Chemistry Fundamentals: Unit Conversion & Elements

Converting Derived Units

Introduction to Derived Unit Conversion

Derived units are combinations of base units (e.g., miles/hour, km/sec). Converting between different derived units requires a systematic approach using conversion factors.

Key Principles

• Exact Numbers: Numbers given in a formula or definition (e.g., $3600$ seconds per hour, $1.609$ km per mile) are considered exact and do not limit the significant figures in the final answer.
• Significant Figures (Sig Figs): The number of significant figures in the final answer is determined by the least precise initial measurement given in the problem.

Steps for Converting Derived Units

1. Rewrite the given quantity as a fraction: Express the initial derived unit as a numerator over a denominator.
2. Identify initial and final units: Clearly state the units you are starting with (given) and the units you want to end with (desired).
3. Convert the top unit: Use appropriate conversion factors to change the unit in the numerator.
   • Arrange the conversion factor so that the initial unit cancels out and the desired unit remains.
4. Convert the bottom unit: Use appropriate conversion factors to change the unit in the denominator.
   • Arrange the conversion factor so that the initial unit cancels out and the desired unit remains.
5. Multiply and Divide: Multiply all numbers in the numerators and divide by all numbers in the denominators (skip any "$1$"s).
6. Apply Significant Figures: Round the final answer to the correct number of significant figures based on the initial measurement.

Example 1: Convert $70.0 \text{ miles/hour}$ to $\text{km/sec}$

• Given: $70.0 \text{ miles/hour}$
  • Initial units: miles, hour
  • $70.0$ has 3 significant figures.
• Desired Units: km, sec
• Conversion Factors:
  • $1 \text{ hour} = 3600 \text{ sec}$ (exact)
  • $1 \text{ mile} = 1.609 \text{ km}$ (exact)
    Step-by-Step Calculation:

1. Rewrite as a fraction: $\frac{70.0 \text{ miles}}{1 \text{ hour}}$
2. Convert top unit (miles to km): Multiply by $\frac{1.609 \text{ km}}{1 \text{ mile}}$
   • $\frac{70.0 \text{ miles}}{1 \text{ hour}} \times \frac{1.609 \text{ km}}{1 \text{ mile}}$
   • (The 'miles' unit cancels out)
3. Convert bottom unit (hour to sec): Multiply by $\frac{1 \text{ hour}}{3600 \text{ sec}}$
   • $\frac{70.0 \text{ miles}}{1 \text{ hour}} \times \frac{1.609 \text{ km}}{1 \text{ mile}} \times \frac{1 \text{ hour}}{3600 \text{ sec}}$
   • (The 'hour' unit cancels out)
4. Perform Calculation:
   • $= \frac{70.0 \times 1.609}{3600} \text{ km/sec}$
   • $= 0.031286… \text{ km/sec}$
5. Apply Significant Figures: Since $70.0$ has 3 significant figures, the final answer should also have 3 significant figures.
   • $= 0.0313 \text{ km/sec}$

Example 2 (Continuation): Convert $0.0313 \text{ km/sec}$ to $\text{m/sec}$

• Given: $0.0313 \text{ km/sec}$
• Desired Units: m, sec
• Conversion Factor: $1 \text{ km} = 10^3 \text{ m}$
  Calculation:
• $\frac{0.0313 \text{ km}}{1 \text{ sec}} \times \frac{10^3 \text{ m}}{1 \text{ km}}$
• $= 0.0313 \times 10^3 \text{ m/sec}$
• $= 31.3 \text{ m/sec}$

Practice Problem: Convert $70.0 \text{ m/sec}$ to $\text{mi/hr}$

• Given: $70.0 \text{ m/sec}$
  • Initial units: m, sec
  • $70.0$ has 3 significant figures.
• Desired Units: mi, hr
• Conversion Factors:
  • $1 \text{ hr} = 3600 \text{ sec}$ (exact)
  • $1 \text{ mi} = 1.609 \text{ km}$ (exact)
  • $1 \text{ km} = 10^3 \text{ m}$ (or $1 \text{ m} = 10^{-3} \text{ km}$)
    Setup and Calculation:
• $\frac{70.0 \text{ m}}{1 \text{ sec}} \times \frac{1 \text{ km}}{10^3 \text{ m}} \times \frac{3600 \text{ sec}}{1 \text{ hr}} \times \frac{1 \text{ mi}}{1.609 \text{ km}}$
• $= \frac{70.0 \times 3600}{10^3 \times 1.609} \text{ mi/hr}$
• $= \frac{252000}{1609} \text{ mi/hr}$
• $= 156.619… \text{ mi/hr}$
  Apply Significant Figures: Round to 3 significant figures.
• $= 157 \text{ mi/hr}$

Chemistry and Elements

Fundamentals of Chemistry

• Chemistry: The scientific study of matter, energy, and their interactions.
• Matter: Anything that possesses both mass and volume.
  • Example: Air is considered matter because it has mass and occupies space.
  • Non-example: Light is not matter; it is a form of energy.
• Energy: The ability to perform work.
  • Example: Light is a prime example of energy, specifically referred to as electromagnetic radiation.

Chemical Elements: The Building Blocks of Matter

Definition

• Chemical Elements: Pure substances uniquely characterized by consisting of only one distinct type of atom.
  • Examples: Carbon (C), Hydrogen (H), Oxygen (O), and Iron (Fe).

Fundamental Properties

• Unique Atomic Number: Each element is defined by its unique atomic number, which represents the number of protons in its atoms.
• Indivisibility by Chemical Means: Elements are foundational substances that cannot be chemically broken down into simpler constituent substances.

The Periodic Table of Elements

Definition and Purpose

• Periodic Table: An ordered tabular arrangement that systematically organizes all known chemical elements. This organization is based primarily on their atomic number, electron configurations, and recurring chemical properties.
• Number of Elements: Currently, $118$ distinct elements have been discovered and recognized.
• Inventor: Dmitri Mendeleev is credited with inventing the periodic table in $1869$.
• Core Purposes:
  • Property Prediction: Enables accurate prediction of chemical and physical properties of elements, even those not yet discovered (as seen in Mendeleev's work).
  • Relationship Visualization: Illustrates fundamental relationships and trends among elements.

Structural Organization

• Rows (Periods): Elements situated within the same row (period) share an equivalent number of electron energy shells.
• Columns (Groups/Families): Elements organized within the same column (group or family) typically exhibit highly similar chemical properties due to having the same number of valence electrons.
• Major Categories: The periodic table broadly classifies elements into three principal categories:
  • Metals: Generally malleable, ductile, good conductors of heat and electricity (e.g., Sodium (Na)).
  • Nonmetals: Tend to be poor conductors, often brittle, and can appear in various states (e.g., Oxygen (O)).
  • Metalloids: Possess properties intermediate between metals and nonmetals, often acting as semiconductors (e.g., Silicon (Si)).

Abundance of Elements (No memorization required)

Most Abundant Elements in the Universe

• Hydrogen (H): Approximately $75\%$ of the baryonic mass of the universe.
• Helium (He): Roughly $24\%$ of the baryonic mass of the universe.
• Oxygen (O): Accounts for about $1\%$ of the universe's element composition.

Most Abundant Elements on Earth (by mass)

• Oxygen (O): Constitutes about $46\%$ of Earth's crust.
  • Found significantly in: rocks, various minerals, soil, and water.
• Silicon (Si): Makes up approximately $28\%$ of Earth's crust.
  • Prevalent in: sand, quartz, and a wide array of silicate minerals.
• Aluminum (Al): Accounts for roughly $8\%$ of Earth's crust.
  • Commonly found in: bauxite ore, many rock types, and clay minerals.

Most Abundant Elements in the Human Body (by mass)

• Oxygen (O): The most abundant element, comprising approximately $65\%$ of body mass.
  • Essential component of: water, biological tissues, and organs.
• Carbon (C): Makes up about $18\%$ of body mass.
  • Central to: proteins, fats, carbohydrates, and DNA.
• Hydrogen (H): Accounts for around $10\%$ of body mass.
  • Key constituent of: water and all organic molecules.
• Nitrogen (N): Constitutes roughly $$3\