Matter, Measurement, and Problem Solving

The Importance of Units in Chemistry

Units are standardized quantities used to specify measurements and are essential for clear scientific communication. Chemistry relies on the International System of Units (SI), which is based on the metric system and used globally by scientists.

• Metric system: Used in most countries worldwide.

• English system: Used primarily in the United States.

• SI Units: The modern form of the metric system, abbreviated from the French Système International d’Unités.

The Meter: A Measure of Length

The meter (m) is the SI unit for length and is slightly longer than a yard. It is now defined as the distance light travels in a vacuum in 1/299,792,458 of a second.

• 1 meter = 39.37 inches

• 1 yard = 36 inches

The Kilogram: A Measure of Mass

Mass measures the quantity of matter in an object. The SI unit is the kilogram (kg), where 1 kg = 2.205 lb. The gram (g) is also commonly used (1 g = 1/1000 kg). Mass is distinct from weight, which measures the gravitational pull on an object.

The Second: A Measure of Time

The second (s) is the SI unit for time, defined by a specific number of radiation events of the cesium-133 atom.

The Kelvin: A Measure of Temperature

Temperature measures the average kinetic energy of particles in matter. The SI unit is the kelvin (K). Temperature determines the direction of heat flow, always from hot to cold. The Kelvin scale starts at absolute zero (0 K), the lowest possible temperature where molecular motion ceases.

• Absolute zero: -273 °C or -459 °F

• The Celsius and Kelvin scales have the same degree size; Fahrenheit degrees are smaller.

Temperature Scale Conversions

Temperature can be converted between scales using the following formulas:

SI Prefix Multipliers

SI units use prefix multipliers to indicate powers of ten, making it easier to express very large or small quantities. For example, 1 kilometer (km) = 1000 meters (m).

Derived Units: Volume and Density

Volume

Volume is the amount of space an object occupies. It is measured in cubic meters (m3), cubic centimeters (cm3), or liters (L). 1 L = 1000 cm3.

Density

Density is the ratio of mass to volume and is an important property for identifying substances. It is calculated as:

Density determines whether a substance will sink or float in another substance. Less dense substances float on more dense substances.

Measuring Volume and Density

• For regular solids, use geometric formulas for volume and a balance for mass.

• For irregular solids, use water displacement to find volume.

Reading Volumes and Meniscus

When measuring liquid volume in a graduated cylinder, always read the value at the bottom of the meniscus at eye level for accuracy.

Reading Thermometers

Thermometers should be read at eye level, and the value should be recorded to the correct number of significant digits based on the instrument's scale.

Significant Figures and Measurement Precision

Significant Figures

Significant figures reflect the precision of a measured quantity. The more significant figures, the greater the certainty. The rules for counting significant figures are:

• All nonzero digits are significant.

• Interior zeroes (between nonzero digits) are significant.

• Leading zeroes (before the first nonzero digit) are not significant.

• Trailing zeroes after a decimal point are significant; before a decimal point, they are ambiguous unless specified by a decimal point or scientific notation.

Exact Numbers

Exact numbers have an unlimited number of significant figures. These include counted objects, defined quantities, and some conversion factors.

Significant Figures in Calculations

• Multiplication/Division: The result has the same number of significant figures as the factor with the fewest significant figures.

• Addition/Subtraction: The result has the same number of decimal places as the quantity with the fewest decimal places.

Rounding Rules

• Round down if the digit dropped is four or less; round up if it is five or more.

• In multistep calculations, round only the final answer to avoid cumulative rounding errors.

Accuracy and Precision

Definitions

• Accuracy: How close a measured value is to the true value.

• Precision: How close repeated measurements are to each other.

Types of Error

• Random error: Equal probability of being too high or too low; affects precision.

• Systematic error: Consistently too high or too low; affects accuracy.

Dimensional Analysis and Unit Conversions

Dimensional Analysis

Dimensional analysis is a systematic approach to problem solving that uses conversion factors to move from one unit to another. Units are treated algebraically and can be canceled or converted as needed.

• Unit equation: Statement of two equivalent quantities (e.g., 2.54 cm = 1 in).

• Conversion factor: Fraction derived from a unit equation, used to convert between units.

Units Raised to a Power

When converting units raised to a power (e.g., cm2 to in2), both the number and the unit must be raised to the appropriate power.

• For example: so

Summary Table: Common SI Base Units and Prefixes

Example: To convert 1.76 yards to centimeters, use the conversion factors: 1 m = 1.094 yd and 1 m = 100 cm.

Example: To find the mass of jet fuel given volume and density, use the formula and appropriate unit conversions.