Introduction to Matter, Measurement, and Scientific Calculations

Introduction: Matter & Measurement

What is Chemistry?

Chemistry is the study of the properties and behavior of matter. It is fundamental to understanding many science-related fields.

Definition of Matter

• Matter is anything that has mass and takes up space.

Characterization of Matter

• Physical State:

  • Solid

  • Liquid

  • Gas

• Composition:

  • Pure Substance

    • Element: Cannot be decomposed into simpler substances; only one kind of atom.

    • Compound: Composed of two or more elements in fixed proportions.

  • Mixture: Combination of two or more pure substances. Each substance retains its own identity.

    • Homogeneous: Uniform throughout.

    • Heterogeneous: Not uniform; properties and appearance vary.

States of Matter: Macroscopic and Molecular View

State	Properties in Macroscopic View	Behavior in Molecular View
Gas	No fixed volume or shape	Molecules far apart, move at high speeds
Liquid	Volume independent of container	Molecules packed tightly, move rapidly
Solid	Volume and shape fixed	Molecules packed tightly, fixed positions

Atoms, Molecules & Ions

Atoms and Elements

• Atoms are the building blocks of matter.

• There are 118 known elements, each with a unique chemical symbol.

• Elements are organized in the periodic table.

Compounds and Mixtures

• Compound: Substance composed of two or more elements in fixed proportions.

• Mixture: Combination of two or more substances, each retaining its own properties.

Matter & Measurement

SI Units (International System of Units)

Different base units are used for each physical quantity:

Physical Quantity	Name of Unit	Abbreviation
Length	Meter	m
Mass	Kilogram	kg
Temperature	Kelvin	K
Time	Second	s
Amount of substance	Mole	mol
Electric current	Ampere	A
Luminous intensity	Candela	cd

SI Prefixes

Prefix	Abbreviation	Factor	Example
kilo	k	103	1 kilometer (km) = 103 m
centi	c	10-2	1 centimeter (cm) = 10-2 m
milli	m	10-3	1 milligram (mg) = 10-3 g
micro	μ	10-6	1 micrometer (μm) = 10-6 m
nano	n	10-9	1 nanometer (nm) = 10-9 m

Temperature

Celsius and Kelvin Scales

• The Celsius scale is based on water's properties:

  • Freezing point: 0°C

  • Boiling point: 100°C

• The Kelvin scale is the SI unit of temperature. Absolute zero is 0 K.

Conversion formulas:

• $K = ^\circ C + 273.15$

• $^\circ C = K - 273.15$

• $^\circ F = \frac{9}{5}(^\circ C) + 32$

• $^\circ C = \frac{5}{9}(^\circ F - 32)$

Density

• Density is the amount of mass in a unit volume of a substance.

• Formula: $\text{Density} = \frac{\text{Mass}}{\text{Volume}}$

Numbers in Scientific Work

Exact and Inexact Numbers

• Exact numbers: Counted or defined values (e.g., 12 eggs in a dozen).

• Inexact numbers: Measured values, subject to uncertainty.

Accuracy and Precision

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

• Precision: Closeness of repeated measurements to each other.

Significant Figures

Rules for Significant Figures

• All nonzero digits are significant.

• Zeros between significant digits are significant.

• Leading zeros are not significant.

• Trailing zeros are significant if there is a decimal point.

• Trailing zeros in a whole number without a decimal point are ambiguous.

Rounding Off Numbers

• Round off to the desired number of digits.

• If the leftmost non-significant digit is less than 5, leave the preceding digit unchanged.

• If it is 5 or greater, round up.

Scientific Notation

Used to represent very large or very small numbers in the form $m \times 10^n$, where $1 \leq m < 10$.

Significant Figures in Calculations

• Addition/Subtraction: Round to the least number of decimal places.

• Multiplication/Division: Round to the least number of significant figures.

Dimensional Analysis

Conversion Factors

• Used to convert one unit to another (e.g., $1 \text{ inch} = 2.54 \text{ cm}$).

• Write the conversion factor as a fraction so that units cancel appropriately.

• Multiply the given quantity by the conversion factor.

• Cancel units that appear in both numerator and denominator.

Example: Unit Conversion

• Convert 7.89 m to inches:

  • First, convert meters to centimeters, then centimeters to inches.

  • $7.89 \text{ m} \times \frac{100 \text{ cm}}{1 \text{ m}} \times \frac{1 \text{ inch}}{2.54 \text{ cm}} = 311 \text{ inches}$

Note on Significant Figures in Conversions

• Do not use conversion factors to determine the number of significant figures; they are exact numbers.

Additional Examples

• Convert the speed of a nitrogen molecule (515 m/s) to miles per hour.

• Express acceleration due to gravity (9.8 m/s2) as millimeters/millisecond2.