Chemistry Notes: Matter, Measurement, and Problem Solving

Chemistry: The Study of Matter

• Chemistry is the study of matter and its changes.
• Matter is anything that has mass and takes up space.

States of Matter

• Solid, liquid, and gas are the three states of matter.
• Gases can be cooled/compressed into liquids, and liquids can be cooled into crystalline solids.
• The reverse processes occur with heating or reducing pressure.

Matter and Its Composition

• Atoms are the building blocks of matter.
• An element consists of the same kind of atoms.
• A compound consists of two or more different kinds of elements.

Scientific Method

• The scientific Method is a systematic approach to problem-solving that involves:
  • Observations and experiments.
  • Finding patterns, trends, and laws.
  • Formulating and testing hypotheses.
  • Developing theories.

Properties of Matter

• Intensive Properties:
  • Independent of the amount of substance present.
  • Examples: density, boiling point, color.
• Extensive Properties:
  • Dependent on the amount of substance present.
  • Examples: mass, volume, energy.

Changes of Matter

• Physical Changes:
  • Changes that do not alter the composition of the substance.
  • Examples: changes of state, temperature, volume.
• Chemical Changes:
  • Changes that result in new substances.
  • Examples: combustion, oxidation, decomposition.

Separation Techniques

• Distillation:
  • Separates homogeneous mixtures based on boiling point differences.
• Filtration:
  • Separates solid substances from liquids and solutions.
• Chromatography:
  • Separates substances based on differences in solubility in a solvent.

Measurement

• Measurements involve a number and a unit (e.g., 35 m, 0.25 L).

Metric System (SI)

• A decimal system based on 10.
• Used worldwide and universally by scientists.

Units in the Metric System

• Each type of measurement has a specific unit:
  • Length: meter (m)
  • Volume: liter (L), cubic meter (m^3)
  • Mass: gram (g), kilogram (kg)
  • Time: second (s)
  • Temperature: Celsius (°C), Kelvin (K)

Metric System Prefixes

• Prefixes modify base units for appropriate measurements.
• Examples:
  • Giga (G): 10^9 (e.g., 1 Gm = 1 × 10^9 m)
  • Mega (M): 10^6 (e.g., 1 Mm = 1 × 10^6 m)
  • Kilo (k): 10^3 (e.g., 1 km = 1 × 10^3 m)
  • Deci (d): 10^{-1} (e.g., 1 dm = 0.1 m)
  • Centi (c): 10^{-2} (e.g., 1 cm = 0.01 m)
  • Milli (m): 10^{-3} (e.g., 1 mm = 0.001 m)
  • Micro (μ): 10^{-6} (e.g., 1 μm = 1 × 10^{-6} m)
  • Nano (n): 10^{-9} (e.g., 1 nm = 1 × 10^{-9} m)
  • Pico (p): 10^{-12} (e.g., 1 pm = 1 × 10^{-12} m)
  • Femto (f): 10^{-15} (e.g., 1 fm = 1 × 10^{-15} m)

Powers of Ten

• Illustrates the relationship between standard numbers and scientific notation.
• For example:
  • 10,000 = 1 × 10^4
  • 0.0001 = 1 × 10^{-4}

SI Units

• Système International d'Unités.
• Uses a base unit for each quantity.
• Examples:
  • Mass: kilogram (kg)
  • Length: meter (m)
  • Time: second (s)
  • Temperature: Kelvin (K)
  • Amount of substance: mole (mol)
  • Electric current: Ampere (A)
  • Luminous intensity: Candela (cd)

Volume

• Space occupied by a substance.
• Metric unit: liter (L); 1 L = 1.057 qt
• SI unit: cubic meter (m^3)
• Measured using a graduated cylinder.
• 1 L = 1 dm3
• 1 mL = 1 cm3

Volume by Displacement

• A submerged solid displaces its own volume of water.
• Volume calculated from the difference in water levels.
• For example: 45.0 mL - 35.5 mL = 9.5 mL = 9.5 cm3

Temperature Measurement

• Indicates hotness or coldness.
• Metric system: Celsius (°C).
• SI system: Kelvin (K).

Temperature Scales

• Celsius:
  • Water freezes at 0°C.
  • Water boils at 100°C.
• Kelvin:
  • No negative Kelvin temperatures.
  • K = °C + 273.15
• Fahrenheit:
  • Not used in scientific measurements.
  • °F = \,^9/_5(°C) + 32
  • °C = \,^5/_9 (°F − 32)

Length Measurement

• Measured using a meter stick.
• Unit: meter (m) in both metric and SI systems.
• 1 in. = 2.54 cm

Mass Measurement

• Quantity of material.
• Measured on a balance.
• Metric unit: gram (g).
• SI unit: kilogram (kg).

Time Measurement

• Unit: second (s) in both metric and SI systems.
• Based on an atomic clock using cesium atoms.

Exact Numbers

• Obtained by counting or defined relationships.
• Examples:
  • Counted objects (2 soccer balls, 4 pizzas).
  • Defined relationships (1 foot = 12 inches, 1 meter = 100 cm).
  • U.S. System (1 ft = 12 in., 1 lb = 16 ounces, 1 qt = 4 cups).
  • Metric System (1 L = 1000 mL, 1 m = 100 cm, 1 kg = 1000 g).

Measured Numbers

• Determined using a measuring tool.

Reading a Meter Stick

• Read markings to the known digit (e.g., 2.7).
• Estimate the last digit (e.g., 2.75 cm or 2.76 cm).

Known & Estimated Digits

• Certain digits are known.
• The final digit is estimated and uncertain.
• All digits are significant.

Rounding Off Calculated Answers

• Answers should have the same number of significant figures as the measured numbers.
• If the first dropped digit is 4 or less, retain the numbers as they are (e.g., 45.832 rounded to 45.8).
• If the first dropped digit is 5 or greater, increase the last retained digit by 1 (e.g., 2.4884 rounded to 2.5).

Zero as a Measured Number

• If a line ends on a mark, the estimated digit is 0 (e.g., 4.50 cm).

Scientific Notation

• Used for very large or very small numbers.
• A number in scientific notation contains a coefficient and a power of 10.
• The width of a human hair: 0.000 008 m = 8 × 10^{-6} m.
• A large number like 4,500,000 s = 4.5 × 10^6 s.

Writing Numbers in Scientific Notation

• Move the decimal point after the first digit.
• Spaces moved are the power of ten.
• 52,000 = 5.2 × 10^4
• 0.00378 = 3.78 × 10^{-3}

Comparing Numbers in Standard and Scientific Notation

• Diameter of the Earth: 12,800,000 m = 1.28 × 10^7 m
• Mass of a human: 68 kg = 6.8 × 10^1 kg
• Length of a pox virus: 0.000 03 cm = 3 × 10^{-5} cm

Significant Figures in Measured Numbers

• Include all known digits plus the estimated digit.
• Depend on the measuring tool.

Rules for Significant Figures

1. A number is a significant figure if it is
   • not a zero
   • a zero between nonzero digits
   • a zero at the end of a decimal number
   • all digits in the coefficient of a number written in scientific notation
2. A zero is not significant if it is
   • at the beginning of a decimal number
   • used as a placeholder in a large number without a decimal point

Examples

4. 5 g - 2 SF
5. 0 g - 3 SF
6. 0004 lb - 1 SF
7. 0 × 105 m - 2 SF

Significant Figures in Scientific Notation

• All digits, including zeros in the coefficient, are significant.

Examples

• 8 × 10^4 m - 1 SF
• 8.0 × 10^4 m - 2 SF
• 8.00 × 10^4 m - 3 SF

Adding Significant Zeros

• Sometimes, zeros are added to provide the required number of significant figures.
• 4 becomes 4.00 (3 SF).

Calculations with Measured Numbers

• Significant figures or decimal places are counted to determine the number of figures in the final answer.

Multiplication and Division

• Use the same number of significant figures as the measurement with the fewest significant figures.
• 110.5 × 0.048 = 5.304 = 5.3 (rounded).

Addition and Subtraction

• Use the same number of decimal places as the measurement with the fewest decimal places.
• 25.2 + 1.34 = 26.54 = 26.5

Conversion Factors

• Conversion factors must have at least as many significant figures as the data being converted because they are derrived from equivalencies that are essentially