Introduction to Matter, Measurement, and Scientific Calculations

Introduction: Matter, Energy, and Measurement

Definition and Scope of Chemistry

Chemistry is the study of the properties and behavior of matter. It is fundamental to understanding many science-related fields. Chemistry explains the properties of matter in the macroscopic world based on the behavior of atoms and molecules at the molecular level.

Characterization of Matter

• Matter: Anything that has mass and takes up space.

• Physical State:

  • Solid

  • Liquid

  • Gas

• Composition:

  • Pure Substance: Element or Compound

  • Mixture: Heterogeneous or Homogeneous

States of Matter: Properties and Behavior

State	Properties in Macroscopic View	Behavior in 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	Volume and shape fixed	Molecules packed tightly, fixed positions

Composition of Matter

Pure Substances and Mixtures

• 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 substances. Each substance retains its own identity.

  • Homogeneous: Uniform throughout.

  • Heterogeneous: Not uniform; properties and appearance vary.

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.

Example: Learn the names and symbols of the elements (e.g., Carbon - C, Iron - Fe, Sodium - Na).

Measurement in Chemistry

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

Prefixes convert base units into units appropriate for common usage or measurement. For example, 1 nanometer (nm) = $1 \times 10^{-9}$ meters.

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

Temperature Scales

Celsius and Kelvin

• Celsius scale is based on water properties:

  • Freezing point: $0^\circ$C

  • Boiling point: $100^\circ$C

• Kelvin scale is the SI unit of temperature:

  • Absolute zero: $0$ K

  • Conversion: $K = ^\circ C + 273.15$

Fahrenheit

• Conversion formulas:

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

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

Example: What is the temperature of the human body, 37.2$^\circ$C, in $^\circ$F?

Density

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

Equation:

$\text{Density} = \frac{\text{Mass}}{\text{Volume}}$

Example: Given 25 g of a solution with a density of 4.23 g/mL, how many liters of solution do you have?

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 instrument limitations.

• Uncertainties always exist in measured quantities.

Accuracy and Precision

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

• Precision: Proximity of several measurements to each other.

Significant Figures

All digits of a measured quantity are called significant figures.

• All nonzero digits are significant.

• Zeroes between significant figures are significant.

• Zeroes at the beginning of a number are not significant.

• Zeroes at the end of a number are significant if a decimal point is present.

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

Example: 0.0034 m (one significant figure), 5.007 m (four significant figures), 2.06 x 103 (three significant figures).

Rounding Off Numbers

• When rounding, look at all digits beyond the last place desired.

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

• If the leftmost non-significant digit is 5 or greater, round up.

Scientific Notation

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

Example Table:

Number	Scientific Notation	# of Significant Figures
2.456 m	$2.456 \times 10^0$	4
47.840 g	$4.7840 \times 10^1$	5
0.00641 km	$6.41 \times 10^{-3}$	3
9061 cm3	$9.061 \times 10^3$	4
12000 km	$1.2 \times 10^4$	2 (if ambiguous, clarify with context)

Significant Figures in Calculations

• For addition/subtraction: Round to the fewest number of decimal places.

• For multiplication/division: Round to the fewest number of significant digits.

Example: $6.221 \times 5.2 = 32.3492$ (calculator), but correct answer is $32$ (2 significant figures).

Dimensional Analysis

Convert one quantity to another using conversion factors (e.g., 1 inch = 2.54 cm).

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

2. Multiply the given quantity by the conversion factor.

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

Example: Convert 7.89 m to inches:

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

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.

Note: Do not use conversion factors to determine the number of significant figures in a calculation; they are exact numbers.