Chemical Tools: Experimentation, Measurement, and Fundamental Units

Scientific Method: Experimentation, Hypotheses, and Theories

  • The natural world is too complex to be understood by passive observation and abstract thinking alone; an active experimental approach is required.
  • Specific questions must be asked, and structured experiments must be carried out to discover answers.
  • Hypothesis: A tentative interpretation or explanation formulated only after the results of many experiments are known.
  • Hypotheses are utilized to generate further predictions and suggest additional experiments until a consistent explanation is established.
  • Theory: A consistent, comprehensive explanation derived from repeated testing and refinement of hypotheses.
  • Observations and experimental data always precede theories in chemistry and scientific inquiry.
  • Scientific theories are distinct from laws of nature and can never be absolutely proven.
  • A theory represents the best available explanation at any given time. If new experimental data cannot be explained by an existing theory, that theory must be modified or entirely replaced.

Experimentation and Measurement in Chemistry

  • Chemistry is an experimental science that requires reproducible results.
  • Reproducibility demands precise descriptions of measured quantities, including substance amounts, volumes, temperatures, and pressures.
  • International System of Units (SI): Formally adopted in 1960 under international agreement (Système Internationale d'Unités).
  • The SI system is built upon the metric system, which is used universally across all nations except the United States, Liberia, and Myanmar.
  • The SI system consists of seven fundamental base units from which all other physical quantities are derived.

Fundamental SI Units

  • Mass: kilogram (kg\text{kg})
  • Length: meter (m\text{m})
  • Temperature: kelvin (K\text{K})
  • Amount of substance: mole (mol\text{mol})
  • Time: second (s\text{s})
  • Electric current: ampere (A\text{A})
  • Luminous intensity: candela (cd\text{cd})

SI Unit Prefixes and Multiples

  • Standard base units can be inconveniently large or small for specific measurements (e.g., the diameter of a sodium atom is 0.000 000 000 372 m0.000\,000\,000\,372\,\text{m}, whereas the distance from Earth to the Sun is 150,000,000,000 m150,000,000,000\,\text{m}).
  • SI prefixes modify base units by factors of 10 to represent larger or smaller quantities.
  • Common Prefixes and Multiplication Factors:
    • tera (T): 1,000,000,000,000=10121,000,000,000,000 = 10^{12} (e.g., 1 teragram (Tg)=1012 g1\,\text{teragram (Tg)} = 10^{12}\,\text{g})
    • giga (G): 1,000,000,000=1091,000,000,000 = 10^9 (e.g., 1 gigameter (Gm)=109 m1\,\text{gigameter (Gm)} = 10^9\,\text{m})
    • mega (M): 1,000,000=1061,000,000 = 10^6 (e.g., 1 megameter (Mm)=106 m1\,\text{megameter (Mm)} = 10^6\,\text{m})
    • kilo (k): 1,000=1031,000 = 10^3 (e.g., 1 kilogram (kg)=103 g1\,\text{kilogram (kg)} = 10^3\,\text{g})
    • hecto (h): 100=102100 = 10^2 (e.g., 1 hectogram (hg)=100 g1\,\text{hectogram (hg)} = 100\,\text{g})
    • deka (da): 10=10110 = 10^1 (e.g., 1 dekagram (dag)=10 g1\,\text{dekagram (dag)} = 10\,\text{g})
    • deci (d): 0.1=10−10.1 = 10^{-1} (e.g., 1 decimeter (dm)=0.1 m1\,\text{decimeter (dm)} = 0.1\,\text{m})
    • centi (c): 0.01=10−20.01 = 10^{-2} (e.g., 1 centimeter (cm)=0.01 m1\,\text{centimeter (cm)} = 0.01\,\text{m})
    • milli (m): 0.001=10−30.001 = 10^{-3} (e.g., 1 milligram (mg)=0.001 g1\,\text{milligram (mg)} = 0.001\,\text{g})
    • micro (μ\mu): 0.000 001=10−60.000\,001 = 10^{-6} (e.g., 1 micrometer (μm)=10−6 m1\,\text{micrometer }(\mu\text{m}) = 10^{-6}\,\text{m})
    • nano (n): 0.000 000 001=10−90.000\,000\,001 = 10^{-9} (e.g., 1 nanosecond (ns)=10−9 s1\,\text{nanosecond (ns)} = 10^{-9}\,\text{s})
    • pico (p): 0.000 000 000 001=10−120.000\,000\,000\,001 = 10^{-12} (e.g., 1 picosecond (ps)=10−12 s1\,\text{picosecond (ps)} = 10^{-12}\,\text{s})
    • femto (f): 0.000 000 000 000 001=10−150.000\,000\,000\,000\,001 = 10^{-15} (e.g., 1 femtomole (fmol)=10−15 mol1\,\text{femtomole (fmol)} = 10^{-15}\,\text{mol})
  • Scientific practice leaves a thin space every three digits to the right of the decimal point in very small numbers, mirroring the comma placed every three digits to the left in large numbers.

Scientific Notation and Measurement Requirements

  • Scientific notation expresses numbers as a product of a number between 1 and 10 multiplied by a power of 10 (a×10ba \times 10^b).
    • Example: 55,00055,000 is expressed as 5.5×1045.5 \times 10^4.
    • Example: 0.003 200.003\,20 is expressed as 3.20×10−33.20 \times 10^{-3}.
  • Every measurement must include both a numerical value and a unit label. A number without a unit label is ambiguous.

Fundamental Units: Measuring Mass

  • Mass: The measure of the amount of matter in an object.
  • Matter: Anything that possesses a physical presence—anything that can be touched, tasted, smelled, or occupies space by having mass.
  • The fundamental SI unit of mass is the kilogram (kg\text{kg}).
    • 1 kg=2.205 U.S. lb1\,\text{kg} = 2.205\,\text{U.S. lb}
  • Standard Kilogram Definition: Defined by the international prototype kilogram, a cylindrical bar made of a platinum-iridium alloy stored in a vault in a suburb of Paris, France. Forty original copies are distributed globally, including two official standards (Numbers K4 and K20) housed at the U.S. National Institute of Standards and Technology near Washington, D.C.
  • Commonly used smaller metric mass units in chemistry:
    • Gram (g): 1 g=0.001 kg=10−3 kg1\,\text{g} = 0.001\,\text{kg} = 10^{-3}\,\text{kg}. One gram is slightly less than half the mass of a new U.S. dime (2.27 g2.27\,\text{g}).
    • Milligram (mg): 1 mg=0.001 g=10−6 kg1\,\text{mg} = 0.001\,\text{g} = 10^{-6}\,\text{kg}
    • Microgram (μg\mu\text{g}): 1 μg=0.001 mg=10−6 g=10−9 kg1\,\mu\text{g} = 0.001\,\text{mg} = 10^{-6}\,\text{g} = 10^{-9}\,\text{kg}
  • Mass Unit Equivalences:
    • 1 kg=1000 g=1,000,000 mg=1,000,000,000 μg1\,\text{kg} = 1000\,\text{g} = 1,000,000\,\text{mg} = 1,000,000,000\,\mu\text{g} (2.205 lb2.205\,\text{lb})
    • 1 g=1000 mg=1,000,000 μg1\,\text{g} = 1000\,\text{mg} = 1,000,000\,\mu\text{g} (0.03527 oz0.03527\,\text{oz})
    • 1 mg=1000 μg1\,\text{mg} = 1000\,\mu\text{g}
  • Distinction Between Mass and Weight:
    • Mass measures the total quantity of matter in an object and is completely independent of location.
    • Weight measures the force of gravity exerted on an object and varies with local gravitational field strength.
    • An individual weighing 140 lb140\,\text{lb} on Earth weighs approximately 23 lb23\,\text{lb} on the Moon due to reduced lunar gravity, but their mass remains identical in both locations.
    • At any single location on Earth, two objects with equal mass experience an identical gravitational force and weigh the same. Mass is measured in laboratories by comparing the weight of an sample to a reference standard of known mass using balances.

Some balances used for measuring mass in the laboratory

Fundamental Units: Measuring Length

  • The fundamental SI unit of length is the meter (m\text{m}).
  • Historical Definitions of the Meter:
    • 1790: Defined as 1 ten-millionth of the distance from the equator to the North Pole.
    • 1889: Redefined as the physical distance between two fine lines engraved on a platinum-iridium alloy bar kept near Paris, France.
    • 1983: Redefined as the distance traveled by light through a vacuum in 1299,792,458 second\frac{1}{299,792,458}\,\text{second}. This definition provides extreme precision and cannot be physically damaged or lost.
  • Commonly used smaller length units in chemistry:
    • 1 m=39.37 inches1\,\text{m} = 39.37\,\text{inches} (approximately 10% longer than an English yard, or 1.0936 yd1.0936\,\text{yd}).
    • Centimeter (cm): 1 cm=0.01 m=10−2 m1\,\text{cm} = 0.01\,\text{m} = 10^{-2}\,\text{m} (0.3937 in0.3937\,\text{in}, slightly less than half an inch).
    • Millimeter (mm): 1 mm=0.001 m=10−3 m1\,\text{mm} = 0.001\,\text{m} = 10^{-3}\,\text{m} (roughly the thickness of a U.S. dime).
    • Micrometer (μm\mu\text{m}): 1 μm=10−6 m1\,\mu\text{m} = 10^{-6}\,\text{m}
    • Nanometer (nm): 1 nm=10−9 m1\,\text{nm} = 10^{-9}\,\text{m}
    • Picometer (pm): 1 pm=10−12 m1\,\text{pm} = 10^{-12}\,\text{m} (e.g., sodium atom diameter =372 pm=3.72×10−10 m= 372\,\text{pm} = 3.72 \times 10^{-10}\,\text{m}).
  • Length Unit Equivalences:
    • 1 m=100 cm=1000 mm=1,000,000 μm=1,000,000,000 nm1\,\text{m} = 100\,\text{cm} = 1000\,\text{mm} = 1,000,000\,\mu\text{m} = 1,000,000,000\,\text{nm}
    • 1 cm=10 mm=10,000 μm=10,000,000 nm1\,\text{cm} = 10\,\text{mm} = 10,000\,\mu\text{m} = 10,000,000\,\text{nm}
    • 1 mm=1000 μm=1,000,000 nm1\,\text{mm} = 1000\,\mu\text{m} = 1,000,000\,\text{nm}

Fundamental Units: Measuring Temperature

  • The degree Celsius (∘C^\circ\text{C}) is the common metric unit for temperature, whereas the kelvin (K\text{K}) is the SI base unit used in scientific work.
  • Note on terminology: The unit name is "kelvin" (K\text{K}), never "degree kelvin".
  • Celsius vs. Kelvin Scales:
    • The magnitude of one kelvin is identical to the magnitude of one degree Celsius; both represent 1100\frac{1}{100} of the temperature difference between the freezing point and boiling point of water at standard atmospheric pressure.
    • The scales differ only in their designated zero points:
    • Celsius assigns 0 ∘C0\,^\circ\text{C} to the freezing point of water and 100 ∘C100\,^\circ\text{C} to the boiling point of water.
    • Kelvin assigns 0 K0\,\text{K} to absolute zero, the theoretical lowest possible temperature, which corresponds to −273.15 ∘C-273.15\,^\circ\text{C}.
    • Zero-point equivalences: 0 K=−273.15 ∘C0\,\text{K} = -273.15\,^\circ\text{C} and 273.15 K=0 ∘C273.15\,\text{K} = 0\,^\circ\text{C}.
    • Temperature conversion formulas:     Temperature in K=Temperature in ∘C+273.15\text{Temperature in K} = \text{Temperature in }^\circ\text{C} + 273.15Temperature in ∘C=Temperature in K−273.15\text{Temperature in }^\circ\text{C} = \text{Temperature in K} - 273.15
    • Example: A temperature of 25 ∘C25\,^\circ\text{C} corresponds to 25+273.15=298.15 K25 + 273.15 = 298.15\,\text{K} (rounded to 298 K298\,\text{K}).
  • Fahrenheit Scale Comparisons:
    • Freezing point of water = 32 ∘F32\,^\circ\text{F}; Boiling point of water = 212 ∘F212\,^\circ\text{F}.
    • The Fahrenheit scale defines an interval of 180∘180^\circ between the freezing and boiling points of water.
    • Scale ratio comparison: 180180 Fahrenheit degrees cover the same temperature span as 100100 Celsius degrees (or kelvins).
    • Degree size conversion factor: 1 ∘F=100180=59 ∘C1\,^\circ\text{F} = \frac{100}{180} = \frac{5}{9}\,^\circ\text{C}, or 1 ∘C=95 ∘F1\,^\circ\text{C} = \frac{9}{5}\,^\circ\text{F}.
  • Fahrenheit and Celsius Interconversion Adjustments:
    1. Degree size adjustment: Multiply by the ratio 95\frac{9}{5} or 59\frac{5}{9}.
    2. Zero-point adjustment: Account for the 32∘32^\circ offset (water freezing point is 32∘32^\circ higher on the Fahrenheit scale).
  • Exact conversion equations:
    • Celsius to Fahrenheit:     ∘F=(9 ∘F5 ∘C× ∘C)+32 ∘F^\circ\text{F} = \left(\frac{9\,^\circ\text{F}}{5\,^\circ\text{C}} \times \,^\circ\text{C}\right) + 32\,^\circ\text{F}
    • Fahrenheit to Celsius:     ∘C=5 ∘C9 ∘F×( ∘F−32 ∘F)^\circ\text{C} = \frac{5\,^\circ\text{C}}{9\,^\circ\text{F}} \times \left(\,^\circ\text{F} - 32\,^\circ\text{F}\right)

A comparison of the Fahrenheit, Celsius, and Kelvin temperature scales

Temperature Conversions and Worked Examples

  • Worked Example 0.1: Converting Salt Melting Point (1474 ∘F1474\,^\circ\text{F}) to Celsius and Kelvin
    • Formula Approach:     ∘C=(5 ∘C9 ∘F)×(1474 ∘F−32 ∘F)=801 ∘C^\circ\text{C} = \left(\frac{5\,^\circ\text{C}}{9\,^\circ\text{F}}\right) \times (1474\,^\circ\text{F} - 32\,^\circ\text{F}) = 801\,^\circ\text{C}K=801 ∘C+273.15=1074 K\text{K} = 801\,^\circ\text{C} + 273.15 = 1074\,\text{K}
    • Conceptual Thinking Approach:
    • Step 1: Calculate degrees above freezing in Fahrenheit: 1474 ∘F−32 ∘F=1442 ∘F1474\,^\circ\text{F} - 32\,^\circ\text{F} = 1442\,^\circ\text{F} above the freezing point of water.
    • Step 2: Convert degree size: Since a Fahrenheit degree is 59\frac{5}{9} the size of a Celsius degree, 1442×59=801 ∘C1442 \times \frac{5}{9} = 801\,^\circ\text{C} above freezing (0 ∘C0\,^\circ\text{C}), giving 801 ∘C801\,^\circ\text{C}.
    • Step 3: Add freezing baseline on Kelvin scale: 273.15+801=1074.15 K273.15 + 801 = 1074.15\,\text{K} (rounded to 1074 K1074\,\text{K}).
  • Problem 0.1 Solutions:
    • (a) Diameter of a sodium atom (0.000 000 000 372 m0.000\,000\,000\,372\,\text{m}): 3.72×10−10 m3.72 \times 10^{-10}\,\text{m}
    • (b) Distance from Earth to Sun (150,000,000,000 m150,000,000,000\,\text{m}): 1.50×1011 m1.50 \times 10^{11}\,\text{m}
  • Problem 0.2 Solutions (Unit Name Abbreviations):
    • (a) μg\mu\text{g} = microgram
    • (b) dm\text{dm} = decimeter
    • (c) ps\text{ps} = picosecond
    • (d) kA\text{kA} = kiloampere
    • (e) mmol\text{mmol} = millimole
  • Problem 0.3 Solution (Human Body Temperature 98.6 ∘F98.6\,^\circ\text{F}):
    • Celsius: ∘C=59×(98.6−32)=37.0 ∘C^\circ\text{C} = \frac{5}{9} \times (98.6 - 32) = 37.0\,^\circ\text{C}
    • Kelvin: K=37.0+273.15=310.15 K\text{K} = 37.0 + 273.15 = 310.15\,\text{K}
  • Problem 0.4 Solutions (Temperature Conversions):
    • (a) −78 ∘C-78\,^\circ\text{C} to Kelvin: −78+273.15=195.15 K-78 + 273.15 = 195.15\,\text{K}
    • (b) 158 ∘C158\,^\circ\text{C} to Fahrenheit: (95×158)+32=284.4+32=316.4 ∘F\left(\frac{9}{5} \times 158\right) + 32 = 284.4 + 32 = 316.4\,^\circ\text{F}
    • (c) 375 K375\,\text{K} to Fahrenheit: 375−273.15=101.85 ∘C375 - 273.15 = 101.85\,^\circ\text{C}; (95×101.85)+32=183.33+32=215.33 ∘F\left(\frac{9}{5} \times 101.85\right) + 32 = 183.33 + 32 = 215.33\,^\circ\text{F}

Derived SI Units

  • Derived Quantities: Physical quantities that are expressed using combinations of one or more of the seven fundamental SI base units.
  • Common Derived Units and Measures:
    • Area: Defined as Length times length | Derived Unit: m2\text{m}^2
    • Volume: Defined as Area times length | Derived Unit: m3\text{m}^3
    • Density: Defined as Mass per unit volume | Derived Unit: kg/m3\text{kg/m}^3
    • Speed: Defined as Distance per unit time | Derived Unit: m/s\text{m/s}
    • Acceleration: Defined as Change in speed per unit time | Derived Unit: m/s2\text{m/s}^2
    • Force: Defined as Mass times acceleration | Derived Unit: (kg⋅m)/s2(\text{kg}\cdot\text{m})/\text{s}^2 (named the newton, N)
    • Pressure: Defined as Force per unit area | Derived Unit: kg/(m⋅s2)\text{kg}/(\text{m}\cdot\text{s}^2) (named the pascal, Pa)
    • Energy: Defined as Force times distance | Derived Unit: (kg⋅m2)/s2(\text{kg}\cdot\text{m}^2)/\text{s}^2 (named the joule, J)