CHEM 115 Chapter 1 Detailed Study Notes

Chemistry in Context

• Definition of Chemistry:

  • Chemistry is the study of the composition, structure, and properties of matter.
  • It is a science grounded in observation and experimentation.

• Scientific Method Foundations:

  • Hypothesis: A tentative explanation of observations.
  • Natural Law (Laws of Nature): Summarizes a vast number of experimental observations, and describes or predicts some facet of the natural world.
  • Theory: A well-substantiated, comprehensive, testable explanation of a particular aspect of nature.

• Concept Verification & Practice:

  • Question: The statement "The total mass of materials is not affected by a chemical change in those materials" is called a(n):
  • A) observation
  • B) measurement
  • C) theory
  • D) natural law
  • E) experiment
  • Answer: D) natural law

Phases and Classification of Matter

• Definition of Matter:

  • Matter is defined as anything that occupies space and has mass, encompassing everything around us.

• Characterization of Matter:

  • Matter is characterized by state (solid, liquid, or gas) or by composition (element, compound, or mixture).

• States of Matter (Macroscopic Level Properties):

  • Gas: Has no fixed volume or shape; conforms to the shape of its container; highly compressible. Always takes the volume and shape of its container.
  • Liquid: Has a fixed volume independent of its container, but no fixed shape; takes the shape of its container; incompressible.
  • Solid: Has a fixed volume and rigid shape independent of its container; rigid and incompressible.

• States of Matter (Molecular Level Properties):

  • Gas: Molecules are far apart, move at high speeds, and collide often.
  • Liquid: Molecules are closer together than in a gas, moving rapidly but able to slide over each other.
  • Solid: Molecules are packed closely together in definite arrangements.

• Plasma:

  • A gaseous state of matter that contains an appreciable amount of electrically charged particles.

• Classification by Composition:

  • Depending on its properties, a given substance can be classified as a homogeneous mixture, a heterogeneous mixture, a compound, or an element.
  • Pure Substances:
  • Element: A type of pure substance that cannot be broken down into simpler substances by chemical changes. Consists of only one type of element.
    • Examples: Gold ($Au$), Phosphorus ($P_4$), Oxygen ($O_2$).
  • Compound: Pure substances that CAN be broken down into simpler substances by chemical changes. Consists of two or more types of elements chemically bonded in fixed, definite proportions.
    • Examples: Water ($H_2O$), Glucose ($C_6H_{12}O_6$), Silver Chloride ($AgCl$).
    • The physical and chemical properties of compounds differ significantly from the uncombined elements that make up the compound.
  • Mixtures:
  • Composed of two or more types of matter that can be present in varying amounts and can be separated by physical changes.
  • Homogeneous Mixture (Solution): Exhibits a uniform composition and appears visually identical throughout.
  • Heterogeneous Mixture: Has a composition that varies from point to point.

• Submicroscopic Building Blocks:

  • Atom: The smallest particle of an element that retains the properties of that element and can enter into a chemical combination.
  • Molecule: Consists of two or more atoms connected by strong forces known as chemical bonds.

• Methods for Separating Mixtures:

  • Mixtures can be separated based on the physical properties of the components:
  • Filtration: Solid substances are separated from liquids and solutions.
  • Distillation: Uses differences in the boiling points of substances to separate a homogeneous mixture into its components by boiling off the more volatile liquid.
  • Chromatography: Separates substances on the basis of differences in the ability of substances to adhere to a solid surface (e.g., dyes adhering to paper).

• Concept Verification & Practice:

  • Question 1: Solids have a _____ shape and are not appreciably _____.
  • A) definite, compressible
  • B) definite, incompressible
  • C) indefinite, compressible
  • D) indefinite, incompressible
  • E) sharp, convertible
  • Answer: A) definite, compressible
  • Question 2: A substance composed of two or more elements in a fixed, definite proportion is a(n):
  • A) homogeneous mixture.
  • B) heterogeneous mixture.
  • C) compound.
  • D) solution.
  • E) alloy.
  • Answer: C) a compound.
  • Question 3: A solution is also called a:
  • A) homogeneous mixture
  • B) heterogeneous mixture
  • C) pure mixture
  • D) compound
  • E) distilled mixture
  • Answer: A) homogeneous mixture
  • Question 4: Choose the element from the list below:
  • A) sodium chloride
  • B) water
  • C) hydrogen peroxide
  • D) helium
  • E) rust
  • Answer: D) helium
  • Question 5: A blueberry scone is an example of a:
  • A) compound.
  • B) element.
  • C) heterogeneous mixture.
  • D) homogeneous mixture.
  • Answer: C) a heterogeneous mixture.
  • Question 6: Gases and liquids share the property of _____.
  • A) compressibility
  • B) definite volume
  • C) incompressibility
  • D) indefinite shape
  • E) definite shape
  • Answer: D) indefinite shape
  • Question 7: Distillation is:
  • A) a process in which the more volatile liquid is boiled off.
  • B) dissolving a solid into a liquid.
  • C) separating a solid from a liquid by pouring off the liquid.
  • D) pouring a mixture through a filter paper to separate the solid from the liquid.
  • E) heating a mixture of two solids to fuse them together.
  • Answer: A) a process in which the more volatile liquid is boiled off.

Physical and Chemical Properties

• Physical Property:

  • A characteristic of matter that is not associated with a change in its chemical composition.
  • Examples: Density, color, hardness, melting point, boiling point, electrical conductivity.

• Chemical Property:

  • The change of one type of matter into another type (or the inability to change).
  • Examples: Flammability, toxicity, acidity, reactivity, heat of combustion.

• Physical Change:

  • A change in the state or properties of matter without any accompanying change in its chemical composition.
  • Example: Steam condensing inside a cooking pot.

• Chemical Change:

  • Always produces one or more types of matter that differ from the matter present before the change.
  • Examples: The formation of rust; the explosion of nitroglycerin.

• Extensive vs. Intensive Properties:

  • Extensive Property: Depends directly on the amount of matter present.
  • Examples: Mass, volume, heat.
  • Intensive Property: Does not depend on the amount of matter present.
  • Examples: Density, temperature.

• Concept Verification & Practice:

  • Question 1: A physical change:
  • A) occurs when iron rusts.
  • B) occurs when sugar is heated into caramel.
  • C) occurs when glucose is converted into energy within your cells.
  • D) occurs when water is evaporated.
  • E) occurs when propane is burned for heat.
  • Answer: D) occurs when water is evaporated.
  • Question 2: Which of the following represents a chemical property of hydrogen gas?
  • A) It is gaseous at room temperature.
  • B) It is less dense than air.
  • C) It reacts explosively with oxygen.
  • D) It is colorless.
  • E) It is tasteless.
  • Answer: C) It reacts explosively with oxygen.
  • Question 3: Which of the following are examples of intensive properties?
  • A) density
  • B) volume
  • C) mass
  • D) None of the above are examples of intensive properties.
  • E) All of the above are examples of intensive properties.
  • Answer: A) density
  • Question 4: Of the following, only _____ is an extensive property.
  • A) density
  • B) volume
  • C) boiling point
  • D) freezing point
  • E) temperature
  • Answer: B) volume

Measurements

• Information Provided by Measurements:

  • Measurements provide the information that forms the basis of most hypotheses, theories, and laws in chemistry.
  • Every measurement provides three items of information:
  1. The size or magnitude of the measurement (a number).
  2. A standard of comparison for the measurement (a unit).
  3. An indication of the uncertainty of the measurement.

• SI Base Units:

  • Length: meter ($m$)
  • Mass: kilogram ($kg$)
  • Time: second ($s$)
  • Temperature: kelvin ($K$)
  • Electric Current: ampere ($A$)
  • Amount of Substance: mole ($mol$)
  • Luminous Intensity: candela ($cd$)

• Temperature Scales:

  • Celsius Scale ($^\circ\text{C}$): Used most often in scientific measurements along with Kelvin. Based on properties of water:
  • Freezing point of water = $0\,^\circ\text{C}$
  • Boiling point of water = $100\,^\circ\text{C}$
  • Kelvin Scale ($K$): The official SI base unit of temperature. Based on the properties of gases:
  • Contains no negative Kelvin temperatures.
  • Lowest possible temperature is absolute zero ($0\,K$).
  • Conversion formula: $K = ^\circ\text{C} + 273.15$

• SI Unit Prefixes:

  • Femto ($f$): $10^{-15}$
  • Pico ($p$): $10^{-12}$
  • Nano ($n$): $10^{-9}$
  • Micro ($\mu$): $10^{-6}$
  • Milli ($m$): $10^{-3}$
  • Centi ($c$): $10^{-2}$
  • Deci ($d$): $10^{-1}$
  • Kilo ($k$): $10^{3}$
  • Mega ($M$): $10^{6}$
  • Giga ($G$): $10^{9}$
  • Tera ($T$): $10^{12}$

• Derived SI Units (Volume and Density):

  • Standard SI unit for Volume: cubic meter ($m^3$).
  • Other common units for volume: liter ($L$) and milliliter ($mL$).
  • $1\,dm^3 = 1\,L$
  • $1\,cm^3 = 1\,mL$
  • Density:
  • The ratio of the mass of a sample of the substance to its volume:     $\text{Density} = \frac{\text{Mass}}{\text{Volume}}$

• Worked Density Examples:

  • Example 1 (Lead vs. Gold Brick):
  • Gold density = $19.3\,g/cm^3$. A hollow brick filled with lead is tested. Lead cube edge length = $2.00\,cm$, mass = $90.7\,g$.
  • Volume of cube = $(2.00\,cm)^3 = 8.00\,cm^3$.
  • Density of lead = $\frac{90.7\,g}{8.00\,cm^3} = 11.3375\,g/cm^3 \approx 11.3\,g/cm^3$.
  • Example 2 (Volume Determination from Density):
  • Gold sample 1: Volume = $1.68\,cm^3$, mass = $32.4\,g$.
  • Gold sample 2: Mass = $34.6\,g$.
  • Density of gold = $\frac{32.4\,g}{1.68\,cm^3} = 19.2857\,g/cm^3$
  • Volume of sample 2 = $\frac{34.6\,g}{19.2857\,g/cm^3} = 1.794\,cm^3 = 1.79\,mL$.
  • Example 3 (Water Displacement Method):
  • Small metal object mass = $54\,g$.
  • Initial water level in cylinder = $40\,mL$; submerged water level = $60\,mL$.
  • Volume of object = $60\,mL - 40\,mL = 20\,mL$.
  • Density = $\frac{54\,g}{20\,mL} = 2.7\,g/mL$

• Concept Verification & Practice:

  • Question 1: What symbol is used to represent the factor $10^3$?
  • A) M
  • B) k
  • C) $\mu$
  • D) n
  • Answer: B) k
  • Question 2: Which of the following metric relationships is incorrect?
  • A) $1\,\mu L = 10^{-6}\,L$
  • B) $1\,g = 10^3\,kg$
  • C) $10^3\,mL = 1\,L$
  • D) $1\,g = 10^2\,cg$
  • E) $10\,dm = 1\,m$
  • Answer: B) $1\,g = 10^3\,kg$ (Incorrect because $1\,kg = 10^3\,g$)
  • Question 3: The outside temperature is $35\,^\circ\text{C}$, what is the temperature in $K$?
  • A) $-238\,K$
  • B) $308\,K$
  • C) $95\,K$
  • D) $31\,K$
  • E) $63\,K$
  • Calculation: $35 + 273.15 = 308.15\,K \approx 308\,K$
  • Answer: B) $308\,K$
  • Question 4: A temperature of $400.\,K$ is the same as _____ $^\circ\text{F}$.
  • A) 260
  • B) 286
  • C) 88
  • D) 103
  • E) 127
  • Calculation: $^\circ\text{C} = 400. - 273.15 = 126.85\,^\circ\text{C}$; $^\circ\text{F} = \left(126.85 \times \frac{9}{5}\right) + 32 = 228.33 + 32 = 260.33\,^\circ\text{F} \approx 260$
  • Answer: A) 260
  • Question 5: Determine the density of an object that has a mass of $149.8\,g$ and displaces $12.1\,mL$ of water when placed in a graduated cylinder.
  • A) $8.08\,g/mL$
  • B) $1.38\,g/mL$
  • C) $12.4\,g/mL$
  • D) $18.1\,g/mL$
  • E) $11.4\,g/mL$
  • Calculation: $\frac{149.8\,g}{12.1\,mL} = 12.38\,g/mL \approx 12.4\,g/mL$
  • Answer: C) $12.4\,g/mL$
  • Question 6: Determine the volume of an object that has a mass of $455.6\,g$ and a density of $19.3\,g/cm^3$
  • A) $87.9\,mL$
  • B) $42.4\,mL$
  • C) $18.5\,mL$
  • D) $23.6\,mL$
  • E) $31.2\,mL$
  • Calculation: $\frac{455.6\,g}{19.3\,g/cm^3} = 23.606\,cm^3 = 23.6\,mL$
  • Answer: D) $23.6\,mL$

Measurement Uncertainty, Accuracy, and Precision

• Exact vs. Uncertain Numbers:

  • Counting is the only type of measurement free from uncertainty, producing an exact number.
  • Numbers for defined quantities are also exact:
  • $1\,\text{foot} = 12\,\text{inches}$ (exact)
  • $1\,\text{inch} = 2.54\,\text{cm}$ (exact)
  • $1\,\text{gram} = 0.001\,\text{kg}$ (exact)
  • Quantities derived from measurements other than counting are uncertain to varying extents due to practical limitations of the measurement process.
  • When recording a measurement, standard procedure permits estimating exactly one uncertain digit.

• Rules for Significant Figures:

  • The greater the number of significant figures, the greater the certainty of the measurement.
  • Always Significant:
  • Nonzero digits.
  • Captive zeros (zeros between nonzero digits).
  • Trailing zeros to the right of the decimal place.
  • Trailing zeros when in scientific notation.
  • Not Significant:
  • Leading zeros (zeros to the left of the first nonzero digit).
  • Trailing zeros to the left of an unwritten decimal place.

• Significant Figures Practice Examples:

  • $53\,\text{cm}$: 2 significant figures.
  • $2.05 \times 10^8\,\text{m}$: 3 significant figures.
  • $86,002\,\text{J}$: 5 significant figures.
  • $9.740 \times 10^4\,\text{m/s}$: 4 significant figures.
  • $10.0613\,\text{m}^3$: 6 significant figures.
  • $0.17\,\text{g/mL}$: 2 significant figures.
  • $0.88400\,\text{s}$: 5 significant figures.
  • Commercial Product Labels:
  • $0.0055\,\text{g}$ active ingredients: 2 significant figures.
  • $12\text{ tablets}$: Exact number (counting).
  • $3\%$ hydrogen peroxide: 1 significant figure.
  • $5.5\text{ ounces}$: 2 significant figures.
  • $473\,\text{mL}$: 3 significant figures.
  • $1.75\%$ bismuth: 3 significant figures.
  • $0.001\%$ phosphoric acid: 1 significant figure.
  • $99.80\%$ inert ingredients: 4 significant figures.

• Significant Figures in Calculations:

  • Results calculated from a measurement are at least as uncertain as the measurement itself.
  • Addition and Subtraction Rule: Round the result to the same number of decimal places as the number with the least number of decimal places.
  • Multiplication and Division Rule: Round the result to the same number of digits as the number with the least number of significant figures.
  • Rounding Rules:
  • If the digit to be dropped is less than 5, round down (leave retained digit unchanged).
  • If the digit to be dropped is greater than 5, round up (increase retained digit by 1).
  • If the digit to be dropped is 5:
    • If followed by any nonzero digits, round up.
    • If it is the last digit or followed only by zeros, round up or down to yield an even value for the retained digit.

• Calculation Rounding Worked Examples:

  • Rounding to indicated significant figures:
  • $31.57$ (to two sig figs) $\rightarrow 32$
  • $8.1649$ (to three sig figs) $\rightarrow 8.16$
  • $0.051065$ (to four sig figs) $\rightarrow 0.05106$
  • $0.90275$ (to four sig figs) $\rightarrow 0.9028$
  • Addition and Subtraction:
  • $1.0023\,\text{g} + 4.383\,\text{g} = 5.3853\,\text{g} \rightarrow 5.385\,\text{g}$ (3 decimal places)
  • $486\,\text{g} - 421.23\,\text{g} = 64.77\,\text{g} \rightarrow 65\,\text{g}$ (0 decimal places)
  • Multiplication and Division:
  • $0.6238\,\text{cm} \times 6.6\,\text{cm} = 4.11708\,\text{cm}^2 \rightarrow 4.1\,\text{cm}^2$ (2 sig figs)
  • $421.23\,\text{g} / 486\,\text{mL} = 0.866728...\,\text{g/mL} \rightarrow 0.867\,\text{g/mL}$ (3 sig figs)
  • Multi-step Calculations:
  • Calculation 1: $(433.621 - 333.9) \times 11.900$
    • Subtraction: $433.621 - 333.9 = 99.721 \rightarrow 99.7$ (1 decimal place, 3 sig figs)
    • Multiplication: $99.721 \times 11.900 = 1186.6799 \rightarrow 1190$ or $1.19 \times 10^3$ (3 sig figs)
  • Calculation 2: $(249.362 + 41) / 63.498$
    • Addition: $249.362 + 41 = 290.362 \rightarrow 290$ (0 decimal places, 3 sig figs)
    • Division: $290.362 / 63.498 = 4.57277... \rightarrow 4.57$ (3 sig figs)
  • Calculation 3: $(965.43 \times 3.911) + 9413.4136$
    • Multiplication: $965.43 \times 3.911 = 3775.79673 \rightarrow 3776$ (4 sig figs, precise to units place)
    • Addition: $3775.79673 + 9413.4136 = 13189.21033 \rightarrow 13189$ (rounded to units place)

• Accuracy and Precision:

  • Precision: Measurements yield very similar results when repeated in the same manner.
  • Accuracy: Measurement yields a result that is very close to the true or accepted value.
  • Dispenser Case Study (Target volume = $296\,\text{mL}$ cough medicine):
  • Dispenser #1 values: $283.3, 284.1, 283.9, 284.0, 284.1\,\text{mL}$ $\rightarrow$ Precise, but not accurate.
  • Dispenser #2 values: $298.3, 294.2, 296.0, 297.8, 293.9\,\text{mL}$ $\rightarrow$ Neither precise nor accurate.
  • Dispenser #3 values: $296.1, 295.9, 296.1, 296.0, 296.1\,\text{mL}$ $\rightarrow$ Both precise and accurate.

• Concept Verification & Practice:

  • Question 1: A student obtains density results of $1.11\,g/mL$, $1.81\,g/mL$, $1.95\,g/mL$, and $1.75\,g/mL$ for a sugar solution (actual value = $1.75\,g/mL$). Which statement best describes her results?
  • A) Precise, but not accurate.
  • B) Accurate, but not precise.
  • C) Both precise and accurate.
  • D) Neither precise nor accurate.
  • E) Cannot be determined.
  • Answer: D) Her results are neither precise nor accurate.
  • Question 2: Which of the following numbers has the greatest number of significant figures?
  • A) 0.5070
  • B) 0.201
  • C) 418000
  • D) $6.02 \times 10^{24}$
  • Answer: A) 0.5070 (4 sig figs vs. 3 for B, C, D)
  • Question 3: How many significant figures are in the measurement, $20.300\,\text{m}$?
  • A) 3
  • B) 4
  • C) 5
  • D) 1
  • E) 2
  • Answer: C) 5
  • Question 4: Consider the numbers 23.68 and 4.12. The sum of these numbers has ____ significant figures, and the product of these numbers has ____ significant figures.
  • A) 3, 3
  • B) 4, 4
  • C) 3, 4
  • D) 4, 3
  • E) none of these
  • Calculation: Sum = $23.68 + 4.12 = 27.80$ (4 sig figs); Product = $23.68 \times 4.12 = 97.5616 \rightarrow 97.6$ (3 sig figs).
  • Answer: D) 4, 3
  • Question 5: Round $0.00222755$ to four significant figures and express the result in standard exponential notation:
  • A) $0.2228 \times 10^{-2}$
  • B) 0.002228
  • C) $2.228 \times 10^3$
  • D) $2.228 \times 10^{-3}$
  • E) $22.28 \times 10^2$
  • Answer: D) $2.228 \times 10^{-3}$

Mathematical Treatment of Measurement Results

• Dimensional Analysis:

  • Grounded on the premise that the units of quantities must be subjected to the same mathematical operations as their associated numbers.

• Dimensional Analysis Worked Examples:

  • Example 1.8 (Mass Unit Conversion):
  • Competition frisbee mass = $125\,g$. Conversion factor: $1\,oz = 28.349\,g$.
  • Calculation:       $125\,g \times \frac{1\,oz}{28.349\,g} = 4.4093\,oz \approx 4.41\,oz$
  • Example 1.10 (Fuel Economy & Expense Calculation):
  • Distance from Philadelphia to Atlanta = $1250\,km$. Gas used = $213\,L$
  • (a) Fuel economy in miles per gallon (mpg):
    • Convert distance: $1250\,km \times \frac{0.621371\,mi}{1\,km} = 776.71\,mi$
    • Convert volume: $213\,L \times \frac{1\,gal}{3.78541\,L} = 56.268\,gal$
    • Calculate mpg: $\frac{776.71\,mi}{56.268\,gal} = 13.804\,mpg \approx 13.8\,mpg$
  • (b) Fuel cost for trip at $\$3.80$ per gallon:       $\text{Cost} = 56.268\,gal \times \frac{\$3.80}{1\,gal} = \$213.82 \approx \$214$
  • Pressure Conversion Example:
  • Pressure = $125\,lb/m^2$. Convert to $kg/cm^2$.
  • Relationships: $1\,lb = 0.453592\,kg$; $1\,m^2 = 10,000\,cm^3$
  • Calculation:       $\frac{125\,lb}{1\,m^2} \times \frac{0.453592\,kg}{1\,lb} \times \frac{1\,m^2}{10000\,cm^2} = 0.0056699\,kg/cm^2 = 5.67 \times 10^{-3}\,kg/cm^2$

• Concept Verification & Practice:

  • Question 1: If an object has a density of $8.65\,g/cm^3$, what is its density in units of $kg/m^3$?
  • A) $8.65 \times 10^{-3}\,kg/m^3$
  • B) $8.65 \times 10^{-7}\,kg/m^3$
  • C) $8.65 \times 10^3\,kg/m^3$
  • D) $8.65 \times 10^1\,kg/m^3$
  • E) $8.65 \times 10^{-1}\,kg/m^3$
  • Calculation: $\frac{8.65\,g}{1\,cm^3} \times \frac{1\,kg}{1000\,g} \times \frac{10^6\,cm^3}{1\,m^3} = 8.65 \times 10^3\,kg/m^3$
  • Answer: C) $8.65 \times 10^3\,kg/m^3$
  • Question 2: The mass of a single zinc atom is $1.086 \times 10^{-22}\,g$. This is the same mass as:
  • A) $1.086 \times 10^{-16}\,mg$
  • B) $1.086 \times 10^{-25}\,kg$
  • C) $1.086 \times 10^{-28}\,\mu g$
  • D) $1.086 \times 10^{-31}\,ng$
  • Calculation: $1.086 \times 10^{-22}\,g \times \frac{1\,kg}{1000\,g} = 1.086 \times 10^{-25}\,kg$
  • Answer: B) $1.086 \times 10^{-25}\,kg$
  • Question 3: Which of the following volumes is equal to $40\,mL$?
  • A) $40\,cm^3$
  • B) $40\,dm^3$
  • C) $0.40\,L$
  • D) $0.00040\,kL$
  • Answer: A) $40\,cm^3$
  • Question 4: The recommended adult dose of Elixophyllin is $6.00\,mg/kg$ of body mass. Calculate the dose in milligrams for a $134-lb$ person.
  • A) 10.1
  • B) 1773
  • C) 13.2
  • D) 365
  • E) $3.6 \times 10^5$
  • Calculation:       $\text{Mass in kg} = 134\,lb \times \frac{1\,kg}{2.20462\,lb} = 60.781\,kg$$\text{Dose in mg} = 60.781\,kg \times 6.00\,mg/kg = 364.68\,mg \approx 365\,mg$
  • Answer: D) 365