Measurement, Scientific Notation, and SI Units in General Chemistry

Measurement and Significant Figures

Rounding and Significant Figures

Accurate measurement and correct use of significant figures are essential in chemistry to ensure data reliability and proper communication of results.

• Rounding Rules:

  • If the digit to be dropped is 1-4, round down.

  • If the digit to be dropped is 5-9, round up.

• Reporting Uncertainty: Measurements should be reported with their associated uncertainty, e.g., 10.2 ± 0.3 mg.

• Significant Figures (Sig Figs): The number of meaningful digits in a measurement. For example, 4.6 × 105 has 2 significant figures.

Scientific Notation and Exponential Form

Expressing Large and Small Numbers

Scientific notation is used to conveniently express very large or very small numbers, which are common in chemistry.

• Format: A number is written as a × 10n, where 1 ≤ a < 10 and n is an integer.

• Examples:

  • 1,130,000,000,000 = $1.13 \times 10^{12}$

  • 100,000,000,000 = $1 \times 10^{11}$

  • Speed of sound: $3.4 \times 10^4$ cm/s

• Operations: When multiplying or dividing numbers in scientific notation, add or subtract the exponents accordingly.

SI Units and Metric Prefixes

Base Units and Derived Units

The International System of Units (SI) is the standard metric system used in science. It consists of base units for fundamental quantities and derived units for compound measurements.

• Base SI Units:

  • Length: meter (m)

  • Mass: kilogram (kg)

  • Time: second (s)

  • Temperature: kelvin (K)

  • Amount of substance: mole (mol)

  • Electric current: ampere (A)

  • Luminous intensity: candela (cd)

• Derived Units: Formed by combining base units. For example, the joule (J) is the unit of energy:

  • $1~\text{J} = 1~\text{kg}~\text{m}^2~\text{s}^{-2}$

• Pressure: Often measured in mm Hg (millimeters of mercury).

Metric Prefixes

Metric prefixes are used to indicate multiples or fractions of units.

Prefix	Symbol	Factor
pico	p	10-12
nano	n	10-9
micro	μ	10-6
milli	m	10-3
centi	c	10-2
deci	d	10-1
deca	da	101
hecto	h	102
kilo	k	103
mega	M	106
giga	G	109
tera	T	1012
peta	P	1015
exa	E	1018

Unit Conversions and Dimensional Analysis

Converting Between Units

Unit conversions are performed using conversion factors, which are ratios equal to one that relate two units.

• Example: To convert 0.127 L to mL:

  • $0.127~\text{L} \times \frac{1000~\text{mL}}{1~\text{L}} = 127~\text{mL}$

• Volume Relationships: $1~\text{L} = 1~\text{dm}^3$, $1~\text{mL} = 1~\text{cm}^3$

Density and Properties of Matter

Intensive and Extensive Properties

Physical properties of matter are classified as intensive or extensive:

• Intensive Properties: Do not depend on the amount of substance (e.g., density, temperature).

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

Density Calculations

Density is defined as mass per unit volume:

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

• Example: What is the mass of 3.5 L of water? (Density of water = 1 g/cm3)

  • Convert 3.5 L to m3:

    • $3.5~\text{L} \times \frac{1~\text{dm}^3}{1~\text{L}} \times \frac{10^{-3}~\text{m}^3}{1~\text{dm}^3} = 3.5 \times 10^{-3}~\text{m}^3$

  • Convert to mass:

    • $3.5 \times 10^3~\text{cm}^3 \times \frac{1~\text{g}}{1~\text{cm}^3} \times \frac{1~\text{kg}}{1000~\text{g}} = 3.5~\text{kg}$

Temperature Scales

Celsius and Kelvin

Temperature is measured in degrees Celsius (°C) or kelvins (K). The Kelvin scale is the SI unit for temperature.

• Conversion: $T(\text{K}) = T(\degree\text{C}) + 273.15$

• Absolute Zero: 0 K is the lowest possible temperature, where particles have minimum kinetic energy.

Avogadro's Number and the Mole

Amount of Substance

The mole (mol) is the SI unit for the amount of substance. One mole contains Avogadro's number of entities (atoms, molecules, etc.).

• Avogadro's Number: $6.022 \times 10^{23}$

Summary Table: SI Base Units

Quantity	Unit Name	Symbol
Length	meter	m
Mass	kilogram	kg
Time	second	s
Temperature	kelvin	K
Amount of substance	mole	mol
Electric current	ampere	A
Luminous intensity	candela	cd

Additional info: Some explanations and examples were expanded for clarity and completeness based on standard General Chemistry curriculum.