Chemistry and Measurements

Introduction

Chemistry relies on precise measurements to describe matter and its changes. Understanding units, measurement systems, and how to handle measured data is foundational for success in General, Organic, and Biological (GOB) Chemistry.

Units of Measurement

Metric System and SI Units

The metric system is the standard system of measurement used in chemistry. Scientists worldwide use a modified version called the International System of Units (SI) for consistency.

• Metric system and SI are used for length, volume, mass, temperature, and time.

• SI units are used globally and by scientists everywhere.

Common Units and Abbreviations

Key units in the metric and SI systems are summarized below:

Examples of Units

• Length: A person is 2.0 m tall.

• Mass: A 10.0 lb bag of tomatoes is 4.5 kg.

• Volume: A bottle contains 1.5 L of water.

Measured Numbers and Significant Figures

Measured vs. Exact Numbers

Measured numbers are obtained using measuring devices and have a degree of uncertainty. Exact numbers are counted or defined and have no uncertainty.

• Measured numbers: Obtained by measurement (e.g., length, mass, volume).

• Exact numbers: Obtained by counting (e.g., 8 cookies) or by definition (e.g., 1 kg = 1000 g).

Significant Figures (SFs)

Significant figures in a measured number include all certain digits plus one estimated digit. They represent the precision of a measurement.

• All nonzero digits are significant.

• Zeros between nonzero digits are significant.

• Leading zeros (to the left of the first nonzero digit) are not significant.

• Trailing zeros (to the right and after the decimal) are significant.

Example: 0.02009 has 4 significant figures.

Counting Significant Figures

• 1.457 cm → 4 SFs

• 0.025 m → 2 SFs

• 1005 kg → 4 SFs

• 0.002 g → 1 SF

Scientific Notation and Significant Zeros

Scientific notation clarifies which zeros are significant. For example:

• 5,000 kg (1 SF) → kg

• 5,000. kg (4 SFs) → kg

Rounding and Calculations with Significant Figures

Rounding Rules

• If the first digit to be dropped is less than 5, drop it and all following digits.

• If the first digit to be dropped is 5 or greater, increase the last retained digit by 1.

Multiplication and Division

For multiplication or division, the final answer should have the same number of significant figures as the measurement with the fewest SFs.

• Example: (calculator), answer = 0.74 (2 SFs)

Addition and Subtraction

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

• Example: (calculator), answer = 66.1 (rounded to tenths place)

Prefixes and Equalities

Metric Prefixes

Prefixes are used to indicate multiples or fractions of units. They change the size of the unit by powers of ten.

Cubic Centimeter and Milliliter

• 1 cm3 (cubic centimeter) = 1 mL (milliliter)

• 1 L = 1000 mL = 1000 cm3

Conversion Factors and Equalities

Writing Conversion Factors

Conversion factors are ratios that express the relationship between two units. They are used to convert from one unit to another.

• Example: 1 m = 100 cm can be written as or

• Exact equalities (e.g., 1 kg = 1000 g) do not affect significant figures.

• Measured equalities (e.g., 1 lb = 454 g) do affect significant figures.

Problem Solving Using Unit Conversions

Steps for Unit Conversion Problems

1. Identify the given quantity and units.

2. Determine the needed units.

3. Identify conversion factors that connect the given and needed units.

4. Set up the problem so units cancel appropriately.

5. Calculate the answer and round to the correct number of significant figures.

Example: Convert 1.4 days to minutes.

• Given: 1.4 days

• Needed: minutes

• Conversion factors: 1 day = 24 hours, 1 hour = 60 minutes

• Calculation: minutes

Density and Specific Gravity

Density

Density is the ratio of mass to volume and is used to characterize substances.

• Formula:

• Units: g/mL, g/cm3 for solids and liquids; g/L for gases

• 1 mL = 1 cm3

Example: A metal sample has a mass of 48.0 g and displaces water from 25.0 mL to 33.0 mL. Volume = 8.0 mL. Density =

Specific Gravity

Specific gravity is the ratio of the density of a substance to the density of water (1.00 g/mL at 4°C). It is a unitless quantity.

• Formula:

• Used in medical and laboratory settings to compare substances to water.

Summary Table: Densities of Common Substances

Applications in Health and Toxicology

Toxicology and LD50

Toxicology uses measurements to assess the risk of substances. The LD50 (lethal dose, 50%) is the amount of a substance that causes death in 50% of test animals, usually measured in mg/kg or μg/kg of body mass.

• Lower LD50 values indicate higher toxicity.

• Example: Caffeine LD50 = 192 mg/kg

Key Equations

Conclusion

Mastery of measurement units, significant figures, conversion factors, and density calculations is essential for success in GOB Chemistry and for understanding chemical processes in health and biological contexts.