Chemistry Lecture Notes Review

Chemistry: The Science of Matter

• Chemistry is the study of the structure and behavior of matter.

The Scientific Method

• There is no single, rigid way to conduct scientific investigations.
• Different scientific fields may develop their own specific procedures.
• Individual scientists may approach knowledge pursuit differently.
• However, scientific methods generally share common characteristics.

Parkinson's Disease: A Case Study

• Parkinson's disease is a degenerative disorder affecting the central nervous system.
• Symptoms include shaking, rigidity, slow movement, and difficulty walking.
• Thinking and behavioral issues can emerge later in the disease progression.
• Onset usually occurs after age 50.

Steps in the Scientific Method

1. Observation and Data Collection

   • Example: In the 1960s, scientists noted Parkinson's-like symptoms in South American manganese miners.

2. Initial Hypothesis

   • The working hypothesis was that the symptoms seen in manganese miners and Parkinson's sufferers shared a common origin.

3. Systematic Research and Experimentation

   • Research indicated that manganese disrupts dopamine, a crucial brain chemical for muscle control.
   • High manganese absorption was linked to movement problems.

4. Hypothesis Refinement

   • Researchers then hypothesized that Parkinson's patients had low dopamine levels in their brains.
   • Brain studies later confirmed this.

5. Publication of Results

   • The flow of the scientific method involves:
     • Observation and information gathering leading to a testable hypothesis.
     • The hypothesis is tested through experimentation.
     • If the experiment fails, the hypothesis is disproven, and further research is conducted to refine applications.
     • If the experiment is successful, applications are sought.
     • Successful results are published.
     • The experiment is repeated.
     • If the experiment is not repeated successfully then it is disproven.

6. Confirmation by Other Scientists

   • Other scientists independently replicate the research to validate or refute the conclusions.
   • In this case, the dopamine research findings were confirmed by other scientists.

7. Search for Useful Applications

   • Key challenge: Dopamine cannot cross from the bloodstream into brain tissue.
   • Researchers sought a compound that could penetrate the brain and convert into dopamine.
   • Levodopa (L-dopa) fulfilled these requirements.

8. Development and Refinement of Applications

   • L-dopa had side effects like nausea, gastrointestinal distress, low blood pressure, delusions, and mental disturbance.
   • The blood pressure effects were due to L-dopa converting to dopamine outside the brain.
   • Solution: Co-administer L-dopa with levocarbidopa, which inhibits the conversion process outside the brain.

• The scientific method is a continuous cycle of observation, hypothesis, experimentation, and application.

Measurement and Units

• A value from a measurement includes both a numerical quantity and a unit.
• Example: In "100 meters," "meter" is the unit of distance, and "100" is the number of units.
• Units are standardized quantities that facilitate comparison between events or objects.

Base Units (International System of Measurement)

• Length: meter (m) - Distance light travels in a vacuum in 1/299,792,458 of a second
• Mass: kilogram (kg) - Mass of a platinum-iridium alloy cylinder in a vault in France
• Time: second (s) - Duration of 9,192,631,770 periods of radiation emitted by cesium-133 during a specific energy level transition
• Temperature: kelvin (K) - 1/273.16 of the temperature difference between absolute zero and the triple point of water

Derived Units

• Example: cubic meter

  1 \, \text{cubic meter} = 1000 \, \text{liters}

  1 \, L = 10^{-3} m^3

  10^3 \, L = 1 \, m^3

Common Base Units and Abbreviations

• Length: meter (m)
• Mass: gram (g)
• Volume: liter (L or l)
• Energy: joule (J)

Scientific (Exponential) Notation

• Numbers written in scientific notation take the form:

  a \times 10^b

  • a is the coefficient (a number with one non-zero digit to the left of the decimal point).
  • 10^b is the exponential term.
  • b is the exponent (a positive or negative integer).

Example

• 5.5 \times 10^{21} carbon atoms in a 0.55 carat diamond

  • 5. 5 is the coefficient.
  • 10^{21} is the exponential term.
  • 21 is the exponent.

Uncertainty

• The coefficient reflects the level of uncertainty.
• Unless otherwise stated, it's generally assumed the coefficient has an uncertainty of plus or minus one in the last reported position.
• Example: 5.5 \times 10^{21} carbon atoms implies a range from 5.4 \times 10^{21} to 5.6 \times 10^{21} carbon atoms.

Magnitude

• The exponential term indicates the size or magnitude of the number.
• Positive exponents represent large numbers.
  • Example: The moon orbits the sun at 2.2 \times 10^4 or 22,000 mi/hr.
  • 2.2 \times 10^4 = 2.2 \times 10 \times 10 \times 10 \times 10 = 22,000
• Negative exponents represent small numbers.
  • Example: A red blood cell has a diameter of about 5.6 \times 10^{-4} or 0.00056 inches.

Converting Decimal Numbers to Scientific Notation

1. Move the decimal point until there is one non-zero digit to its left. Count the number of positions the decimal point moves.
2. Write the resulting coefficient multiplied by 10^b. If the decimal was moved to the left, b is positive; if moved to the right, b is negative. The number in the exponent matches the number of positions the decimal point was shifted.

Example

• 22,000 becomes 2.2 \times 10^4 (shifted four positions to the left).
• 0.00056 becomes 5.6 \times 10^{-4} (shifted four positions to the right).

Converting Scientific Notation to Decimal Numbers

• Move the decimal point in the coefficient to the right if the exponent is positive and to the left if it is negative.
• The number in the exponent indicates the number of positions to move the decimal point.

Example

• 2.2 \times 10^4 becomes 22,000
• 5.6 \times 10^{-4} becomes 0.00056

Reasons for Using Scientific Notation

• Convenience: Easier to represent very large or small numbers.
  • Example: Mass of an electron is 9.1096 \times 10^{-28} g instead of
    0.00000000000000000000000000091096 g.
• Clarity in reporting uncertainty.
  • Example: 1.4 \times 10^3 kJ per peanut butter sandwich suggests a range of 1.3 \times 10^3 kJ to 1.5 \times 10^3 kJ. Reporting 1400 kJ is less clear.

Metric Prefixes

• giga (G) - 10^9 or 1,000,000,000
• mega (M) - 10^6 or 1,000,000
• kilo (k) - 10^3 or 1000
• centi (c) - 10^{-2} or 0.01
• milli (m) - 10^{-3} or 0.001
• micro ($\mu$) - 10^{-6} or 0.000001
• nano (n) - 10^{-9} or 0.000000001
• pico (p) - 10^{-12} or 0.000000000001

Multiplying Exponential Terms

• When multiplying exponential terms, add the exponents.

  • 10^3 \times 10^6 = 10^{3+6} = 10^9
  • 10^3 \times 10^{-6} = 10^{3+(-6)} = 10^{-3}
  • 3.2 \times 10^{-4} \times 1.5 \times 10^9 = 3.2 \times 1.5 \times 10^{-4+9} = 4.8 \times 10^5

Dividing Exponential Terms

• When dividing exponential terms, subtract the exponents.

  • \frac{10^{12}}{10^3} = 10^{12-3} = 10^9

  • \frac{10^{6}}{10^{-3}} = 10^{6-(-3)} = 10^9

  • \frac{9.0 \times 10^{11}}{1.5 \times 10^{-6}} = \frac{9.0}{1.5} \times 10^{11-(-6)} = 6.0 \times 10^{17}

  • \frac{1.5 \times 10^{2} \times 10^{-3}}{2.0 \times 10^{12} \times 10^{6}} = \frac{1.5}{2.0} \times \frac{10^{2+(-3)}}{10^{12+6}} = \frac{1.5}{2.0} \times 10^{-1-18} = 7.5 \times 10^{-20}

Raising Exponential Terms to a Power

• When raising exponential terms to a power, multiply the exponents.

  • (10^4)^3 = 10^{4 \cdot 3} = 10^{12}
  • (3 \times 10^5)^2 = (3)^2 \times (10^5)^2 = 9 \times 10^{10}

Length

• 1 km = 0.6214 mi

• 1 mi = 1.609 km

• 1 m = 3.281 ft

• 1 ft = 0.3048 m

• 1 in. = 2.54 cm = 25.4 mm

• 1 cm = 0.3937 in.

• 1 mm = 0.03937 in.

Range of Lengths (Approximate)

• Diameter of a proton: 2 \times 10^{-15} \, m
• Diameter of an atom: 10^{-10} \, m
• Diameter of a human hair: 3 \times 10^{-6} \, m
• Length of a blue whale: 30.5 m
• Diameter of the sun: 10^9 \, m
• Proposed distance to the boundary of the known universe: 10^{29} \, m

Volume

• 1 mL = 0.03381 fl oz

• 1 fl oz = 29.57 mL

• 1 gal = 3.785 L

• 1 L = 1.057 qt = 0.2642 gal

• 1 qt = 0.9464 L

Range of Volumes (Approximate)

• Proton in an atom: 10^{-42} \, L
• Atom: 10^{-27} \, L
• Raindrop: 10^{-5} \, L
• Basketball: 7.3 L
• Oceans of Earth: 1.5 \times 10^{21} \, L
• Sun: 10^{30} \, L

Mass and Weight

• Mass is a measure of the amount of matter in an object.
• Mass is the property of matter that leads to gravitational attractions between objects, thus giving rise to weight.
• Matter is anything that occupies volume and has mass.
• Weight on Earth is the measure of the force of gravitational attraction between the object and Earth.

Mass and Weight Comparison (65 kg Person)

Common Mass Units

• 1 oz = 28.35 g
• 1 lb = 453.6 g
• 1 kg = 2.205 lb
• 1 Mg = 1000 kg = 1 t

Range of Masses (Approximate)

• Electron in atom: 9.1096 \times 10^{-28} \, g
• Atom: 1.6735 \times 10^{-24} \, g
• Basketball: 612 g
• Egyptian pyramid: 10^{13} \, g
• Earth: 10^{27} \, g
• The universe: 10^{54} \, g

Temperature

• Ice water: 0 °C, 32 °F
• Boiling water: 100 °C, 212 °F

Comparison of Temperature Scales

• Celsius to Kelvin: Add 273.15 to Celsius value.
• Kelvin to Celsius: Subtract 273.15 from Kelvin Value.

Reporting Values from Measurements

Precision and Accuracy

• Precision reflects the closeness of repeated measurements to each other.
• Accuracy describes how close a measurement is to the true value of the property being measured.
• High precision does not guarantee accuracy.

Examples

• High precision, low accuracy: Archer's arrows are tightly grouped but far from the bullseye.
• High precision, high accuracy: Archer's arrows are tightly grouped around the bullseye.
• Low precision, low accuracy: Archer's arrows are scattered randomly.

Conventions for Reporting Measurements

• Report all certain digits, plus one estimated (uncertain) digit.

Graduated Cylinder Example

• Reading between marks: 8.74 mL.
• If the cylinder is accurate to ±0.1 mL, report 8.7 mL.

Trailing Zeros

• Reporting 8.00 mL indicates an accuracy of ±0.01 mL.
• If accurate to ±0.1 mL, report 8.0 mL.

Digital Readouts

• Report all digits displayed unless instructed otherwise.

Rounding

• It may be best to round values to fewer decimal places than displayed on a digital readout.
• Example: Display of 100.4325 g, reporting 100.432 g indicates accuracy to ±0.001 g.