Measurement and Units

Comparing Quantities and Unit Conversions

Understanding how to compare quantities expressed in different units is essential in chemistry. This often requires converting between units using appropriate conversion factors.

• Milliliters (mL) and microliters (μL) are both units of volume. 1 mL = 1,000 μL.

• To compare 5.3 × 102 mL and 6.4 × 105 μL, convert both to the same unit:

Example Calculation:

• Thus, 6.4 × 105 μL is larger.

Density and Volume Calculations

Density Determination

Density is a fundamental property defined as mass per unit volume.

• Formula:

• When a solid is placed in a container and the container is filled with a liquid, the density of the solid can be determined by measuring the mass difference and knowing the density of the liquid.

Example: A block of solid (58.16 g) is placed in a 100 mL container, filled to capacity with benzene (density = 0.864 g/mL), and the total mass is 96.15 g.

• Mass of benzene added:

• Volume of benzene:

• Volume of solid:

• Density of solid:

Physical and Chemical Changes

Identifying Types of Changes

Distinguishing between physical and chemical changes is crucial in chemistry.

• Physical Change: Alters the form or appearance of matter but does not change its composition (e.g., melting, dissolving).

• Chemical Change: Results in the formation of new substances with different properties (e.g., rusting, burning).

• Changes in mass and appearance often indicate a physical change, while changes in color and texture may indicate a chemical change.

Exact Numbers and Significant Figures

Exact Numbers

Exact numbers are values that are known with complete certainty, often from definitions or counting.

• Examples: 1 inch = 2.54 cm (defined), 1 US quart = 32 US fluid ounces (defined).

• Measured values (e.g., height of Eiffel Tower, world record times) are not exact numbers.

Significant Figures

Significant figures reflect the precision of a measured quantity.

• When calculating volume from measurements, the number of significant figures in the result should match the least precise measurement.

Intensive and Extensive Properties

Classification of Properties

Properties of matter are classified as intensive or extensive.

• Intensive Properties: Do not depend on the amount of substance (e.g., refractive index, melting point, density).

• Extensive Properties: Depend on the amount of substance (e.g., mass, volume).

Mixtures and Density Calculations

Calculating Volumes in Mixtures

When combining immiscible liquids, their individual volumes can be calculated using their densities and the total mass.

• Formula:

• Example: Water (d = 1.00 g/mL) and hexane (d = 0.66 g/mL) are mixed to a total mass of 312.9 g and total volume of 354.4 mL.

Density and Floating/Sinking

Application to Real Materials

Whether an object floats or sinks depends on its density relative to the fluid.

• If density of object < density of fluid, it floats.

• If density of object > density of fluid, it sinks.

• Example: Persimmon wood sphere (mass = 234 g, diameter = 8.32 cm):

• Volume of sphere:

• Density:

• Floats in water (density = 1.00 g/cm3), sinks in petroleum ether (density = 0.653 g/cm3).

Dalton's Atomic Theory and Law of Multiple Proportions

Key Postulates

Dalton's atomic theory laid the foundation for modern chemistry.

• Law of Multiple Proportions: Compounds are made of two or more different types of atoms in fixed, simple, whole number ratios.

Atomic Structure: Ions, Electrons, and Protons

Determining Ion Composition

Ions are atoms or molecules with a net electric charge due to loss or gain of electrons.

Law of Multiple Proportions: Calculations

Hydrogen Reaction with Carbon

Using the law of multiple proportions, the amount of hydrogen reacting with a fixed amount of carbon to form different compounds can be calculated.

• Example: For methane (CH4) and ethylene (C2H2), calculate hydrogen needed for 1.78 g carbon.

States of Matter and Periodic Table

Elemental States

Most elements are solids at room temperature, with a few exceptions (e.g., mercury is liquid, noble gases are gases).

Isotopes and Atomic Weight

Calculating Atomic Weight

The atomic weight of an element is the weighted average of the masses of its isotopes.

• Formula:

• Example for Sulfur:

Atomic Models and Rutherford's Experiment

Plum-Pudding Model vs. Nuclear Model

The plum-pudding model proposed electrons embedded in a positively charged 'pudding.' Rutherford's gold foil experiment showed that atoms have a small, dense nucleus, contradicting the plum-pudding model.

• If the plum-pudding model were correct, alpha particles would pass through with little deflection.

Periodic Table Groups and Ion Formation

Group Numbers and Ion Charges

Elements in different groups form ions with characteristic charges.

• Group 2A elements form 2+ ions (e.g., Mg2+).

• Group 7A elements form 1- ions (e.g., Cl-).

Chemical Nomenclature

Element Names and Symbols

Knowing the names and symbols of elements is fundamental.

• Rh: Rhodium

• Si: Silicon

• O: Oxygen

• P: Phosphorus

Binary Compound Formulas

Binary compounds consist of two elements. Their formulas are determined by the charges of the ions.

Hydrated Ionic Compounds

Hydrated compounds contain water molecules in their structure.

• K2CrO4·3H2O is named potassium chromate trihydrate.

Chemical Equations and Stoichiometry

Balanced Equations

Balanced chemical equations show the conservation of mass and charge.

• Example: Detonation of TNT (C7H5N3O6):

Stoichiometry and Yield Calculations

Stoichiometry allows calculation of product amounts from reactant quantities, considering reaction yields.

• Example: Extraction of iron from hematite (Fe2O3) via a series of reactions, with percent yield applied to each step.

Summary Table: Key Properties

Additional info: These notes expand on the original problems by providing definitions, formulas, and context for each concept, suitable for exam preparation in General Chemistry.