Chapter 1 Study Notes: Chemical Tools, Experimentation and Measurement

SI Units and Scientific Notation

• SI base units (Table 1.1):
  • Mass — Name: kilogram; Abbreviation: kg; Definition: base unit for mass
  • Length — Name: meter; Abbreviation: m; Definition: base unit for length
  • Temperature — Name: kelvin; Abbreviation: K; Definition: base unit for temperature
  • Amount of substance — Name: mole; Abbreviation: mol; Definition: base unit for amount of substance
  • Time — Name: second; Abbreviation: s; Definition: base unit for time
  • Electric current — Name: ampere; Abbreviation: A; Definition: base unit for electric current
  • Luminous intensity — Name: candela; Abbreviation: cd; Definition: base unit for luminous intensity
• All other SI units are derived from these fundamental units.

SI Prefixes for Multiples (Table 1.2, 1 of 2 and 2 of 2)

• Common prefixes in chemical sciences (with symbol and examples):
  • tera (T): 10^{12}; e.g., teragram Tg = 10^{12} g
  • giga (G): 10^{9}; e.g., gigameter Gm = 10^{9} m
  • mega (M): 10^{6}; e.g., megameter Mm = 10^{6} m
  • kilo (k): 10^{3}; e.g., kilogram kg = 10^{3} g
  • hecto (h): 10^{2}; e.g., hectogram hg = 100 g
  • deka (da): 10^{1}; e.g., dekagram dag = 10 g
  • deci (d): 10^{-1}; e.g., decimeter dm = 0.1 m
  • centi (c): 10^{-2}; e.g., centimeter cm = 0.01 m
• Very small prefixes:
  • micro (μ): 10^{-6}; e.g., micrometer μm = 10^{-6} m
  • nano (n): 10^{-9}; e.g., nanosecond ns = 10^{-9} s
  • pico (p): 10^{-12}; e.g., picosecond ps = 10^{-12} s
• Note: For very small numbers, a thin space may be used every three digits to the right of the decimal point in scientific work.

Mass and Its Measurement

• Mass measures the amount of matter in an object.
• Weight measures the force with which gravity pulls on the object.
• Distinction: mass is intrinsic; weight depends on local gravity.

Length and Its Measurement

• History of the meter:
  • 1790: One ten-millionth of the distance from the equator to the North Pole along a meridian through Paris
  • 1889: Distance between two lines on a platinum–iridium bar stored near Paris
  • 1983: The distance light travels in vacuum in 1/299,792,458 of a second

Temperature and Its Measurement

• Temperature scales and relationships:
  • 1 degree Fahrenheit is 5/9 of a degree Celsius (delta T equivalence)
  • Boiling water: 212 °F ⇔ 100 °C ⇔ 373 K
  • Freezing water: 32 °F ⇔ 0 °C ⇔ 273 K
• Conversions:
  • Celsius to Fahrenheit and vice versa:
  • $^ ext{°C} = \frac{5}{9} (^ ext{°F} - 32)$
  • Kelvin relation:
  • $K = {}^ ext{°C} + 273.15$

Derived Units: Volume and Its Measurement (1 of 2)

• Derived quantities and their units:
  • Area: Definition — Length × Length; Unit — m^2
  • Volume: Definition — Area × Length; Unit — m^3
  • Density: Definition — Mass per unit volume; Unit — kg/m^3
  • Speed: Definition — Distance per unit time; Unit — m/s
  • Acceleration: Definition — Change in speed per unit time; Unit — m/s^2
  • Force: Definition — Mass × acceleration; Unit — N (Newton)
  • $1\,\text{N} = 1\,\text{kg} \cdot \text{m}/\text{s}^2$
  • Pressure: Definition — Force per unit area; Unit — Pa (Pascal)
  • $1\,\text{Pa} = 1\,\text{N}/\text{m}^2 = 1\,\text{kg}/(\text{m}·\text{s}^2)$
  • Energy: Definition — Force × distance; Unit — J (Joule)
  • $1\,\text{J} = 1\,\text{N} \cdot 1\,\text{m} = (\text{kg} \cdot \text{m}/\text{s}^2) \cdot \text{m} = \text{kg} \cdot \text{m}^2/\text{s}^2$

Derived Units: Volume and Its Measurement (2 of 2)

• Visual relationships (as in Figure 1.7):
  • $1\,\text{m}^3 = 1000\,\text{dm}^3$
  • $1\,\text{dm}^3 = 1\,\text{L}$
  • $1\,\text{dm}^3 = 1000\,\text{cm}^3$
  • $1\,\text{cm}^3 = 1\,\text{mL}$
• Additional conversions:
  • $1\,\text{m}^3 = 1000\,\text{L}$
  • $1\,\text{m} = 100\,\text{cm}$
• Note: Each cubic meter contains 1000 cubic decimeters (liters); each cubic decimeter contains 1000 cubic centimeters (milliliters).

Derived Units: Density and Its Measurement

• Densities of common materials (Table 1.4):
  • Ice (0 °C): $\rho = 0.917 \ \text{g/cm}^3$
  • Water (3.98 °C): $\rho = 1.0000 \ \text{g/cm}^3$
  • Gold: $\rho = 19.31 \ \text{g/cm}^3$
  • Helium (25 °C): $\rho = 0.000164 \ \text{g/cm}^3$
  • Air (25 °C): $\rho = 0.001185 \ \text{g/cm}^3$
  • Human fat: $\rho \approx 0.94 \ \text{g/cm}^3$
  • Human muscle: $\rho \approx 1.06 \ \text{g/cm}^3$
  • Cork: \rho \approx 0.22$–$0.26 \ \text{g/cm}^3
  • Balsa wood: $\rho \approx 0.12 \ \text{g/cm}^3$
  • Earth: $\rho \approx 5.54 \ \text{g/cm}^3$
• Relationship to density: $\rho = \dfrac{m}{V}$ with units $\text{kg/m}^3$ or $\text{g/cm}^3$ depending on context.

Derived Units: Energy and Its Measurement

• Kinetic energy: $E_ ext{K} = \tfrac{1}{2} m v^2$
• Potential energy: $E_ ext{P} = m g h$ (conceptual description: stored energy)
• Units for energy: Joule, $\text{J} = \text{kg} \cdot \text{m}^2/\text{s}^2$

Accuracy, Precision, and Significant Figures in Measurement (1 of 9 to 9 of 9)

• Accuracy: How close a measurement is to the true value.
• Precision: How well a set of independent measurements agree with each other.
• Significant figures (SF): The total number of digits recorded for a measurement; the last digit is typically uncertain/estimated.
• Exact numbers (counts, definitions) have infinite significant figures (e.g., 7 days in a week, 30 students in a class).

Significant Figures: Counting Rules (Left-to-Right)

• Zeros in the middle are significant (example: 4.803 cm has 4 SFs).
• Zeros at the beginning are not significant (placeholders) (example: 0.00661 g has 3 SFs).
• Zeros at the end of a number and after the decimal point are significant (example: 55.220 K has 5 SFs).
• Zeros at the end of a number and before the decimal point may or may not be significant (example: 34,200 m has ambiguous SFs).

Significant Figures: Calculations (1 of 4 to 4 of 4)

• For multiplication or division: The result cannot have more significant figures than any of the original numbers.
• For addition or subtraction: The result cannot have more digits to the right of the decimal point than any of the original numbers.

Rounding Rules (1 of 4 to 4 of 4)

• If the first digit removed is less than 5, round down (drop it and all following numbers).
  • Example: 5.664525 rounds to 5.66 when following this rule.
• If the first digit removed is 5 or greater, round up by increasing the digit to the left by 1.
  • Example: 5.664525 rounds to 5.7 under this rule when applying the standard halfway rule.

Converting from One Unit to Another: Dimensional Analysis (1 of 3)

• Dimensional analysis uses a conversion factor to convert a quantity from one unit to another.
• Conversion factor expresses the relationship between two different units.
• Core idea: Original quantity × Conversion factor = Equivalent quantity in desired units.

Converting from One Unit to Another: The Basic Relationship (2 of 3)

• Example relationship: 1 meter = 39.37 inches.
• Conversion factor: Converts inches to meters or meters to inches with appropriate factors.
• Practical note: Choose a factor so that units cancel appropriately and leave the desired unit.

Converting from One Unit to Another: (3 of 3)

• Note: Practice with dimensional analysis helps ensure correct unit cancellation and correct final units.

Quick Reference: Key Equations and Units (LaTeX)

• Base units and SI: $ext{Mass} = ext{kg}, \, \text{Length} = ext{m}, \, \text{Time} = \text{s}, \, \text{Temperature} = \text{K}, \, \text{Amount} = \text{mol}, \, \text{Electric current} = \text{A}, \, \text{Luminous intensity} = \text{cd}$
• Derived units: $1\,\text{J} = 1\,\text{N} \cdot 1\,\text{m} = (\text{kg} \cdot \text{m}/\text{s}^2) \cdot \text{m} = \text{kg} \cdot \text{m}^2/\text{s}^2$
• Density: $\rho = \dfrac{m}{V}, \quad \text{kg/m}^3$
• Volume relationships: $1\,\text{m}^3 = 1000\,\text{dm}^3, \quad 1\,\text{dm}^3 = 1\,\text{L}, \quad 1\,\text{dm}^3 = 1000\,\text{cm}^3, \quad 1\,\text{cm}^3 = 1\,\text{mL}$
• Temperature conversions: $^ ext{°C} = \frac{5}{9} (^{\circ}\text{F} - 32), \quad K = ^{\circ}\text{C} + 273.15$
• Dimensional analysis concept: $ext{Original quantity} \times \text{Conversion factor} = \text{Equivalent quantity in desired units}$

Real-World and Foundational Connections

• SI units and prefixes underpin all quantitative chemistry calculations, experiments, and data reporting.
• Accurate measurement and proper significant figures are essential for reproducibility and meaningful comparisons.
• Dimensional analysis is a fundamental tool for unit consistency in calculations across laboratory and theoretical work.

Ethical, Philosophical, and Practical Implications

• Precise measurement practices reduce ambiguity in scientific communication.
• Clear distinctions between mass and weight prevent misinterpretation in experiments, design, and when comparing data across environments with different gravity.
• Adherence to standard units and reporting conventions fosters global collaboration and data sharing.