Measurement, Significant Figures, and Introduction to Matter in Chemistry

Measurement and Problem Solving

Significant Figures

Significant figures are the digits in a measurement that are known with certainty plus one digit that is estimated. They are crucial for reporting scientific data accurately and reflect the precision of the measuring instrument.

• Nonzero digits are always significant.

• Zeros between nonzero digits are significant.

• Leading zeros (zeros before the first nonzero digit) are not significant.

• Trailing zeros in a number with a decimal point are significant.

• Trailing zeros in a number without a decimal point are ambiguous and should be avoided by using scientific notation.

Example: 0.00450 has three significant figures (4, 5, and the trailing 0).

Number	Significant Figures
0.00450	3
1200	2 (unless specified otherwise)
1200.	4
1.200 x 103	4

Rounding Off Numbers

When rounding numbers, if the digit to be dropped is less than 5, the last retained digit remains unchanged. If it is 5 or greater, the last retained digit is increased by one.

• Example: 2.346 rounded to three significant figures is 2.35.

Significant Figures in Calculations

• Multiplication/Division: The result should have the same number of significant figures as the measurement with the fewest significant figures.

• Addition/Subtraction: The result should have the same number of decimal places as the measurement with the fewest decimal places.

Example: 2.5 x 3.42 = 8.6 (2 significant figures)

Scientific Notation and Powers of Ten

Expressing Numbers in Scientific Notation

Scientific notation expresses numbers as a product of a coefficient (between 1 and 10) and a power of ten. This is useful for very large or very small numbers.

• General form: $a \times 10^n$

• Example: 0.00056 = $5.6 \times 10^{-4}$

Mathematical Operations with Powers of Ten

• Multiplication: Multiply the coefficients and add the exponents. $(a \times 10^m) \times (b \times 10^n) = (a \times b) \times 10^{m+n}$

• Division: Divide the coefficients and subtract the exponents. $\frac{a \times 10^m}{b \times 10^n} = \frac{a}{b} \times 10^{m-n}$

• Addition/Subtraction: Express both numbers with the same exponent, then add or subtract the coefficients. $(a \times 10^n) + (b \times 10^n) = (a + b) \times 10^n$

Measurements and Conversions

Metric System and SI Units

The metric system is used worldwide in science for consistency. The International System of Units (SI) is based on the metric system and includes standard units for mass, length, and volume.

Quantity	SI Unit	Symbol
Mass	kilogram	kg
Length	meter	m
Volume	liter	L

Metric Prefixes

Prefix	Symbol	Value
kilo	k	$10^3$
centi	c	$10^{-2}$
milli	m	$10^{-3}$
micro	\mu	$10^{-6}$

Unit Conversions

Unit conversions use conversion factors, which are ratios equal to one, to change from one unit to another.

• Example: Convert 2.5 kg to grams: $2.5 \text{ kg} \times \frac{1000 \text{ g}}{1 \text{ kg}} = 2500 \text{ g}$

English and Metric Units

Quantity	English Unit	Metric Equivalent
Length	1 inch	2.54 cm
Mass	1 lb	454 g
Volume	1 qt	0.946 L

Density and Specific Gravity

Density is the mass of a substance per unit volume. Specific gravity is the ratio of the density of a substance to the density of water.

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

• Specific gravity formula: $\text{Specific gravity} = \frac{\text{Density of substance}}{\text{Density of water}}$

Volume of Solids

• Water Displacement: The volume of an irregular solid can be found by the amount of water it displaces.

• Mathematical Formula: For regular solids, use $V = l \times w \times h$.

Temperature Conversions

• Celsius to Kelvin: $K = ^\circ C + 273$

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

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

Calorimetry and Heat Transfer

Calorimetry is the measurement of heat transfer during physical and chemical changes. The amount of heat absorbed or released is calculated using:

• $q = m \times c \times \Delta T$

• Where q is heat (J), m is mass (g), c is specific heat (J/g·°C), and $\Delta T$ is the change in temperature (°C).

Matter and Energy

Classification of Matter

Matter is anything that has mass and occupies space. It can be classified as a pure substance (element or compound) or a mixture (homogeneous or heterogeneous).

Type	Description	Example
Element	Cannot be broken down into simpler substances	Oxygen (O2)
Compound	Composed of two or more elements chemically combined	Water (H2O)
Homogeneous Mixture	Uniform composition throughout	Saltwater
Heterogeneous Mixture	Non-uniform composition	Sand and iron filings

States of Matter

• Solid: Definite shape and volume

• Liquid: Definite volume, takes shape of container

• Gas: No definite shape or volume

Physical and Chemical Properties

• Physical properties: Can be observed without changing the substance (e.g., color, melting point, density).

• Chemical properties: Describe how a substance reacts with other substances (e.g., flammability, reactivity).

Atoms and Elements

Atomic Structure

Atoms are the basic units of matter, composed of protons, neutrons, and electrons. The nucleus contains protons and neutrons, while electrons occupy the surrounding space.

• Atomic number (Z): Number of protons in the nucleus.

• Mass number (A): Total number of protons and neutrons.

• Isotopes: Atoms of the same element with different numbers of neutrons.

Elements and the Periodic Table

Elements are pure substances that cannot be broken down into simpler substances. Each element is represented by a symbol and organized in the periodic table by atomic number.

Element	Symbol	Atomic Number
Hydrogen	H	1
Carbon	C	6
Oxygen	O	8
Sodium	Na	11

Metals, Nonmetals, and Metalloids

• Metals: Good conductors of heat and electricity, malleable, ductile, shiny.

• Nonmetals: Poor conductors, not malleable or ductile, dull appearance.

• Metalloids: Properties intermediate between metals and nonmetals.

Physical Properties of Elements

Property	Metals	Nonmetals	Metalloids
Conductivity	High	Low	Intermediate
Malleability	Yes	No	Varies
Luster	Shiny	Dull	Varies

Additional info:

• Some tables and diagrams were inferred and summarized for clarity.

• Practice problems and worked examples are included throughout the notes to reinforce concepts.