Comprehensive Chemistry Notes

Chemistry: The Science of Matter

• Chemistry is the science that studies the structure and behavior of matter.

The Scientific Method

• There isn't just one way to do science; different scientific fields have their own methods, and scientists also vary in their approaches.
• However, some characteristics are commonly shared.

Steps in the Scientific Method

1. Observation and Data Collection
   • Example: In the 1960s, scientists noticed that manganese miners in South America developed Parkinson's-like symptoms, such as muscle tremors and rigidity.
2. Initial Hypothesis
   • Based on observations, an initial hypothesis is formed.
   • Example: The symptoms observed in manganese miners and Parkinson's disease sufferers share a common cause.
3. Systematic Research and Experimentation
   • Research is conducted to test the hypothesis.
   • Example: Research revealed that manganese disrupts dopamine, a brain chemical crucial for muscle function control. High manganese levels were expected to cause movement problems.
4. Hypothesis Refinement
   • Hypotheses are refined based on research findings.
   • Example: Researchers hypothesized that Parkinson's patients have low dopamine levels in their brains, which brain studies confirmed.
5. Publication of Results
   • The results are published for peer review and further testing.
6. Confirmation or Refutation by Other Scientists
   • Other scientists repeat the research to either confirm or refute the conclusions.
   • Example: Other scientists validated the dopamine research findings.
7. Search for Useful Applications
   • Scientists seek practical uses for the research.
   • Example: Since dopamine can't cross from the bloodstream into brain tissue, researchers looked for a compound that could enter the brain and convert into dopamine. Levodopa (L-dopa) fit these requirements.
8. Development and Refinement of Applications
   • This often triggers new rounds of hypothesizing and testing.
   • Example: L-dopa had side effects like nausea, gastrointestinal issues, low blood pressure, delusions, and mental disturbances. The blood pressure effects were due to L-dopa converting to dopamine outside the brain. Now, L-dopa is administered with levocarbidopa to inhibit this conversion.
9. And the cycle then continues.

Measurement and Units

• A value from a measurement is a quantitative description with both a unit and a number.
  • For example, in "100 meters", "meter" is the unit of distance, and "100" is the number of units.
• Units are standard quantities agreed upon for comparing events or objects.

Base Units in the International System of Measurement

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

Derived Units

• Example: 1 cubic meter = 1000 liters
• 1 L = 10^{-3} m^3
• 10^3 L = 1 m^3

Other Base Units and Abbreviations

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

Scientific (Exponential) Notation

• Numbers in scientific notation are expressed as:

  a \times 10^b

  • Where 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 uncertainty.
• It's generally assumed to be plus or minus one in the last reported position, unless stated otherwise.
• 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 number's size or magnitude.
  • Positive exponents for 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 for 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 one non-zero digit remains to its left, counting the number of positions shifted.
2. Write the resulting coefficient multiplied by an exponential term.
   • The exponent is positive if the decimal moved left and negative if it moved right.
   • The exponent's number equals the number of positions the decimal shifted.

Examples

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

Converting from Scientific Notation to Decimal Numbers

• Shift the decimal point in the coefficient to the right if the exponent is positive and to the left if negative.
• The number in the exponent indicates the number of positions to shift the decimal point.
  • 2.2 \times 10^4 becomes 22,000
  • 5.6 \times 10^{-4} becomes 0.00056

Reasons for Using Scientific Notation

• Convenience: It saves time and space.
  • Example: The mass of an electron is 9.1096 \times 10^{-28} g, rather than 0.00000000000000000000000000091096 g.
• Clarity in Reporting Uncertainty:
  • Example: 1.4 \times 10^3 kJ per peanut butter sandwich suggests a range from 1.3 \times 10^3 kJ to 1.5 \times 10^3 kJ. Reporting it as 1400 kJ doesn't clearly convey the uncertainty (could be 1400 \pm 1, 1400 \pm 10, or 1400 \pm 100).

Multiplying Exponential Terms

• Add 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

• Subtract 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}

Raising Exponential Terms to a Power

• Multiply 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 \text{ km} = 0.6214 \text{ mi}
• 1 \text{ mi} = 1.609 \text{ km}
• 1 \text{ m} = 3.281 \text{ ft}
• 1 \text{ ft} = 0.3048 \text{ m}
• 1 \text{ in.} = 2.54 \text{ cm} = 25.4 \text{ mm}
• 1 \text{ cm} = 0.3937 \text{ in.}
• 1 \text{ mm} = 0.03937 \text{ in.}

Range of Lengths

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

Volume

• 1 \text{ mL} = 0.03381 \text{ fl oz}
• 1 \text{ fl oz} = 29.57 \text{ mL}
• 1 \text{ gal} = 3.785 \text{ L}
• 1 \text{ qt} = 0.9464 \text{ L}
• 1 \text{ L} = 1.057 \text{ qt} = 0.2642 \text{ gal}

Range of Volumes

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

Mass and Weight

• Mass is a measure of the amount of matter in an object or the property leading to gravitational attractions.
• Matter is anything that occupies a volume and has a mass.
• Weight on Earth is a measure of the gravitational attraction between an object and the Earth.

Comparison of Mass and Weight on Earth and Moon (for a 65 kg Person)

Mass Units

• 1 \text{ oz} = 28.35 \text{ g}
• 1 \text{ lb} = 453.6 \text{ g}
• 1 \text{ kg} = 2.205 \text{ lb}
• 1 \text{ Mg} = 1000 \text{ kg} = 1 \text{ t}

Range of Masses

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

Temperature

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

Comparing Temperature Scales

Reporting Values from Measurements

Precision and Accuracy

• Precision: How closely multiple measurements of the same object resemble each other. High precision means the measurements are close together.
• Accuracy: How close a measurement is to the true value of the property.

Conventions for Reporting Measurements

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

Graduated Cylinder Example

• If the bottom of the meniscus is at 8.74 mL, report 8.7 mL if the cylinder is accurate to ±0.1 mL.

Trailing Zeros

• Report 8.00 mL to indicate an uncertainty of ±0.01 mL.
• If the graduated cylinder is only accurate to ±0.1 mL, report 8.0 mL.

Digital Readout

• Report all digits unless instructed otherwise.
• In many cases, it is best to round to fewer decimal positions than displayed.
• For example, if a balance displays 100.432 g, reporting 100.432 g would indicate \pm 0.001 \text{ g}.