Units, Significant Figures, and Problem Solving in General Chemistry

Units, Significant Figures, and Solving Chemical Problems

Course Overview and Relevance

This study guide covers foundational concepts from General Chemistry, including matter, measurement, scientific method, physical and chemical changes, separation techniques, units, significant figures, and dimensional analysis. These topics are essential for understanding chemical reactions, laboratory procedures, and quantitative problem solving.

Scientific Approach

Basic Vocabulary and Process

• Observation: Noticing phenomena or facts in the natural world.

• Hypothesis: A testable explanation or guess for an observation.

• Experiment: A controlled test to prove or disprove a hypothesis.

• Law: A general summary of what happens in a given context, often expressed mathematically.

• Theory: A well-tested explanation for why things work the way they do; broader and more substantiated than a hypothesis.

Scientific inquiry is iterative, always changing as new data is collected. Scientists must be comfortable with uncertainty and willing to revise ideas.

Matter and Its Composition

Classification of Matter

• Pure Substance: Has a uniform and definite composition.

  • Element: Cannot be broken down into simpler substances (e.g., Helium).

  • Compound: Composed of two or more elements chemically combined (e.g., Pure water).

• Mixture: Physical blend of two or more substances.

  • Heterogeneous: Non-uniform composition (e.g., Wet sand).

  • Homogeneous (Solution): Uniform composition throughout (e.g., Tea with sugar).

Physical vs. Chemical Changes

Types of Changes

• Chemical Change: Alters the chemical composition by breaking or forming chemical bonds (e.g., reaction of molecules).

• Physical Change: Changes phase or appearance without altering chemical composition (e.g., melting, dissolving).

Examples

• Sugar Dissolving in Water: Physical change—chemical composition remains unchanged.

• Sublimation of Dry Ice (CO2): Physical change—solid CO2 becomes gaseous CO2 without passing through liquid phase.

Separation Techniques

Filtration and Decanting

• Filtration: Physical process—separates solids from liquids using a filter.

• Decanting: Physical process—pouring off liquid from a solid or another liquid.

Distillation

• Distillation: Physical process—separates mixtures based on differences in boiling points.

Measurement and Units

Importance of Units

Accurate measurement and correct use of units are critical in chemistry. Errors in unit conversion can lead to significant mistakes, as illustrated by historical events (e.g., NASA probe loss).

SI Base Units

Quantity	Unit	Symbol
Length	Meter	m
Mass	Kilogram	kg
Time	Second	s
Temperature	Kelvin	K
Amount of substance	Mole	mol

Temperature Conversions

• Celsius to Kelvin: $K = ^ ext{∘}C + 273.15$

• Kelvin to Celsius: $^ ext{∘}C = K - 273.15$

Prefix Multipliers

Prefix	Symbol	Multiplier
kilo	k	$10^3$
centi	c	$10^{-2}$
milli	m	$10^{-3}$
micro	μ	$10^{-6}$
nano	n	$10^{-9}$
pico	p	$10^{-12}$

Volume Calculations and Pitfalls

Volume Units

• Volume is calculated as length × width × height.

• Be careful with unit conversions: $1 ext{mm} imes 1 ext{mm} imes 1 ext{mm} = 1 ext{mm}^3$

• For larger dimensions: $10 ext{mm} imes 10 ext{mm} imes 10 ext{mm} = 1,000 ext{mm}^3$

Unit Conversions and Dimensional Analysis

Steps for Dimensional Analysis

1. Sort: List given information with units.

2. Strategize: Identify conversion steps; ensure units cancel appropriately.

3. Solve: Perform calculations, keeping units throughout.

4. Check: Assess if the answer is reasonable (e.g., no negative mass).

Example

• Convert $173,231$ L of jet fuel (density $0.768 ext{g/cm}^3$) to kilograms: $173,231 ext{L} imes rac{1000 ext{mL}}{1 ext{L}} imes rac{1 ext{cm}^3}{1 ext{mL}} imes rac{0.768 ext{g}}{1 ext{cm}^3} imes rac{1 ext{kg}}{1000 ext{g}} = 1.33 imes 10^5 ext{kg}$

Density

Definition and Formula

• Density ($d$): Mass per unit volume. $d = rac{m}{V}$

• Common units: $ext{g/cm}^3$ or $ext{g/mL}$

• Intensive property: Does not depend on amount of substance.

Example Calculation

• For a cylinder: $V = ext{π} r^2 l$ $d = rac{m}{V}$

Significant Figures (Sig Figs)

Accuracy vs. Precision

• Accuracy: Closeness to the true value.

• Precision: Consistency of repeated measurements.

Counting Significant Figures

• Non-zero digits: always significant.

• Interior zeros: significant.

• Leading zeros: not significant.

• Trailing zeros: significant if after decimal point.

Exact Numbers

• Discrete objects, defined quantities, and numbers integral to equations have infinite significant figures.

Sig Figs in Calculations

• Multiplication/Division: Keep the smallest number of sig figs from inputs.

• Addition/Subtraction: Keep the fewest decimals from inputs.

• Round only at the end of calculations.

Scientific Notation and Sig Figs

• Count sig figs from the decimal representation, not the exponent.

Order-of-Magnitude Estimations

Purpose and Method

• Quick calculations to check reasonableness.

• Round numbers to nearest power of 10.

• Example: $rac{m_p}{m_e} = rac{1.67492728 imes 10^{-27} ext{kg}}{9.10938262 imes 10^{-31} ext{kg}} ightarrow 10^3$

Problems Involving Equations

General Strategy

• Write the equation with units and conversion factors before substituting numbers.

• Example: Density of a cylinder $d = rac{m}{V}$ $V = ext{π} r^2 l$

Practice Problems

Unit Conversion Example

• Convert $9255 ext{cm}^3$ to gallons, knowing $1 ext{gal} = 3.785 ext{L}$ and $1 ext{cm}^3 = 1 ext{mL}$.

Applied Problem

• A vineyard has $145$acres. Soil supplement requires $5.50$ g per square meter. How many kilograms are needed? Provided: $1 ext{km}^2 = 247 ext{acres}$

Summary

Mastery of units, significant figures, and dimensional analysis is essential for success in General Chemistry. These skills underpin accurate measurement, data analysis, and problem solving in all areas of chemistry.