Chapter 1: Chemical Tools: Experimentation and Measurement

The Scientific Method: Nanoparticle Catalysts for Fuel Cells (Overview)

• Nanoscience: production and study of structures with at least one dimension between 1 and 100 nanometers; fast-growing, multidisciplinary enterprise.
• Fuel Cells: devices that use a fuel such as hydrogen to produce electricity; operate like a battery and require a continuous input of fuel.
• Scientific Method Components (as introduced):
  • Observations: Recording qualitative or quantitative data.
  • Hypothesis: Explanation of observations.
  • Experiments: Change one variable at a time to test the hypothesis.
  • Theory: Explains the experiment and predicts further outcomes.

The Seven Fundamental SI Units of Measure (SI Base Units)

• Mass: name = kilogram, abbreviation = kg.
• Length: name = meter, abbreviation = m.
• Temperature: name = kelvin, abbreviation = K.
• Amount of substance: name = mole, abbreviation = mol.
• Time: name = second, abbreviation = s.
• Electric current: name = ampere, abbreviation = A.
• Luminous intensity: name = candela, abbreviation = cd.
• All other units are derived from these fundamental units.

SI Prefixes for Multiples of SI Units

• Common prefixes and symbols (as shown in the text):
  • tera (T): 10^{12} — example: 1 teragram = 10^{12} g.
  • giga (G): 10^{9} — example: 1 gigameter = 10^{9} m.
  • mega (M): 10^{6} — example: 1 Megameter = 10^{6} m.
  • kilo (k): 10^{3} — example: 1 kilogram = 10^{3} g.
  • hecto (h): 10^{2} — example: 1 hectogram = 100 g.
  • deka (da): 10^{1} — example: 1 dekagram = 10 g.
  • deci (d): 10^{-1} — example: 1 decimeter = 0.1 m.
  • centi (c): 10^{-2} — example: 1 centimeter = 0.01 m.
  • milli (m): 10^{-3} — example: 1 milligram = 0.001 g.
• For very small numbers, a thin space is commonly left every three digits to the right of the decimal point to aid readability (analogous to thousands separators to the left of the decimal).
• micro (μ): 10^{-6} — example: 1 micrometer = 10^{-6} m.
• nano (n): 10^{-9} — example: 1 nanosecond = 10^{-9} s.
• pico (p): 10^{-12} — example: 1 picosecond = 10^{-12} s.
• femto (f): 10^{-15} — example: 1 femtomole = 10^{-15} mol.

Mass and Its Measurement

• Mass: amount of matter in an object.
• Weight: the force with which gravity pulls on an object.

Length and Its Measurement

• Meter definitions over time:
  • 1790: one ten-millionth of the distance from the equator to the North Pole along a meridian through Paris.
  • 1889: distance between two thin lines on a platinum–iridium alloy 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:
  • Fahrenheit, Celsius, and Kelvin scales are related; the familiar conversions include:
  • Absolute zero is 0 K, which corresponds to -273.15 °C.
• Conversion relationships (typical form):
  • $^ ext{°C} = \frac{5}{9}( ^{\circ}F - 32 )$
  • $K = ^{\circ}C + 273.15$
• Example reference points on a temperature diagram (from the figure):
  • Boiling water: 212 °F, 100 °C, 373 K.
  • Freezing water: 32 °F, 0 °C, 273 K.

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

• Derived quantities and their definitions:
  • Area: defined as length times length.
  • Volume: defined as area times length.
  • Density: mass per unit volume.
  • Speed: distance per unit time.
  • Acceleration: change in speed per unit time.
  • Force: mass times acceleration.
  • Pressure: force per unit area.
  • Energy: force times distance.
• Derived units (names):
  • Area: m^2.
  • Volume: m^3.
  • Density: kg · m^{-3}.
  • Speed: m · s^{-1}.
  • Acceleration: m · s^{-2}.
  • Force: N (newton).
  • Pressure: Pa (pascal).
  • Energy: J (joule).
• Basic definitions in symbols:
  • $ext{Area} = ext{length} imes ext{length}$
  • $A = L \times L = L^2$
  • $V = A \times L = L^3$
  • $\rho = \frac{m}{V} = \mathrm{kg\, m^{-3}}$
  • $v = \frac{d}{t} = \mathrm{m\, s^{-1}}$
  • $a = \frac{\Delta v}{\Delta t} = \mathrm{m\, s^{-2}}$
  • $F = m a = \mathrm{kg\, m\, s^{-2}} = \mathrm{N}$
  • $P = \frac{F}{A} = \mathrm{kg\, m^{-1} s^{-2}} = \mathrm{Pa}$
  • $E = F d = \mathrm{kg\, m^{2} s^{-2}} = \mathrm{J}$
• Additional note: 1 m^3 contains 1000 dm^3 (liters); 1 dm^3 contains 1000 cm^3 (mL).

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

• (Reinforcement of volume-related relationships from the text.)

Derived Units: Density and Its Measurement

• Table of common materials and densities (in g per cm^3):
  • Ice (0 °C): 0.917
  • Water (4 °C): 1.000
  • Gold: 19.31
  • Helium (25 °C): 0.000164
  • Air (25 °C): 0.001185
  • Human fat: 0.94
  • Human muscle: 1.06
  • Cork: 0.22–0.26
  • Balsa wood: 0.12
  • Earth: 5.54
• Note on units: densities are typically given in g cm^{-3} (which equals kg m^{-3} when converted by 1 g cm^{-3} = 1000 kg m^{-3}).

Derived Units: Energy and Its Measurement

• Kinetic energy: energy of motion.
• Potential energy: stored energy.
• The unit of energy is the joule (J).
• In SI base units: $1\ \mathrm{J} = 1\ \mathrm{kg}\ \mathrm{m^{2}}\ \mathrm{s^{-2}}$

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

• Accuracy: how close a measurement is to the true value.
• Precision: how well a set of independent measurements agree with each other.

Accuracy, Precision, and Significant Figures in Measurement (2 of 9)

• Tennis ball mass example (true mass = 54.441778 g): three measurement methods yield:
  • Bathroom scale: 54.4 g; Lab balance: 54.4417 g; Analytical balance: 54.4418 g.
  • Averages and interpretation:
  • For measurement 1: 0.01 kg, 54.4 g, 54.4418 g.
  • For measurement 2: 0.0 kg, 54.5 g, 54.4417 g.
  • For measurement 3: 0.1 kg, 54.3 g, 54.4418 g.
  • Conclusions from the data:
  • Average values (roughly 54.4 g) indicate good accuracy with some instrument precision variation.
  • The Analytical balance yields the most precise reading (54.4418 g) across trials in this example.
• Terms: good accuracy, good precision; good accuracy, poor precision; poor accuracy, poor precision (as described in the figures).

Accuracy, Precision, and Significant Figures in Measurement (3 of 9)

• Reiteration of the tennis ball example emphasizing accuracy vs precision visually.

Accuracy, Precision, and Significant Figures in Measurement (4 of 9)

• Reiteration of the tennis ball example showing outcomes with the same labels (accuracy/precision).

Accuracy, Precision, and Significant Figures in Measurement (5 of 9)

• Significant Figures: The total number of digits recorded for a measurement.
• Principle: The last digit in a reported measurement is generally uncertain (estimated).
• Exact numbers and defined relationships (e.g., 7 days in a week, 30 students in a class) effectively have infinite significant figures.

Accuracy, Precision, and Significant Figures in Measurement (6 of 9)

• Rules for counting significant figures (Left-to-Right):
  • Zeros in the middle of a number are always significant.
  • Zeros at the beginning of a number are not significant (placeholders).

Accuracy, Precision, and Significant Figures in Measurement (7 of 9)

• Continued rule: zeros in the middle of a number remain significant; leading zeros are not significant (placeholders).

Accuracy, Precision, and Significant Figures in Measurement (8 of 9)

• Rules continue: zeros at the end of a number and after the decimal point are always significant.

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

• Final rule in the sequence: zeros at the end of a number and before the decimal point may or may not be significant.
• Example given: 34,200 meters ? SFs (significant figures) – interpretation depends on notation (ambiguous in the absence of a decimal point).

Significant Figures in Calculations (1 of 4)

• Rules for keeping track of significant figures in calculations:
  • Multiplication or Division: the result cannot have more significant figures than any of the original numbers.

Significant Figures in Calculations (2 of 4)

• Rules for multiplication/division and addition/subtraction:
  • Multiplication/Division: limit by the smallest number of significant figures among the factors.
  • Addition/Subtraction: limit by the number of decimal places in the term with the fewest decimal places.

Significant Figures in Calculations (3 of 4)

• Rounding off numbers: If the first digit removed is less than 5, round down (truncate).
  • Example: 5.664525 → 5.66 (to 3 significant figures, or as shown by the rule).

Significant Figures in Calculations (4 of 4)

• Rounding rules continuation: If the first removed digit is 5 or greater, round up by increasing the digit on the left by 1.
• Example: 5.664525 → 5.7 (depending on the specified precision).

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

• Dimensional analysis is a method using a conversion factor to convert a quantity expressed in one unit to an equivalent quantity in another unit.
• Conversion Factor: expresses the relationship between two different units.
• Core idea: The original quantity times a conversion factor equals the equivalent quantity in the target unit.

Converting from One Unit to Another (2 of 3)

• Example relationship: 1 meter = 39.37 inches.
• Conversion factors:
  • To convert inches to meters: use a factor that cancels inches and introduces meters.
  • To convert meters to inches: use a factor that cancels meters and introduces inches.

Converting from One Unit to Another (3 of 3)

• Practical application: apply the conversion factor so units cancel appropriately and the desired unit remains.

Additional Notes on Density and Energy (from Table and Figures)

• The density table shows various common materials with densities in g/cm^3, illustrating a wide range from nearly 0 (Helium) to dense materials like Gold.
• The energy section emphasizes the two primary energy types: kinetic and potential, with joule as the unit of energy.

Dimensional Analysis Example (Practical)

• Original quantity with units, multiply by conversion factor(s) to obtain the desired units.
• Ensure the units cancel properly and the numerical value reflects the proper significant figures.

Quick Reference Formulas and Facts (summarized)

• Area: $A = L \times L = L^2$
• Volume: $V = A \times L = L^3$
• Density: $\rho = \frac{m}{V},\quad \rho = \mathrm{kg\, m^{-3}}$
• Speed: $v = \frac{d}{t},\quad v \in \mathrm{m\, s^{-1}}$
• Acceleration: $a = \frac{\Delta v}{\Delta t},\quad a \in \mathrm{m\, s^{-2}}$
• Force: $F = m a,\quad F \in \mathrm{N},\; 1\mathrm{N} = 1\; \mathrm{kg\, m\, s^{-2}}$
• Pressure: $P = \frac{F}{A},\quad P \in \mathrm{Pa},\; 1\mathrm{Pa} = 1\; \mathrm{N}\, \mathrm{m^{-2}}$
• Energy: $E = F d = \mathrm{kg\, m^{2}\, s^{-2}} = \mathrm{J}$
• Temperature conversions:
  • $^ ext{°C} = \frac{5}{9}( ^{\circ}F - 32 )$
  • $K = ^{\circ}C + 273.15$
• Unit conversions example: $1\ ext{meter} = 39.37\ ext{inches}$ and related dimensional-analysis practice.

Note on Notes and Figures

• The material references specific figure examples (e.g., the Fahrenheit-Celsius-Kelvin relationships) and table entries (Table 1.1, Table 1.2, Table 1.3, Table 1.4) to anchor definitions and real-world values.
• The content emphasizes the practical use of significant figures in experimental measurements and the rules for carrying and rounding figures in calculations.