General, Organic, & Biological Chemistry - Lecture Notes Review

Chemistry: Concepts, Measurement, and Properties

Fundamental Concepts of Chemistry

• Definition of Chemistry: The study of matter, including its composition, properties, and the transformations it undergoes.
• Definition of Matter: Anything that possesses mass and occupies volume. Matter can exist in three primary states: solid, liquid, and gas.

States of Matter

• The Solid State:
  • Has a definite volume.
  • Maintains its shape regardless of the container it is placed in.
  • Solid particles are positioned close together in a highly regular pattern.
• The Liquid State:
  • Has a definite volume.
  • Takes the shape of its container.
  • Liquid particles are close together but retain the ability to move past one another.
• The Gas State:
  • Has no definite shape; it assumes the shape of its container.
  • Has no definite volume; it assumes the volume of its container.
  • Gas particles are positioned very far apart and move around in a random fashion.

Properties and Changes in Matter

• Physical Properties: These can be observed or measured without altering the composition of the material. Examples include:
  • Boiling point
  • Color
  • Melting point
  • Odor
  • Solubility
  • State of matter
• Physical Change: An alteration of the material that does not change its chemical composition. For example, the transformation of water from solid (ice) to liquid and then to water vapor is a series of physical changes involving melting and boiling.
• Chemical Properties: These determine how a substance can be converted into a different substance.
• Chemical Change: A chemical reaction that converts one substance into another substance.

Classification of Matter

• Pure Substances:
  • Composed of only a single component (atom or molecule).
  • Possess a constant composition, regardless of the sample size or origin.
  • Cannot be broken down into other pure substances through physical changes.
  • Elements: Pure substances that cannot be broken down by chemical changes.
  • Compounds: Pure substances formed by chemically joining two or more elements.
• Mixtures:
  • Composed of more than one component.
  • Can have varying compositions (any combination of solid, liquid, and gas).
  • Can be separated into their constituent components by physical processes.
  • Example: Sugar dissolved in water is a mixture of sugar and water.

Measurement and the Metric System

• Components of Measurement: Every measurement consists of a number and a unit. A number is meaningless without its associated unit.
  • Example: A proper aspirin dosage is $325\,mg$. Without the unit milligrams, the number 325 is ambiguous.
  • Example: A fast time for a 100-meter dash is $10.00\,s$.

The Basic Metric Units

Common Metric Prefixes

Units are related to the base unit by powers of 10. The prefix indicates whether the unit is larger or smaller than the base unit.

Specific Metric Measurements

• Length:
  • Base unit: meter ($m$).
  • $1\,kilometer\,(km) = 1,000\,m$
  • $1\,millimeter\,(mm) = 0.001\,m$
  • $1\,centimeter\,(cm) = 0.01\,m$
• Mass:
  • Mass is a measure of the amount of matter in an object, while weight is the force felt due to gravity.
  • Base unit: gram ($g$).
  • $1\,kilogram\,(kg) = 1,000\,g$
  • $1\,milligram\,(mg) = 0.001\,g$
• Volume:
  • Base unit: liter ($L$).
  • $1\,kiloliter\,(kL) = 1,000\,L$
  • $1\,milliliter\,(mL) = 0.001\,L$
  • Volume can also be expressed as $Length \times Width \times Height$, resulting in cubic units like $cm^3$. Note: $1\,mL = 1\,cm^3$.

English Units and Metric Equivalents

Length

• $1\,ft = 12\,in.$
• $1\,yd = 3\,ft$
• $1\,mi = 5,280\,ft$
• Metric Relationships:
  • $2.54\,cm = 1\,in.$ (exact)
  • $1\,m = 39.37\,in.$
  • $1\,km = 0.6214\,mi$

Mass

• $1\,lb = 16.00\,oz$
• $1\,ton = 2,000\,lb$ (exact)
• Metric Relationships:
  • $1\,kg = 2.205\,lb$
  • $453.59237\,g = 1\,lb$ (exact)
  • $28.35\,g = 1\,oz$

Volume

• $1\,qt = 4\,cups$
• $1\,qt = 2\,pints$
• $1\,qt = 32\,fl\,oz$
• $1\,gal = 4\,qt$
• Metric Relationships:
  • $946.4\,mL = 1\,qt$
  • $1\,L = 1.057\,qt$
  • $29.57\,mL = 1\,fl\,oz$

Significant Figures

• Exact Numbers: Result from counting objects or are part of a definition (e.g., 10 fingers, 10 toes, $1\,meter = 100\,centimeters$). These have no uncertainty.
• Inexact Numbers: Result from measurements or observations and contain some degree of uncertainty (e.g., $15.3\,cm$, $1000.8\,g$, $0.0034\,mL$).
• Definition: Significant figures include all digits in a measured number, plus one estimated digit.

Rules for Determining Significant Figures

1. All nonzero digits are always significant.
   • $65.2\,g$: 3 sig. figures.
   • $255.345\,g$: 6 sig. figures.
2. Rules for Zeros:
   • A zero counts if it is between two nonzero digits ($29.05\,g$: 4 sig. figures; $1.0087\,mL$: 5 sig. figures).
   • A zero counts at the end of a number with a decimal place ($3.7500\,cm$: 5 sig. figures; $620.\,lb$: 3 sig. figures).
   • A zero does not count if it is at the beginning of a number ($0.00245\,mg$: 3 sig. figures; $0.008\,mL$: 1 sig. figure).
   • A zero does not count at the end of a number that lacks a decimal point ($2570\,m$: 3 sig. figures; $1245500\,m$: 5 sig. figures).

Calculations with Significant Figures

• Multiplication and Division: The answer must contain the same number of significant figures as the original number with the fewest significant figures.
  • Example: $61.2\,mi / 0.95843\,hr$ yields a calculator result of $63.854545\,mi/hr$. Since the limiting number ($61.2$) has 3 sig. figures, the answer is rounded to $63.9\,mi/hr$.
• Addition and Subtraction: The answer must have the same number of decimal places as the original number with the fewest decimal places.
  • Example: $10.11\,kg$ (2 decimal places) - $3.6\,kg$ (1 decimal place) = $6.51\,kg$. The final answer is rounded to $6.5\,kg$ (1 decimal place).

Rounding Rules

• If the first digit to be dropped is 4 or fewer, drop it and all following numbers.
• If the first digit to be dropped is 5 or greater, round the last retained digit up by one.

Scientific Notation

Numbers are written as: $Coefficient \times 10^{Exponent}$.

• Coefficient: A number between 1 and 10.
• Exponent: A positive or negative whole number.

Conversion Steps

1. Move the decimal point to create a number between 1 and 10.
2. Multiply by $10^x$, where $x$ is the number of places the decimal was moved.
   • Move decimal left: $x$ is positive.
     • Example: $2500 = 2.5 \times 10^3$
   • Move decimal right: $x$ is negative.
     • Example: $0.036 = 3.6 \times 10^{-2}$

Standard Number Conversion

• If exponent is positive, move decimal $x$ places to the right.
  • $2.800 \times 10^2 = 280.0$
• If exponent is negative, move decimal $x$ places to the left.
  • $2.80 \times 10^{-2} = 0.0280$

Problem Solving and Conversion Factors

• Conversion Factor: A term used to convert a quantity in one unit to its equivalent in another unit.
• Relationship: $original\,quantity \times conversion\,factor = desired\,quantity$
• Conversion factors are typically written as equalities (e.g., $2.205\,lb = 1\,kg$) and must be set up as fractions to cancel unwanted units.

Multi-Step Problems

Arrange factors so the denominator of one term cancels the numerator of the preceding term.

• Example: Liters in 1.0 pint:
  • Knowns: $2\,pints = 1\,quart$ and $1.06\,quarts = 1\,liter$.
  • Setup: $1.0\,pt \times \frac{1\,qt}{2\,pt} \times \frac{1\,L}{1.06\,qt}$
  • Note: $1.0\,pt$ has 2 sig. figures, and $1.06\,qt$ has 3 sig. figures. The result must have 2 sig. figures.

Temperature

Temperature measures the heat or coldness of an object using three scales: Fahrenheit ($^{\circ}F$), Celsius ($^{\circ}C$), and Kelvin ($K$).

Temperature Conversions

• Celsius to Fahrenheit: $T_F = 1.8(T_C) + 32$
• Fahrenheit to Celsius: $T_C = \frac{T_F - 32}{1.8}$
• Celsius to Kelvin: $T_K = T_C + 273.15$
• Kelvin to Celsius: $T_C = T_K - 273.15$

Temperature Reference Points

Density and Specific Gravity

Density

• Definition: A physical property relating the mass of a substance to its volume.
• Formulas:
  • Convert volume to mass: $volume\,(mL) \times density\,\left(\frac{g}{mL}\right) = mass\,(g)$
  • Convert mass to volume: $mass\,(g) \times inverse\,of\,density\,\left(\frac{mL}{g}\right) = volume\,(mL)$
• Example Calculation: If the density of acetic acid is $1.05\,g/mL$, find the volume of $5.0\,g$.
  • $5.0\,g \times \frac{1\,mL}{1.05\,g} = 4.76190...\,mL$
  • Rounding to 2 sig. figures (as in $5.0\,g$) = $4.8\,mL$.

Specific Gravity

• Definition: A unitless quantity that compares the density of a substance to the density of water at the same temperature.
• Unit Cancellation: Since it is the ratio of subance density ($g/mL$) to water density ($g/mL$), the units cancel out.
• Key Fact: The specific gravity of a substance numerically equals its density but has no units.