Chapter 2 – Chemistry & Measurements (Complete Notes)

Foundations & Chapter Scope

• The instructor urges you to read Chapter 1, even though it is not officially on the syllabus.

  • Chapter 1 reviews arithmetic, powers of 10, scientific notation, the metric-prefix table, and calculator keystrokes that underpin everything in Chapter 2 and the remainder of the course.

• Chapter 2 (“Chemistry & Measurements”) is the operational core:

  • What a measurement is and why units are indispensable.

  • English, Metric, and SI systems; how and why scientists use SI.

  • How to make, record, and convert measurements.

  • Scientific notation and prefixes for very large/small quantities.

  • Precision, uncertainty, significant figures (sig figs), rounding.

  • Dimensional analysis (factor-label method) for unit conversions.

  • Density as a conversion factor and as an identification tool.

Units and Measurement Systems

• A number without a unit is meaningless. 65 alone conveys nothing; 65\;\text{in} instantly signals a length.

• English (U.S. customary) system

  • Length \bigl(\text{ft},\;\text{yd},\;\text{mi}\bigr)

  • Mass/weight \bigl(\text{lb},\;\text{oz}\bigr)

  • Volume \bigl(\text{qt},\;\text{gal}\bigr)

• Metric system

  • Uses prefixes to scale the same base unit (e.g.
    \text{g},\;\text{kg},\;\text{mg} are all masses).

• SI (Système International)

  • Global scientific standard built on 7 fundamental quantities.

  • Official SI base units used throughout research & medicine.

  • Scientists in every country, including the U.S., publish and communicate in SI even if day-to-day life relies on English units.

SI Base Quantities Discussed

Scientific Notation

• Purpose: compress extremely large or small numbers; minimize transcription errors; reveal sig figs.

• General form: \bigl(\text{coefficient}\bigr) \times 10^{\text{exponent}}

  • Coefficient contains one non-zero digit to the left of the decimal.

  • Exponent tells how many times the decimal shifts.

  • + exponent ⇒ move right ⇒ number >1.

  • - exponent ⇒ move left ⇒ number <1.

• Examples (standard → scientific)

  • 2500000=2.5\times10^{6} (moved 6 places left, positive exponent).

  • 0.000142 = 1.42\times10^{-4} (moved 4 places right, negative exponent).

• Examples (scientific → standard)

  • 1.35\times10^{-5}=0.0000135.

  • 4.27\times10^{3}=4270.

• Calculator entry: type coefficient, press \text{EE} / \text{EXP} / \times10^{x}, then exponent (e.g. 1.53\,\text{EE}\,16).

Metric Prefixes (Powers of 10)

• Increase unit size (positive exponent)

  • \text{kilo }(\text{k}) = 10^{3}

  • \text{mega }(\text{M}) = 10^{6}

  • \text{tera }(\text{T}) = 10^{12}

• Decrease unit size (negative exponent)

  • \text{deci }(\text{d})=10^{-1}

  • \text{centi }(\text{c})=10^{-2}

  • \text{milli }(\text{m})=10^{-3}

  • \text{micro }(\mu\text{ or }\text{mc})=10^{-6}

• Using a prefix: replace it by its numerical meaning.

  • 1\,\text{km}=10^{3}\,\text{m}=1000\,\text{m}

  • 1\,\text{mg}=10^{-3}\,\text{g}=0.001\,\text{g}

• Why useful? Eliminates unwieldy strings of zeros (cf. astronomical distances, micro-organism widths).

Core Laboratory Quantities & Typical Units

• Length: \text{m},\;\text{cm},\;\text{in},\;\text{ft}

  • 1\,\text{in}=2.54\,\text{cm} (exact, \infty sig figs).

• Volume: \text{L},\;\text{mL},\;\text{cm}^{3},\;\text{qt},\;\text{gal}

  • 1\,\text{mL}=1\,\text{cm}^{3} (useful for solids ↔ liquids).

  • 1000\,\text{mL}=1\,\text{L} because \text{milli}=10^{-3}.

• Mass: \text{g},\;\text{kg},\;\text{lb},\;\text{oz}

  • 1\,\text{kg}=2.205\,\text{lb}.

• Temperature: ^{\circ}\text{C},\;^{\circ}\text{F},\;\text{K} (conversions later in course).

• Time: \text{s},\;\text{min},\;\text{h},\;\text{day} (all exact relations: 60\,\text{s}=1\,\text{min}, etc.).

Making & Reporting a Measurement

• Every measurement = certain digits + one estimated digit.

  • Certainty comes from scale marks; the last digit is always uncertain (subjective estimation).

• Instrument dictates precision.

  • Beaker gradations 10\,\text{mL} apart ⇒ volume known to \pm1\,\text{mL}.

  • Buret gradations 0.1\,\text{mL} apart ⇒ volume known to \pm0.01\,\text{mL}.

• Rule of thumb: smallest graduation \div 10 gives place value of estimated digit.

• Meniscus reading: use bottom of curve; eye level; avoid parallax.

Significant Figures (Counting Rules)

1. All non-zero digits are significant. 456 has 3 sig figs.

2. Interior (sandwiched) zeros are significant. 409.07 ⇒ 5 sig figs.

3. Trailing zeros with a decimal point are significant. 50.00 ⇒ 4 sig figs.

4. Leading zeros are not significant. 0.0023 ⇒ 2 sig figs.

5. Trailing zeros without a decimal are ambiguous; assume not significant unless a bar/decimal/scientific notation clarifies.

6. Exact numbers (counted items, definitions) possess infinite sig figs and never limit precision (e.g. 1\,\text{in}=2.54\,\text{cm exactly}).

Rounding Rules

• If the digit to be dropped is \le4 ⇒ leave preceding digit unchanged.

• If the digit to be dropped is \ge5 ⇒ raise preceding digit by 1.

• When necessary, insert zeros as placeholders to keep magnitude (e.g. 3256\to3.26\times10^{3} for 3 sig figs).

Calculations & Sig Figs

• Multiplication / Division: Result keeps the fewest sig figs among operands.

  • Example: (5.4\,\text{cm})(3.21\,\text{cm})(2.15\,\text{cm})=37.2\,\text{cm}^{3} (three-sig-fig limit).

• Addition / Subtraction: Align decimals; answer cut off at left-most uncertain digit.

  • Example: 34.1+2.045=36.1 (tenths place is the first uncertain column).

Dimensional Analysis (Factor-Label Method)

• Treat units like algebraic variables: they multiply, divide, and cancel.

• General template: \frac{\text{given value}\;\cancel{\text{unit}}}{1}\times\frac{\text{desired unit}}{\cancel{\text{unit}}}=\text{answer in desired unit}

• Single-step example: 128\,\text{lb}\times\frac{1\,\text{kg}}{2.205\,\text{lb}}=5.81\times10^{1}\,\text{kg}.

• Multi-step example (days → minutes):
  1.4\,\text{day}\times\frac{24\,\text{h}}{1\,\text{day}}\times\frac{60\,\text{min}}{1\,\text{h}}=2.0\times10^{3}\,\text{min} (two sig figs).

Squared & Cubed Units

• Square or cube the entire conversion factor:
  \Bigl(1\,\text{yd}=3\,\text{ft}\Bigr)^{2}\;\Rightarrow\;1\,\text{yd}^{2}=9\,\text{ft}^{2}.

• Apply same logic for \text{cm}^{3}\leftrightarrow\text{mL}, etc.

Density

• Definition: \text{density}=\dfrac{\text{mass}}{\text{volume}}.

  • Solids/liquids: \text{g}\,/\,\text{cm}^{3}\;(\text{or }\text{g}\,/\,\text{mL}).

  • Gases: \text{g}\,/\,\text{L} (particles occupy larger volume).

• Physical insight

  • Higher density than the fluid ⇒ object sinks.

  • Lower density ⇒ object floats (e.g. wood vs. water).

• Typical values

  • Aluminum \approx2.7\,\text{g/cm}^{3}, Lead \approx11.3\,\text{g/cm}^{3}, Ice \approx0.92\,\text{g/cm}^{3}.

• Measuring volume of irregular solids: water-displacement method.

  1. Record initial liquid level V_{i}.

  2. Immerse solid; record new level V_{f}.

  3. V{\text{solid}}=V{f}-V_{i}.

• Density as a conversion factor

  • Given \rho=1.06\,\text{g/mL}, interpret \frac{1.06\,\text{g}}{1\,\text{mL}} or its reciprocal as needed to jump between mass ↔ volume.

Calculator Tips & Exam Readiness

• Locate the \text{EE}/\text{EXP} key now; practice entries like 3.52\,\text{EE}\,-7.

• Always copy units through every stage; if unwanted units survive, your set-up is wrong.

• For the first test, instructor expects you to memorize these prefixes:

  • Large: \text{mega},\;\text{kilo}

  • Small: \text{deci},\;\text{centi},\;\text{milli},\;\text{micro}

• Exact conversion constants (e.g. 1\,\text{in}=2.54\,\text{cm}) are supplied; prefix relationships are not.

Practice & Self-Check Prompts

• Convert 0.032\,\text{g} to \mu\text{g} using the exponent method.

• Express the speed 1.00\times10^{8}\,\text{bit/s} in \text{Mb/s}.

• A graduated cylinder reads 47.36\,\text{mL}; record to correct sig figs.

• Carry out \bigl(8.0\times10^{3}\bigr)/(2.00) with proper sig figs.

• If a metal block (mass 258\,\text{g}) displaces 95.6\,\text{mL} of water, identify the metal via its density.

Ethical & practical angle: unit errors kill (Mars Climate Orbiter, heparin dosage mis-conversions). Master these skills—lives and billions of dollars can hinge on a unit.