the uncertain one.

·         There are three rules for determining the number of significant digits:

1)      Zeros between nonzero digits are always significant.

2)      Zeros to the left of the number are not significant and are only used to locate the decimal point.

3)      Zeros to the right of the number are significant if the number contains a decimal point.

• Examples: 0.0034 has two significant figures; 1240 has four; 201.454 has six.
• Example: 152,000 has six significant figures; when it is written in scientific notation, 1.52 x 10⁵, it has three.

• When making calculation, the last certain measurement limits the certainty of the calculated quantity.
• The least certain measurement determines the number of significant figures in the final answer.
• When multiplying or dividing, the product or quotient must contain the same number of significant figures as the measurement with the fewest significant figures.
• Example: 45.6 x 1.342 = 61.1952, the answer is rounded to three significant figures, 61.2, because 45.6 is the number with the least significant figures.
• When adding or subtracting, the sum or difference has the same number of decimal places as the measurement with the fewest decimal places.
• Example: 1023.2 + 2.34 = 1025.54, the answer is rounded to one decimal place, 1025.5, because 1023.2 has the least number of decimal places.

1) Units of Measurement

• Many properties of matter are quantitative; they are related to numbers.
• The metric system contains the units used for scientific measurements.
• SI units are a particular choice of metric units commonly used in scientific measurements.
• The SI system contains seven base units from which all other units are derived.

• Prefixes are used to indicate decimal fractions or multiples of units.

• The SI base unit for length is meter.
• Mass is the amount of matter in an object; the base unit of mass is kilogram.
• Temperature is the measure of hotness or coldness of an object.
• Temperature is a physical property that determines heat flow.
• Heat always flows from substances of higher temperature to substances of lower temperature.
• The Celsius scale is based on 0^oC as the freezing point of water and 100^oC as the boiling point of water.
• The Kelvin scale is the SI temperature scale; one unit of Kelvin is equal to one unit of Celsius.
• The absolute zero, or 0 K, is the lowest attainable temperature in Kelvin; it equals -273.15^oC; the freezing point of water, 0^oC, is equal to 273.15 K.
• The Fahrenheit scale is not commonly used in scientific studies; 32^oF is the freezing point of water and 212^oF is the boiling point of water.
• K = ^oC + 273.15 , ^oC = (5/9)(^oF – 32) , ^oF = (9/5)(^oC) + 32
• Derived unit are determined by using the defining equation for the quantity and substituting the appropriate base units.
• Volume is defined as length cubed.
• Liter is the non-SI unit for volume; one liter equals one cubic decimeter (dm³).
• Density is used to characterize substances; it is defined as the amount of mass per unit volume.
• Densities depend on temperature; the density of water is 1.00 g/mL of 1.00 g/cm³.

1) Properties of Matter

• Properties of matter are classified as physical or chemical.
• Physical properties can be measured without changing the identity and composition of the substance.
• Chemical properties describe the way a substance may change or react to form other substances.
• Intensive properties do not depend on the amount of the sample and can be used to identify substances.
• Extensive properties depend on the amount of the sample present.
• Changes in matter can also be classified as physical or chemical.
• A physical change occurs when a substance changes its physical appearance but not its composition.
• A chemical change or chemical reaction occurs when a substance is transformed into a chemically different substance.
• All changes of state are physical changes.
• Three ways to separate mixtures are filtration, distillation, and chromatography.
• These three ways depend on the differences of properties of matter to work.
• Chromatography depends on the differing abilities of substances to adhere to surfaces of various solids.

1) Classifying Matter

• Two principle ways of classifying matter are according to its physical state and according to its composition.
• The three main states of matter are solid, liquid, and gas.
• A gas has no fixed volume or shape; it conforms to the shape and volume of its container; it can be compressed or it can be expanded to fill its container.
• A liquid has a distinct volume but an indefinite shape; its shape conforms to the shape of its container.
• A solid has a definite shape and a definite volume.
• Neither liquids nor solids can be compressed to any appreciable extent.
• Molecules in a gas move freely at high speeds.
• Molecules in a liquid are closer together but move rapidly allowing the liquid to flow.
• Molecules in a solid are tightly packed and vibrate slightly in fixed positions.
• A substance is matter that has distinct properties and a composition that does not vary from sample to sample.
• Substances are either elements or compounds.
• Elements cannot be decomposed into smaller components; they are composed of one kind of atom.
• Compounds are composed of two or more elements of the same or different kinds of atoms.
• A mixture is a combination of two or more substances in which each retains its chemical identity.
• Most elements can interact to form compounds.
• The law of constant composition or law of definite proportions states that the elemental composition of a pure compound is always the same.
• Mixtures come in two forms: heterogeneous or homogeneous.
• Heterogeneous mixtures vary in texture and are not uniform throughout.
• Homogeneous mixtures are uniform throughout and are also called solutions.

1) What is Chemistry?

• Chemistry is the science of understanding properties and behavior of matter by studying the properties and behavior of atoms and molecules.
• Matter is anything that has mass and occupies space.
• A property is any characteristic that allows us to recognize certain types of matter and to distinguish if from other types of matter.
• Elements are the basic structures that combine to form all matter.
• Atoms are the smallest building blocks of matter.
• Each element is composed of a unique kind of atom.
• Properties of matter are dependent on its composition and structure.
• Composition refers to the types of atoms, and structure refers to the arrangement of atoms.
• Molecules form when two or more atoms combine to form specific shapes.
• Differences, minor of major, in composition and structure of molecules can have profound differences in their properties.
• The study of chemistry is divided into macroscopic and submicroscopic.
• Macroscopic refers to ordinary sized objects, and submicroscopic refers to atoms and molecules.