Principles of General Chemistry Study Notes

Chapter 1: Principles of Chemistry

• Chemistry is defined as the science of everyday experience, focusing on the study of matter, including its composition, properties, and transformations.

• Matter is defined as anything that has mass and takes up volume.

• Naturally occurring matter includes:

  • Cotton

  • Sand

  • Digoxin (a cardiac drug)

• Synthetic (human-made) matter includes:

  • Nylon

  • Styrofoam

  • Ibuprofen

States of Matter

• Solid State:

  • Has a definite volume.

  • Maintains its shape regardless of the container it is placed in.

  • Particles lie close together in a regular three-dimensional array.

• Liquid State:

  • Has a definite volume.

  • Takes the shape of the container it occupies.

  • Particles are close together but move randomly, sliding past one another.

• Gas State:

  • Has no definite shape or volume.

  • Expands to fill the volume and assumes the shape of its container.

  • Particles are very far apart and move around randomly.

Properties of Matter and Changes

• Physical Properties:

  • These can be observed or measured without changing the composition of the material.

  • Examples include:

  • Boiling point ($bp$)

  • Melting point ($mp$)

  • Solubility

  • Color

  • Odor

• Physical Change:

  • Alteration of the material that does not change its composition.

  • Examples include state changes:

  • Melting ice (solid water) to form liquid water.

  • Boiling liquid water to form steam (gaseous water).

• Chemical Properties:

  • These determine how a substance can be converted into another substance.

• Chemical Change (Chemical Reaction):

  • Converts one substance into another.

  • Examples:

  • A piece of paper burning.

  • Metabolizing an apple for energy.

  • Oxygen and hydrogen combining to form water.

Classification of Matter

• Pure Substance:

  • Composed of a single component.

  • Has a constant composition regardless of sample size or origin.

  • Cannot be broken down into other pure substances by physical change.

  • Examples: Table sugar ($C_{12}H_{22}O_{11}$) and Water ($H_2O$).

• Mixture:

  • Composed of more than one substance.

  • Can have varying composition (any combination of solid, liquid, or gas) depending on the sample.

  • Can be separated into components by physical charge.

  • Example: Sugar dissolved in water.

• Classification Logic:

  • Can it be separated by a physical process?

  • Yes: Mixture.

  • No: Pure Substance.

  • If it is a Pure Substance, can it be broken down into simpler substances by a chemical reaction?

  • Yes: Compound.

  • No: Element.

• Element vs. Compound:

  • Element: A pure substance that cannot be broken down by chemical change (e.g., aluminum metal, $Al$).

  • Compound: A pure substance formed by chemically joining two or more elements (e.g., table salt, $NaCl$).

Measurement and Units

• Every measurement is composed of a number and a unit.

• The number is meaningless without the unit.

• Examples illustrating unit importance:

  • Aspirin dosage: $325$ (is it milligrams or pounds?).

  • 100-meter dash time: $10.00$ (is it seconds or days?).

• Systems of Measurement:

  • English System: Uses units such as miles (length), gallons (volume), and pounds (weight).

  • Metric System: Uses units such as meters (length), liters (volume), and grams (mass).

• Base Units of the Metric System:

  • Length: Meter ($m$)

  • Mass: Gram ($g$)

  • Volume: Liter ($L$)

  • Time: Second ($s$)

• Metric Relationships:

  • Other units are related to base units by powers of 10, indicated by prefixes.

  • Length:

  • $1,000\,m = 1\,kilometer\,(km)$

  • $1\,m = 0.001\,km$

  • $1\,m = 100\,centimeters\,(cm)$

  • $0.01\,m = 1\,cm$

  • $1\,m = 1,000\,millimeters\,(mm)$

  • $0.001\,m = 1\,mm$

  • Mass:

  • Mass measures the amount of matter; Weight is the gravitational force on matter.

  • $1,000\,g = 1\,kilogram\,(kg)$

  • $1\,g = 0.001\,kg$

  • $1\,g = 1,000\,milligram\,(mg)$

  • $0.001\,g = 1\,mg$

  • Volume:

  • $1,000\,L = 1\,kiloliter\,(kL)$

  • $1\,L = 0.001\,kL$

  • $1\,L = 1,000\,milliliter\,(mL)$

  • $0.001\,L = 1\,mL$

  • $Volume = Length \times Width \times Height = cm \times cm \times cm = cm^3$

  • $1\,mL = 1\,cm^3 = 1\,cc$

English-Metric Equalities

• Length:

  • $1\,ft = 12\,in.$

  • $1\,yd = 3\,ft$

  • $1\,mi = 5,280\,ft$

  • Metric Relationship: $2.54\,cm = 1\,in.$

  • Metric Relationship: $1\,m = 39.4\,in.$

  • Metric Relationship: $1\,km = 0.621\,mi.$

• Mass:

  • $1\,lb = 16\,oz$

  • $1\,ton = 2,000\,lb$

  • Metric Relationship: $1\,kg = 2.20\,lb$

  • Metric Relationship: $454\,g = 1\,lb$

  • Metric Relationship: $28.3\,g = 1\,oz$

• Volume:

  • $1\,qt = 4\,cups$

  • $1\,qt = 2\,pt$

  • $1\,qt = 32\,fl\,oz$

  • $1\,gal = 4\,qt$

  • Metric Relationship: $946\,mL = 1\,qt$

  • Metric Relationship: $1\,L = 1.06\,qt$

  • Metric Relationship: $29.6\,mL = 1\,fl\,oz$

Significant Figures

• Exact Numbers:

  • Result from counting objects or definitions.

  • Examples: $10\,fingers$, $10\,toes$, $1\,m = 100\,cm$.

• Inexact Numbers:

  • Result from measurements or observations and contain uncertainty.

  • Examples: $15.3\,cm$, $1000.8\,g$, $0.0034\,mL$.

• Determining Significant Figures:

  • Significant figures include all digits in a measured number including one estimated digit.

  • All nonzero digits are significant ($65.2\,g$ has 3; $255.345\,g$ has 6).

• Rules for Zeros:

  • Zero counts as significant if:

  • It is between two nonzero digits (e.g., $29.05\,g$ [4 sig figs], $1.0087\,mL$ [5 sig figs]).

  • It is at the end of a number with a decimal place (e.g., $3.7500\,cm$ [5 sig figs], $620.\,lb$ [3 sig figs]).

  • Zero does not count as significant if:

  • It is at the beginning of a number (e.g., $0.00245\,mg$ [3 sig figs], $0.008\,mL$ [1 sig fig]).

  • It is at the end of a number without a decimal (e.g., $2570\,m$ [3 sig figs], $1245500\,m$ [5 sig figs]).

• Rules for Multiplication and Division:

  • The answer must have the same number of significant figures as the original number with the fewest significant figures.

  • Example: $\frac{351.2\,miles}{5.5\,hour} = 63.854545\dots \frac{miles}{hour}$. Output must be restricted to 2 significant figures: $64\,miles/hour$.

  • Example: $23.2 \times 1.1 = 25.52 \rightarrow 26$ (2 sig figs).

  • Example: $25.0 \times 0.50 = 12.5 \rightarrow 13$ (Note: Transcript specifies calculator display 50 and result 50. for $25.0 \times 0.50$; applying standard rules, 2 significant figures should be retained).

• Rules for Rounding:

  • If the first digit to be dropped is between 0 and 4: drop it and remaining digits.

  • If the first digit to be dropped is between 5 and 9: round up the last retained digit by adding 1.

• Rules for Addition and Subtraction:

  • The answer has the same number of decimal places as the original number with the fewest decimal places.

  • Example: $10.11\,kg - 3.6\,kg = 6.51\,kg \rightarrow 6.5\,kg$ (1 decimal place).

Scientific Notation

• Formula: $y \times 10^x$ where $y$ is the coefficient (between 1 and 10) and $x$ is the exponent (whole number).

• Converting Standard to Scientific:

  • Move decimal to create a number between 1 and 10.

  • If decimal moved left, $x$ is positive.

  • If decimal moved right, $x$ is negative.

  • Examples: $2,500 = 2.5 \times 10^3$; $0.036 = 3.6 \times 10^{-2}$.

• Scale Examples:

  • Human body red blood cells: $20,000,000,000,000 = 2 \times 10^{13}$.

  • Red blood cell diameter: $0.000006\,m = 6 \times 10^{-6}\,m$.

• Converting Scientific to Standard:

  • Positive $x$: move decimal $x$ places to the right.

  • Negative $x$: move decimal $x$ places to the left.

  • Examples: $2.800 \times 10^2 = 280.0$; $2.80 \times 10^{-2} = 0.0280$.

Conversion Factors and Problem Solving

• Factor-Label Method:

  • Uses conversion factors to convert units; units are treated like numbers.

  • Formula: $original\,quantity \times conversion\,factor = desired\,quantity$.

• Single Step Example:

  • Convert 130 lb to kg: $130\,lb \times \frac{1\,kg}{2.20\,lb} = 59\,kg$ (2 sig figs).

• Clinic Problem Example:

  • Tablet calculation: $1.25\,g\,amoxicillin \times \frac{1000\,mg}{1\,g} \times \frac{1\,tablet}{250\,mg} = 5\,tablets$.

• Multiple Step Example:

  • Liters in 1.0 pint of blood: $1.0\,pt \times \frac{1\,qt}{2\,pt} \times \frac{1\,L}{1.06\,qt} = 0.47\,L$ (2 sig figs).

Temperature

• Temperature measures how hot or cold an object is.

• Scales:

  • Fahrenheit ($^\circ F$)

  • Celsius ($^\circ C$)

  • Kelvin ($K$)

• Conversion Formulas:

  • Celsius to Fahrenheit: $T_F = 1.8(T_C) + 32$

  • Fahrenheit to Celsius: $T_C = \frac{T_F - 32}{1.8}$

  • Celsius to Kelvin: $T_K = T_C + 273$

  • Kelvin to Celsius: $T_C = T_K - 273$

• Key Comparison Points:

  • Boiling point of water: $212^\circ F$, $100^\circ C$, $373\,K$.

  • Normal body temperature: $98.6^\circ F$, $37^\circ C$, $310\,K$.

  • Freezing point of water: $32^\circ F$, $0^\circ C$, $273\,K$.

  • Absolute zero: $-460^\circ F$, $-273^\circ C$, $0\,K$.

Density and Specific Gravity

• Density:

  • A physical property relating mass to volume.

  • Formula: $density = \frac{mass\,(g)}{volume\,(mL\,or\,cc)}$.

  • To convert volume to mass: $mL \times \frac{g}{mL} = g$ (using density).

  • To convert mass to volume: $g \times \frac{mL}{g} = mL$ (using inverse of density).

• Density Calculation Example:

  • Find mass of 15.0 mL of saline (density $1.05\,g/mL$):

  • $15.0\,mL \times \frac{1.05\,g}{1\,mL} = 15.8\,g$ (3 sig figs).

• Specific Gravity:

  • Compares the density of a substance with the density of water at the same temperature.

  • Formula: $specific\,gravity = \frac{density\,of\,a\,substance\,(g/mL)}{density\,of\,water\,(g/mL)}$.

  • It contains no units because they cancel out.

  • The specific gravity of a substance is numerically equal to its density.