Chapter One: Matter, Measurement, and Problem Solving

The Units of Measurement

Measurement is fundamental to chemistry, allowing scientists to quantify properties and compare results. Units are standardized quantities used to specify measurements, and two main systems are used worldwide: the metric system and the English system. The metric system is prevalent globally, while the English system is mainly used in the United States. In 1960, the General Conference on Weights and Measures established the International System of Units (SI), which includes seven base units from which all other units are derived.

• Metric System: Uses units such as centimeters (cm), meters (m), kilograms (kg), liters (L), etc.

• English System: Uses units such as inches (in), feet (ft), pounds (lb), gallons (gal), etc.

• SI Units: The abbreviation SI stands for Système International d’Unités.

• Base Units: Fundamental units for length, mass, time, temperature, etc.

• Derived Units: Combinations of base units for quantities like volume, density, speed, and force.

SI Base Units

The SI system is built on seven base units, each corresponding to a fundamental physical quantity. These units are used as the foundation for all scientific measurements.

• Length: Measured in meters (m). 1 meter = 1.09361 yards = 39.37 inches

• Mass: Measured in kilograms (kg). 1 kilogram = 1000 grams = 2.205 pounds

• Time: Measured in seconds (s). 1 minute = 60 seconds; 1 hour = 60 minutes

The Kelvin: A Measure of Temperature

Temperature quantifies the thermal energy of a substance and determines the direction of heat transfer. The SI unit for temperature is the kelvin (K). The Kelvin scale starts at absolute zero (0 K), the lowest possible temperature where molecular motion ceases.

• Kelvin (K): SI unit for temperature.

• Absolute Zero: 0 K = -273.15°C = -459°F

• Heat Transfer: Thermal energy moves from hot to cold objects.

Prefix Multipliers

Prefix multipliers are used in the SI system to represent very large or very small numbers, making measurements easier to communicate. Examples include kilo (103), milli (10-3), micro (10-6), and mega (106).

• Kilo (k): 103

• Milli (m): 10-3

• Micro (μ): 10-6

• Mega (M): 106

Derived Units

Derived units are formed by combining two or more base units. They are used to express quantities such as volume, density, speed, and force.

• Volume: Measured in cubic meters (m3), liters (L), milliliters (mL), or gallons (gal). 1 mL = 1 cm3; 1 L = 1000 mL = 1000 cm3; 1 gal = 3.785 L; 1 m3 = 1000 L

• Density: Measured in kilograms per cubic meter (kg/m3) or grams per milliliter (g/mL).

• Speed: Measured in meters per second (m/s).

• Force: Measured in newtons (N), where

Volume Measurement Example

Volume is often measured using graduated cylinders or beakers. For example, if a ring is submerged in water and the water level rises, the difference in volume indicates the ring's volume.

Density Calculation Example

Density is calculated as mass divided by volume. For example, a jeweler examines a 2.50 g ring. When submerged, the water level rises from 10.00 mL to 11.06 mL, indicating a volume of 1.06 mL. The density is:

• Formula:

• Calculation:

• Comparison: Actual density of diamond is 3.51 g/mL. The ring's density is less, so it is likely not a genuine diamond.

Mathematical Operations and Significant Figures

When performing calculations in chemistry, it is important to consider significant figures. The number of significant digits in the result should reflect the precision of the measurements used.

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

• Example: (rounded to two decimal places) (rounded to one decimal place)

Additional info: Significant figures are crucial for reporting scientific measurements accurately. Always round the final answer to reflect the least precise measurement used in the calculation.