Fundamental Measurements and Calculations in GOB Chemistry

Introduction to Measurement in Chemistry

Overview

Accurate measurement and calculation are foundational skills in General, Organic, and Biological (GOB) Chemistry. This module introduces key concepts such as units of measurement, significant figures, prefixes, conversion factors, and density.

• Units of Measurement

• Measured Numbers and Significant Figures

• Prefix and Equivalents

• Writing Conversion Factors

• Units Conversions

• Density

Units of Measurement

Standard Units

Chemistry uses the International System of Units (SI) for consistency in scientific communication. Common units include:

• Length: meter (m)

• Mass: kilogram (kg)

• Volume: liter (L)

• Temperature: Celsius (°C), Kelvin (K)

Examples of Units

• 1 kg = 1000 g

• 1 L = 1000 mL

• 1 m = 100 cm

Measured Numbers and Significant Figures

Measured Numbers

Measured numbers are obtained when you measure a quantity, such as height, weight, or temperature. These numbers are subject to measurement error and require careful reporting.

Significant Figures (SFs)

Significant figures indicate the precision of a measured value. They include all digits known with certainty plus one estimated digit.

• All nonzero digits are significant.

• Zeros between nonzero digits are significant.

• Leading zeros are not significant.

• Trailing zeros in a decimal number are significant.

Examples:

• 45.55 cm (4 SFs)

• 0.30 cm (2 SFs)

• 14.55 cm (4 SFs)

Exact Numbers

Exact numbers are defined values, not measured, and have an infinite number of significant figures. Examples include:

• 1 kg = 1000 g

• 1 L = 1000 mL

• 1 ft = 12 in

Scientific Notation

Purpose and Format

Scientific notation is used to express very large or very small numbers in a concise form:

• $4.00 imes 10^5$

• $8.50 imes 10^5$

Only significant digits are included in the coefficient.

Significant Figures in Calculations

Multiplication and Division

When multiplying or dividing measured numbers, the answer should have the same number of significant figures as the measurement with the fewest SFs.

• Example: $2.46 ext{ cm} imes 0.35 ext{ cm} = 0.861 ext{ cm}^2$ (calculator display) Final answer: $0.86 ext{ cm}^2$ (2 SFs)

Addition and Subtraction

For addition and subtraction, the answer should have the same number of decimal places as the measurement with the fewest decimal places.

• Example: $6.019 + 0.1 = 6.1$ (rounded to tenths place)

Metric Prefixes

Common Prefixes

Prefixes are used to indicate multiples or fractions of units in the metric system.

Prefix	Symbol	Factor
kilo-	k	$10^3$
centi-	c	$10^{-2}$
milli-	m	$10^{-3}$
micro-	μ	$10^{-6}$

Examples

• 1 kilometer (km) = 1000 meters (m)

• 1 milligram (mg) = 0.001 grams (g)

Conversion Factors and Dimensional Analysis

Conversion Factors

Conversion factors are ratios that express how many of one unit are equal to another unit. They are used to convert between units.

• 1 kg = 2.2 lb

• 1 m = 100 cm

• 1 L = 1000 mL

Dimensional Analysis

Dimensional analysis (factor-label method) is a systematic way to convert units using conversion factors.

1. State the given and needed quantities.

2. Write a plan to convert the given unit to the needed unit.

3. Set up the problem to cancel units and calculate the answer.

Example:

• If a person weighs 164 lb, what is the body mass in kilograms? $164 ext{ lb} imes rac{1 ext{ kg}}{2.2 ext{ lb}} = 74.5 ext{ kg}$

Density

Definition and Formula

Density is a physical property that compares the mass of an object to its volume.

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

Units of Density

• g/mL (for liquids and solids)

• g/cm3 (for solids)

Example Calculation

• An unknown liquid has a density of 1.32 g/mL. What is the volume (mL) of a 14.7 g sample? $ext{Volume} = rac{14.7 ext{ g}}{1.32 ext{ g/mL}} = 11.1 ext{ mL}$

Summary Table: Key Concepts

Concept	Definition	Example
Significant Figures	Digits that reflect the precision of a measurement	45.55 cm (4 SFs)
Exact Numbers	Numbers defined by counting or definition	1 kg = 1000 g
Scientific Notation	Expresses large/small numbers concisely	$4.00 imes 10^5$
Density	Mass per unit volume	$ext{Density} = rac{ ext{Mass}}{ ext{Volume}}$
Conversion Factor	Ratio for unit conversion	$1 ext{ kg} = 2.2 ext{ lb}$

Additional info:

• These notes are based on "Chemistry: An Introduction to General, Organic, and Biological Chemistry" (Twelfth Edition, Pearson Education, Inc.).

• Examples and problems are adapted for GOB Chemistry students.