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, ensuring consistency and clarity in scientific communication.

• Metric System: Used globally, includes units such as centimeters (cm), meters (m), kilograms (kg), grams (g), liters (L), milliliters (mL), kilometers (km).

• English System: Used primarily in the United States, includes inches (in), feet (ft), yards (yd), pounds (lb), gallons (gal), miles (mi).

• SI System: The International System of Units (Système International d’Unités, SI) was established in 1960 for universal scientific use. It consists of seven base units, with all other units derived from these.

SI Base Units

The SI system is built on seven base units, each representing a fundamental physical quantity. All other units are derived from these base units.

The Meter: A Measure of Length

Length measures the distance between two points. The SI unit is the meter (m).

• 1 meter = 1.09361 yard

• 1 meter = 39.37 inches

• 1 yard = 36 inches

The Kilogram: A Measure of Mass

Mass quantifies the amount of matter in an object. The SI unit is the kilogram (kg).

• 1 kilogram = 1000 grams

• 1 kilogram = 2.205 pounds

The Second: A Measure of Time

Time measures the duration of events. The SI unit is the second (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 is the kelvin (K).

• The Kelvin scale starts at absolute zero (0 K), where molecular motion ceases.

• 0 K = -273.15°C = -459°F

• Temperature is crucial for understanding energy changes and chemical reactions.

Prefix Multipliers

Prefix multipliers are used in the SI system to represent very large or very small numbers, making measurements easier to communicate.

Example: For a measurement of 5.57 x 10-5 m, the most appropriate prefix is micro (μ).

Derived Units

Derived units are combinations of two or more base units, used to express quantities such as volume, density, speed, and force.

• Volume: Measures space, units include cubic meter (m3), cubic centimeter (cm3), milliliter (mL), liter (L), gallon (gal).

• 1 mL = 1 cm3

• 1 L = 1000 mL = 1000 cm3

• 1 gal = 3.785 L

• 1 m3 = 1000 L

Density

Density is a derived quantity defined as mass per unit volume. It is a key property for identifying substances and understanding their behavior.

• Formula:

• Common units: g/mL, kg/m3

Example: A jeweler examines a 2.50‑g ring claimed to be diamond. When the ring is submerged, the water level in a graduated cylinder rises from 10.00 mL to 11.06 mL. The actual density of diamond is 3.51 g/mL. To determine if the ring is genuine diamond:

• Volume displaced = 11.06 mL - 10.00 mL = 1.06 mL

• Density of ring =

• Since 2.36 g/mL < 3.51 g/mL, the ring is likely not diamond.

Mathematical Operations and Significant Figures

In chemistry, calculations often require attention to significant figures, which reflect the precision of measurements. When adding or subtracting, the result should be rounded to the least precise decimal place. When multiplying or dividing, the result should have the same number of significant figures as the measurement with the fewest significant figures.

• Example (Addition): (rounded to 5.41)

• Example (Subtraction): (rounded to 5.7)

Additional info: Significant figures are essential for reporting scientific measurements accurately and reflect the certainty of the data.