Math Review and Measurement in Science

Introduction to Matter and Measurement

Understanding matter and its measurement is foundational to all physical sciences, including physics and chemistry. This section introduces the classification of matter, its properties, and the quantitative tools used to describe and analyze physical phenomena.

Matter and Its Classification

Definition of Matter

• Matter is anything that has mass and occupies space.

• All physical objects and substances are forms of matter.

Atoms, Elements, Compounds, and Molecules

• Atoms are the fundamental building blocks of matter.

• Elements are substances made of only one kind of atom.

• Compounds are substances composed of two or more different kinds of elements, chemically combined in fixed ratios.

• Molecules are groups of atoms bonded together, representing the smallest unit of a compound that retains its chemical properties.

• Example: Water (H2O) is a molecule composed of two hydrogen atoms and one oxygen atom.

Methods of Classification

• State of Matter (solid, liquid, gas)

• Composition of Matter (element, compound, mixture)

States of Matter

• Solid: Definite shape and volume (e.g., ice).

• Liquid: Definite volume but takes the shape of its container (e.g., liquid water).

• Gas: No definite shape or volume; expands to fill its container (e.g., water vapor).

Classification Based on Composition

• Pure Substances: Have constant composition and distinct properties.

• Elements: Cannot be decomposed into simpler substances.

• Compounds: Can be decomposed into simpler substances.

• Mixtures: Combinations of two or more substances where each retains its own properties.

• Homogeneous Mixture (Solution): Uniform composition throughout.

• Heterogeneous Mixture: Composition varies throughout the sample.

Law of Constant Composition (Law of Definite Proportions)

• In any compound, the relative number of atoms of each element is the same in any sample.

• Example: Water always contains hydrogen and oxygen in a 2:1 ratio.

Properties and Changes of Matter

Physical vs. Chemical Properties

• Physical Properties: Can be observed without changing the substance (e.g., boiling point, density, mass, volume).

• Chemical Properties: Can only be observed when a substance is transformed into another substance (e.g., flammability, reactivity).

Intensive vs. Extensive Properties

• Intensive Properties: Independent of the amount of substance (e.g., density, boiling point, color).

• Extensive Properties: Depend on the amount of substance (e.g., mass, volume, energy).

Physical vs. Chemical Changes

• Physical Changes: Do not alter the composition of a substance (e.g., changes of state, temperature, volume).

• Chemical Changes (Reactions): Result in the formation of new substances (e.g., combustion, oxidation, decomposition).

Changes in State of Matter

• Transitions between solid, liquid, and gas are physical changes (e.g., melting, evaporation).

• The molecular composition remains unchanged during these transitions.

Separation of Mixtures

Methods of Separation

• Filtration: Separates solids from liquids using a porous barrier.

• Distillation: Separates components based on differences in boiling points.

• Chromatography: Separates substances based on their ability to adhere to a solid surface.

Measurement in Science

Numbers and Chemistry

• Many scientific topics are quantitative and require precise measurement and calculation.

• Key concepts include units of measurement, uncertainty, significant figures, and dimensional analysis.

SI Units (Système International d'Unités)

The SI system is the standard for scientific measurements, with a different base unit for each physical quantity.

Metric System Prefixes

Prefixes are used to express multiples or fractions of base units for convenience.

Mass, Length, and Volume

• Mass: Amount of material in an object. SI base unit: kilogram (kg); metric base unit: gram (g).

• Length: Measure of distance. Base unit: meter (m).

• Volume: Derived unit; .

• Common units: liter (L), milliliter (mL), cubic centimeter (cm3).

• ; .

Temperature Scales

• Celsius (°C): Based on water's freezing (0°C) and boiling points (100°C).

• Kelvin (K): SI unit; absolute zero is 0 K. No negative values.

• Conversion:

• Fahrenheit (°F): Not used in scientific contexts; conversion:

Density

• Density (D): Physical property defined as mass per unit volume.

• Common units: g/mL or g/cm3.

• Formula:

Measurement and Calculation

Exact vs. Inexact Numbers

• Exact Numbers: Defined values or counted quantities (e.g., 12 eggs in a dozen).

• Inexact (Measured) Numbers: Obtained by measurement; subject to uncertainty.

Uncertainty in Measurements

• All measurements have some degree of inaccuracy due to instrument limitations.

• Different devices provide different levels of precision.

Accuracy vs. Precision

• Accuracy: Closeness of a measurement to the true value.

• Precision: Closeness of repeated measurements to each other.

Significant Figures

• Digits in a measurement that are known with certainty plus one estimated digit.

• Rules:

  1. All nonzero digits are significant.

  2. Zeroes between significant digits are significant.

  3. Leading zeroes are not significant.

  4. Trailing zeroes are significant if a decimal point is present.

• For addition/subtraction: Round to the least significant decimal place.

• For multiplication/division: Round to the least number of significant figures in any number used.

Dimensional Analysis

• Method for converting between units using conversion factors.

• Set up ratios so that units cancel, leaving the desired unit.

• Example: To convert inches to centimeters, use .