Introduction to Matter, Measurement, and Scientific Calculations in Chemistry

Introduction: Matter, Energy, and Measurement

Properties and Behavior of Matter

Chemistry is the study of the properties and behavior of matter. Understanding matter is fundamental to science, as it explains the macroscopic and microscopic properties of substances.

• Matter: Anything that has mass and occupies space.

• Characterization of Matter:

  • Physical State: Solid, Liquid, Gas

  • Composition:

    • Pure Substance: Element or Compound

    • Mixture: Heterogeneous or Homogeneous

States of Matter

The three physical states of matter are distinguished by their properties and molecular behavior.

State	Properties (Macroscopic)	Behavior (Molecular Level)
Gas	No fixed volume or shape	Molecules far apart, move at high speed
Liquid	Volume independent of container	Molecules packed tightly, move rapidly
Solid	Fixed volume and shape	Molecules packed tightly, fixed positions

Atoms, Molecules, and Ions

Composition of Matter

• Pure Substance: Matter with distinct properties and fixed composition.

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

  • Compound: Composed of two or more elements.

• Mixtures: Combination of two or more pure substances.

  • Homogeneous: Uniform throughout.

  • Heterogeneous: Non-uniform composition, properties, and appearance.

Atoms and Elements

• Atoms: Building blocks of matter.

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

• Elements are organized in the periodic table.

Element	Symbol	Element	Symbol
Carbon	C	Iron	Fe
Nitrogen	N	Sodium	Na
Hydrogen	H	Gold	Au
Calcium	Ca	Chromium	Cr
Helium	He

Matter, Measurement, and SI Units

Quantitative Aspects of Chemistry

Many chemical topics are quantitative and require measurement using standardized units.

• SI Units (International System of Units):

  • Each physical quantity has a base unit.

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

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

Prefix	Symbol	Factor	Example
nano	n	$10^{-9}$	1 nanometer = $1 imes 10^{-9}$ m
micro	μ	$10^{-6}$	1 micrometer = $1 imes 10^{-6}$ m
milli	m	$10^{-3}$	1 milligram = $1 imes 10^{-3}$ g
centi	c	$10^{-2}$	1 centimeter = $1 imes 10^{-2}$ m
kilo	k	$10^{3}$	1 kilogram = $1 imes 10^{3}$ g

Temperature and Density

Temperature Scales

• Celsius Scale: Based on water properties.

  • Freezing point: $0^ ext{o}C$

  • Boiling point: $100^ ext{o}C$

• Kelvin Scale: SI unit for temperature.

  • Absolute zero: $0 ext{ K}$

  • Conversion: $K = ^ ext{o}C + 273.15$

• Fahrenheit Scale:

  • Conversion: $^ ext{o}F = rac{9}{5}(^ ext{o}C) + 32$

  • Conversion: $^ ext{o}C = rac{5}{9}(^ ext{o}F - 32)$

Density

Density is the amount of mass per unit volume of a substance. It changes with temperature.

• Equation: $ext{Density} = rac{ ext{Mass}}{ ext{Volume}}$

Numbers in Scientific Work

Exact and Inexact Numbers

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

• Inexact Numbers: Measured values, subject to instrument limitations and 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.

• Zeros at the end of a number without a decimal point are ambiguous.

Examples

• 5.007 m (four significant figures)

• 0.0003 m (one significant figure)

• 0.3500 g (four significant figures)

• 20600 (three or five significant figures, depending on context)

Rounding Off Numbers

• Round off to the desired decimal place.

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

• If 5 or greater, round up.

Scientific Notation

Representation of Large or Small Numbers

• Format: $m imes 10^n$, where $1 ext{ ≤ } m ext{ < } 10$

• Example: 2.456 m = $2.456 imes 10^0$ m

Significant Figures in Calculations

Addition and Subtraction

• Round to the fewest number of decimal places.

• Example: 23.4 + 0.24 + 2.024 = 25.664 (rounded based on correct sig figs)

Multiplication and Division

• Round to the least number of significant digits.

• Example: $6.221 ext{ cm} imes 5.2 ext{ cm} = 32.3492 ext{ cm}^2$ (rounded to two significant figures)

Dimensional Analysis

Conversion Factors

Dimensional analysis is used to convert one quantity to another using conversion factors.

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

• Multiply the given quantity by the conversion factor.

• Cancel any units that appear in both numerator and denominator.

Example

• Convert 7.89 m to inches: $7.89 ext{ m} imes rac{100 ext{ cm}}{1 ext{ m}} imes rac{1 ext{ inch}}{2.54 ext{ cm}} = 311 ext{ inch}$

Additional Examples

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

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

Additional info: These notes cover foundational concepts from Chapter 1 of General Chemistry, including matter, measurement, SI units, significant figures, and dimensional analysis, which are essential for all subsequent topics in chemistry.