2.1 The Metric Mix-Up: A Cautionary Tale

Introduction to Measurement Errors in Chemistry

Measurement errors can have significant consequences in science and engineering. A famous example is the loss of NASA's Mars Climate Orbiter in 1999 due to a mix-up between metric and imperial units. This incident highlights the importance of using correct units and conversions in all scientific calculations.

• Key Point: Always check and convert units appropriately to avoid costly mistakes.

• Example: The Mars Climate Orbiter was lost because one team used newton-seconds (metric) and another used pound-seconds (imperial) for force calculations.

2.2 Scientific Notation

Using Powers of Ten for Large and Small Numbers

Scientific notation is a method for expressing very large or very small numbers in a compact form using powers of ten. This is essential for clarity and precision in chemistry calculations.

• Definition: A number is written as the product of a coefficient (between 1 and 10) and a power of ten.

• Examples:

  • 10,000 =

  • 0.00001 =

  • 5,963,000 =

  • 0.00042 =

2.3 Significant Figures (Sig Figs)

Rules for Counting and Using Significant Figures

Significant figures reflect the precision of a measured or calculated quantity. The number of significant figures in a value indicates the certainty of the measurement.

• Definition: All nonzero digits are significant; zeros may or may not be significant depending on their position.

• Rules for Counting Sig Figs:

  1. All nonzero digits are significant (e.g., 2.91 has 3 sig figs).

  2. Interior zeros (between nonzero digits) are significant (e.g., 2.001 has 4 sig figs).

  3. Leading zeros (before the first nonzero digit) are not significant (e.g., 0.0032 has 2 sig figs).

  4. Trailing zeros after a decimal point are significant (e.g., 3.00 has 3 sig figs).

  5. Trailing zeros before a decimal point (and after a nonzero digit) are significant if the decimal is shown (e.g., 500. has 3 sig figs).

  6. Trailing zeros in a whole number with no decimal shown are ambiguous (e.g., 500 could have 1, 2, or 3 sig figs).

• Example: 0.00230 has 3 significant figures.

2.4 Significant Figures in Calculations

Applying Sig Fig Rules to Mathematical Operations

• Multiplication and Division: The result should have the same number of significant figures as the measurement with the fewest significant figures.

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

• Example (Multiplication): (rounded to 2 sig figs: 39)

• Example (Addition): (rounded to 2 decimal places: 14.56)

2.5 Units of Measurement

Common and Derived Units in Chemistry

• Common SI Units:

  • Length: meter (m)

  • Mass: kilogram (kg)

  • Time: second (s)

  • Temperature: kelvin (K)

  • Volume: liter (L) or cubic meter (m3)

• Derived Units: Formed by combining base units (e.g., m/s for speed, m3 for volume).

• Unit Conversions: Always include units in calculations and convert as needed.

• Example:

2.7-2.8 Multiplication, Conversion, and Density

Unit Conversions and Density Calculations

• Multiplication and Conversion: Use conversion factors to change units (e.g., ).

• Density: Density is mass per unit volume, calculated as .

• Example: If a liquid has a mass of 13.2 g and a volume of 51.6 mL, its density is .

3.5 Energy

Energy in Chemical and Physical Changes

• Definition: Energy is the capacity to do work or produce heat. It is involved in all chemical and physical changes.

• Types of Energy:

  • Kinetic Energy: Energy of motion

  • Potential Energy: Stored energy due to position or composition

• Units: Joule (J) is the SI unit of energy. 1 calorie (cal) = 4.184 J.

• Example: Calculating energy change:

3.6 Temperature

Temperature Scales and Conversions

• Definition: Temperature measures the average kinetic energy of particles in a substance.

• Scales: Celsius (°C), Kelvin (K), and Fahrenheit (°F).

• Conversions:

3.7 Conservation of Mass

Law of Conservation of Mass in Chemical Reactions

• Definition: In a chemical reaction, matter is neither created nor destroyed.

• Application: The total mass of reactants equals the total mass of products in a closed system.

• Example: If 10 g of hydrogen reacts with 80 g of oxygen, the total mass of water produced is 90 g.

3.1-3.2 Matter and Its Classification

Types of Matter and Their Properties

• Definition: Matter is anything that has mass and occupies space.

• Classification:

  • Pure Substances: Elements and compounds with fixed composition

  • Mixtures: Physical combinations of substances that can be separated by physical means

• States of Matter: Solid, liquid, gas

• Physical vs. Chemical Properties: Physical properties can be observed without changing the substance's identity; chemical properties describe how a substance reacts.

3.3-3.4 Physical and Chemical Changes

Understanding Changes in Matter

• Physical Change: Alters the form or appearance but not the composition (e.g., melting, boiling).

• Chemical Change: Produces new substances with different properties (e.g., burning, rusting).

• Indicators of Chemical Change: Color change, gas production, formation of a precipitate, energy change.

Lab Techniques: Separating Mixtures

Methods for Separating Components of Mixtures

• Decanting: Carefully pouring off a liquid to separate it from a solid or another liquid (e.g., oil and water).

• Filtration: Using a filter to separate a solid from a liquid.

• Distillation: Separating substances based on differences in boiling points.