Measurement in Chemistry

Numbers and Units

Measurements in chemistry always consist of a numerical value and a unit, which together provide quantitative information about a property. Units are essential for clarity and reproducibility in scientific communication.

• Base SI Units: The International System of Units (SI) defines seven base units for fundamental quantities.

• Derived Units: Some quantities, such as volume, are derived from base units (e.g., for volume).

SI Base Units Table

Example:

• Volume:

Significant Figures

Definition and Importance

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

• Exact Numbers: Have no error and are considered to have infinite significant figures (e.g., defined quantities like 1 gallon = 3.785 L).

• Measured Numbers: Include error; all reproducible digits plus one uncertain digit are significant.

Rules for Determining Significant Figures

• If the number is in scientific notation, digits in the exponential part ("10n") are not significant.

• All non-zero digits are significant.

• Zeros between non-zero digits are always significant.

• Zeros at the beginning of a number are never significant; they only indicate the position of the decimal point.

• Zeros at the end of a number are significant if the number contains a decimal point or is in scientific notation; otherwise, it may be unclear.

Examples:

• 123 (3 sig figs)

• 1.23 × 102 (3 sig figs)

• 0.1230 × 103 (4 sig figs)

• 12.3 (3 sig figs)

• 12.30 (4 sig figs)

• 1203 (4 sig figs)

• 1200 (2, 3, or 4 sig figs depending on context)

• 1.200 × 103 (4 sig figs)

Significant Figures in Mathematical Operations

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

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

Example:

• If a dog weighs 32.2 kg, the total weight of 6 dogs is , but the answer should be rounded to 3 sig figs: 193 kg.

• If the height of a dog is 73 cm and a soccer ball on its head adds 22.5 cm, the total height is , but the answer should be rounded to the least number of decimal places.

Scientific Notation

Purpose and Usage

Scientific notation is a method for expressing very large or very small numbers in the form , where and is an integer. It simplifies calculations and clarifies the number of significant figures.

Example:

• The distance between Bethlehem, PA and Minneapolis, MN:

SI Prefixes and Metric System

Common Prefixes

SI prefixes are used to indicate multiples or fractions of units, making it easier to express measurements across a wide range of magnitudes.

Unit Conversion

Converting Between Units

Unit conversion is a fundamental skill in chemistry, allowing measurements to be expressed in the most useful units for a given context. This often involves multiplying by conversion factors.

Example:

• To convert the distance to miles, use the equality :

Calculation:

Uncertainty in Measurement

Understanding Uncertainty

All measured quantities have an associated uncertainty, which reflects the limitations of the measuring instrument and the skill of the experimenter. Reporting uncertainty is essential for scientific accuracy.

• Uncertainty is typically indicated by the last significant figure in a measurement.

• Exact numbers (e.g., defined conversion factors) have no uncertainty.

Example:

• When measuring the volume of liquid in a graduated cylinder, the uncertainty is usually ±0.1 mL if the smallest division is 0.1 mL.

Summary Table: Significant Figures Rules

Additional info: These foundational measurement concepts are essential for all branches of chemistry, including organic chemistry, as they underpin laboratory work, data analysis, and scientific reporting.