CHM 11100 Measurement, Unit Conversions, Density, and Significant Figures Study Notes

Course Logistics, Deadlines, and Integrity Policies

• Course Sections:

  • CHM 11100-02 (2:30 PM)

  • CHM 11100-03 (3:30 PM)

• Course Deadlines (All due at 11:59 PM):

  • Getting to Know You survey: Sunday, August 30, 2026

  • Safety Certification: Sunday, August 30, 2026 (Minimum required score: $20/25$; mandatory prerequisite for laboratory entry)

  • ALEKS Homework 01 (HW01): Friday, September 4, 2026

  • ALEKS Learning Module 1: Sunday, September 6, 2026

  • Syllabus Quiz: Sunday, September 7, 2026 (opens in Brightspace)

• Weekly Assignment Schedule:

  • Pre-Lab Assignments: Completed on LabFlow; due the day before lab at 11:59 PM

  • Lab Reports: Completed on LabFlow; due the day of lab at 11:59 PM

  • Learning Modules: Completed on ALEKS; due Sundays at 11:59 PM

  • Homework: Completed on ALEKS; due Fridays at 11:59 PM

• Academic Integrity Guidelines:

  • Definition in CHM 11100: Doing your own work at all times.

  • Discussion of general chemical concepts is encouraged; however, sharing answers or written work in person or electronically to allow copying is prohibited academic dishonesty.

  • Posting course materials to platforms such as Chegg or generative AI tools like ChatGPT violates copyright laws under the Purdue Intellectual Property Policy.

  • Homework Policy: Working together is acceptable, but looking up answers on Chegg or AI will not prepare students for exams.

  • Laboratory Policy: Collaboration is encouraged during lab work, but every student must turn in work written in their own words.

• Authorized AI Usage by Students in CHM 11100:

  • Generating additional practice study questions and problems.

  • Creating digital flashcards and study modules (e.g., Quizlets).

  • Assisting with editing and proofreading written work.

  • Generating and exploring specific chemistry concept examples to enhance learning.

The First Twenty Chemical Elements

• Required Elements to Memorize (Names and Symbols):

  • Element $1$: Hydrogen ($\text{H}$)

  • Element $2$: Helium ($\text{He}$)

  • Element $3$: Lithium ($\text{Li}$)

  • Element $4$: Beryllium ($\text{Be}$)

  • Element $5$: Boron ($\text{B}$)

  • Element $6$: Carbon ($\text{C}$)

  • Element $7$: Nitrogen ($\text{N}$)

  • Element $8$: Oxygen ($\text{O}$)

  • Element $9$: Fluorine ($\text{F}$)

  • Element $10$: Neon ($\text{Ne}$)

  • Element $11$: Sodium ($\text{Na}$)

  • Element $12$: Magnesium ($\text{Mg}$)

  • Element $13$: Aluminum ($\text{Al}$)

  • Element $14$: Silicon ($\text{Si}$)

  • Element $15$: Phosphorus ($\text{P}$)

  • Element $16$: Sulfur ($\text{S}$)

  • Element $17$: Chlorine ($\text{Cl}$)

  • Element $18$: Argon ($\text{Ar}$)

  • Element $19$: Potassium ($\text{K}$)

  • Element $20$: Calcium ($\text{Ca}$)

Scientific Measurement and Metric System (SI Units)

• Classification of Measured Properties:

  • Quantitative Properties: Measurable physical characteristics that must always include a numerical value and an accompanying unit.

  • Qualitative Properties: Observational traits that do not require explicit measurement tools.

• SI Units: International System of Units; the agreed-upon standard physical units used globally in science and engineering.

• Metric Prefixes and Multipliers:

  • Tera ($\text{T}$): Multiplier = $10^{12}$ ($1,000,000,000,000$ or trillion)

  • Giga ($\text{G}$): Multiplier = $10^9$ ($1,000,000,000$ or billion)

  • Mega ($\text{M}$): Multiplier = $10^6$ ($1,000,000$ or million) (frequently used in chemistry)

  • Kilo ($\text{k}$): Multiplier = $10^3$ ($1,000$ or thousand) (frequently used in chemistry)

  • Hecto ($\text{h}$): Multiplier = $10^2$ ($100$ or hundred)

  • Deka ($\text{da}$): Multiplier = $10^1$ ($10$ or ten)

  • [Base Unit]: Multiplier = $10^0$ ($1$ or one)

  • Deci ($\text{d}$): Multiplier = $10^{-1}$ ($0.1$ or tenth) (frequently used in chemistry)

  • Centi ($\text{c}$): Multiplier = $10^{-2}$ ($0.01$ or hundredth) (frequently used in chemistry)

  • Milli ($\text{m}$): Multiplier = $10^{-3}$ ($0.001$ or thousandth) (frequently used in chemistry)

  • Micro ($\mu$): Multiplier = $10^{-6}$ ($0.000001$ or millionth) (frequently used in chemistry)

  • Nano ($\text{n}$): Multiplier = $10^{-9}$ ($0.000000001$ or billionth) (frequently used in chemistry)

  • Pico ($\text{p}$): Multiplier = $10^{-12}$ ($0.000000000001$ or trillionth) (frequently used in chemistry)

  • Femto ($\text{f}$): Multiplier = $10^{-15}$ ($0.000000000000001$ or quadrillionth)

Unit Conversions and Dimensional Analysis

• Importance of Units in Real-World Applications:

  • Numbers alone are insufficient; units attached to numbers carry equal importance.

  • Historical Case Study: The 1999 Mars Climate Orbiter engineering failure ($\$125\text{ million}$ spacecraft loss) resulted from one engineering team using SI units while another used Imperial units without converting units.

• Conversion Factors:

  • A ratio of equivalent quantities used to express a given measurement in different units.

  • Because numerator and denominator represent identical physical quantities, conversion factors are mathematically equal to $1$

  • Example Relationship $1\,\text{mi} = 2218\,\text{steps}$ yields conversion factors: $\frac{2218\,\text{steps}}{1\,\text{mi}}$ and $\frac{1\,\text{mi}}{2218\,\text{steps}}$

  • Example Relationship $1\,\text{mi} = 1.609\,\text{km}$ yields conversion factors: $\frac{1.609\,\text{km}}{1\,\text{mi}}$ and $\frac{1\,\text{mi}}{1.609\,\text{km}}$

• Dimensional Analysis Problem-Solving Strategy:

  • Step 1: Write down given values, known conversion factors, and units of target quantity.

  • Step 2: Set up problem so units cancel out properly: $\text{given quantity} \times \text{conversion factor} = \text{desired quantity}$

  • Step 3: Validate unit cancellation: $\text{given unit} \times \frac{\text{desired unit}}{\text{given unit}} = \text{desired unit}$

• Dimensional Analysis Examples:

  • Miles to Kilometers ($65\,\text{mph}$): $65\,\text{mi} \times \frac{1.609\,\text{km}}{1\,\text{mi}} = 104.6\,\text{km}$

  • Kilometers to Miles ($65\,\text{km/h}$): $65\,\text{km} \times \frac{1\,\text{mi}}{1.609\,\text{km}} = 40.4\,\text{miles}$

  • Distance Problem: Harrison Hall is $0.73\,\text{miles}$ from WALC. Steps calculation using $1\,\text{mi} = 2218\,\text{steps}$: $0.73\,\text{mi} \times \frac{2218\,\text{steps}}{1\,\text{mi}} = 1619.14\,\text{steps} \approx 1.6 \times 10^3\,\text{steps}$

  • Mass Conversion Example 2.1: A slice of Swiss cheese contains $45\,\text{mg}$ sodium. Convert mass to grams using $1\,\text{g} = 1000\,\text{mg}$: $45\,\text{mg} \times \frac{1\,\text{g}}{1000\,\text{mg}} = 0.045\,\text{g} = 4.5 \times 10^{-2}\,\text{g}$

Density Concepts and Measurements

• Definition: Density is the ratio of mass to the volume it occupies.

  • Formula: $\text{density} = \frac{\text{mass}}{\text{volume}}$

• Units of Density:

  • Solids and Liquids: $\text{g/mL}$ or $\text{g/cm}^3$

  • Gases: $\text{g/L}$

• Sample Density Calculation:

  • Problem: A piece of gold with mass $301\,\text{g}$ has a volume of $15.6\,\text{cm}^3$. Calculate density.

  • Solution: $\text{Density} = \frac{301\,\text{g}}{15.6\,\text{cm}^3} = 19.2948...\,\text{g/cm}^3 = 19.3\,\text{g/cm}^3$

• Densities of Standard Substances at $25^\circ\text{C}$ (Table 1.4):

  • Air (measured at $1\,\text{atm}$): $0.001\,\text{g/cm}^3$

  • Ethanol: $0.79\,\text{g/cm}^3$

  • Water: $1.00\,\text{g/cm}^3$

  • Graphite: $2.2\,\text{g/cm}^3$

  • Table Salt: $2.2\,\text{g/cm}^3$

  • Aluminum: $2.70\,\text{g/cm}^3$

  • Diamond: $3.5\,\text{g/cm}^3$

  • Iron: $7.9\,\text{g/cm}^3$

  • Lead: $11.3\,\text{g/cm}^3$

  • Mercury: $13.6\,\text{g/cm}^3$

  • Gold: $19.3\,\text{g/cm}^3$

  • Osmium ($\text{Os}$): $22.6\,\text{g/cm}^3$ (densest element known)

Scientific Notation

• Purpose: Compact notation used to express extremely large or small numbers.

• General Format: $C \times 10^n$

  • Coefficient ($C$): Single digit before the decimal point ($1 \le C < 10$).

  • Exponent ($n$): Integer value. Negative for numbers smaller than $1$; positive for numbers larger than $1$

• Practice Conversions:

  • $0.000000027 \rightarrow 2.7 \times 10^{-8}$ (2 significant figures)

  • $356 \rightarrow 3.56 \times 10^2$ (3 significant figures)

  • $47764 \rightarrow 4.7764 \times 10^4$ (5 significant figures)

  • $0.096 \rightarrow 9.6 \times 10^{-2}$ (2 significant figures)

Exact vs. Measured Numbers and Significant Figures

• Exact Numbers:

  • Values obtained by counting objects or defined by explicit mathematical relationships.

  • Free from uncertainty; possess infinite significant figures.

  • Examples: $12\,\text{eggs}$ (exactly 12), $1\,\text{dozen} = 12$, $1000\,\text{m} = 1\,\text{km}$, $1\,\text{minute} = 60\,\text{seconds}$.

• Measured Numbers:

  • Values obtained using instruments (e.g., scale, ruler, thermometer, balance).

  • Always contain uncertainty based on instrument precision.

  • The rightmost recorded digit of any measurement is always estimated.

  • Examples of instrument precision levels:

  • Simple balance: $12.4\,\text{g}$ (3 significant figures)

  • More precise balance: $12.43\,\text{g}$ (4 significant figures)

  • Analytical balance: $12.431\,\text{g}$ (5 significant figures)

• Rules for Determining Significant Figures:

  • Non-zero Digits: Always significant ($25$ has 2; $7.389$ has 4; $512$ has 3).

  • Sandwiched Zeros (Zeros between non-zero digits): Always significant ($1002$ has 4; $3.07$ has 3; $502$ has 3).

  • Leading Zeros: Never significant; they serve only to locate the decimal point ($0.0045$ has 2; $0.030$ has 2; $0.0055$ has 2).

  • Trailing Zeros:

  • Significant IF a decimal point is explicitly present ($2.50$ has 3; $100.$ has 3; $1.1300$ has 5; $5300.$ has 4).

  • Ambiguous / Not significant if NO decimal point is shown ($5300$ has 2; $100$ is ambiguous).

  • Scientific notation resolves ambiguity: $1.00 \times 10^2$ (3 significant figures) vs $1 \times 10^2$ (1 significant figure).

• Sample Problems - Identifying Significant Figures:

  • $12\,\text{mL}$: 2 significant figures

  • $8501\,\text{g}$: 4 significant figures

  • $0.0610\,\text{m}^3$: 3 significant figures

  • $6.4 \times 10^4\,\text{molecules}$: 2 significant figures

  • $790\,\text{kg}$: 2 significant figures

Calculations and Rounding Rules

• Addition and Subtraction Rule:

  • The answer must match the fewest number of decimal places of any input value.

  • Example 1: $12.11 + 3.2 = 15.31 \rightarrow 15.3$ (limited to 1 decimal place by $3.2$)

  • Example 2: $18.276 + 2.4 = 20.676 \rightarrow 20.7$ (limited to 1 decimal place by $2.4$; $7$ rounds up)

  • Example 3: $5.72 + 4.6 = 10.32 \rightarrow 10.3$ (limited to 1 decimal place by $4.6$)

• Multiplication and Division Rule:

  • The answer must match the fewest total number of significant figures of any input value.

  • Example 1: $0.00456 \times 123.4$

  • Input count: $0.00456$ (3 sig figs), $123.4$ (4 sig figs)

  • Multiplication step: $0.00456 \times 123.4 = 0.562704$

  • Rounded result: $0.563$ (3 sig figs)

  • Example 2: $2.45 \times 1.3$

  • Input count: $2.45$ (3 sig figs), $1.3$ (2 sig figs)

  • Multiplication step: $2.45 \times 1.3 = 3.185$

  • Rounded result: $3.2$ (2 sig figs)

  • Example 3: $120.4 / 2.5 = 48.16 \rightarrow 48$ (limited to 2 sig figs by $2.5$)

• Rounding Rule Guidelines:

  • Digit to drop is $5$ or greater: Round UP.

  • Digit to drop is $4$ or less: Let it rest / Round DOWN.

• Calculator Troubleshooting Note:

  • If calculated values are consistently off by a factor of $10$, consult instructors on proper scientific calculator exponent entry syntax ($\text{EE}$ / $\text{EXP}$ keys).