General Chemistry I - Atoms, Molecules, and Measurement

Atoms and Molecules

• Chemistry is the science of studying the behavior of matter by studying atoms and molecules.
• The properties of matter depend on the properties of molecules and atoms.
• The properties of water molecules determine how water behaves, and the properties of sugar molecules determine how sugar behaves.
• Examples of representations of water molecules include the molecular formula H2O, Lewis structure, electronic geometry, VSEPR molecular shape, and polarity affecting electron density and molecular interactions, which predict properties.

Atoms and Molecules

• Atoms are submicroscopic particles and the fundamental building blocks of ordinary matter.
• Free atoms are rare; they usually bind together in specific arrangements to form molecules.
• A molecule of water contains two hydrogen atoms and an oxygen atom held together by a chemical bond.

Atoms and Molecules

• Small differences in atoms and molecules can result in large differences in the substances they compose.
• Graphite and diamond are both made of carbon, but their atoms are arranged differently.
• In graphite, carbon atoms are arranged in sheets, while in diamond, they are bound in a three-dimensional structure.

The Scientific Method

• The scientific method uses an empirical approach based on observation and experiment.
• Observations are also known as data, which lead to the formulation of a hypothesis.
• Antoine Lavoisier (1743–1794) observed no change in the total mass of material within a container during combustion.

The Scientific Method

• A hypothesis is a tentative interpretation or explanation of observations.
• Lavoisier hypothesized that when a substance burns, it combines with a component of air.
• A good hypothesis is falsifiable, meaning experiments can either support or disprove it.
• If an experiment proves a hypothesis wrong, it must be modified or discarded.

The Scientific Method

• A law is a brief statement summarizing past observations and predicting future ones; it can be tested with experiments.
• Law of conservation of mass: “In a chemical reaction, matter is neither created nor destroyed.”
• Scientific laws cannot be violated, unlike civil laws.

The Scientific Method

• A theory provides a general explanation for the characteristics and behavior of nature (e.g., Dalton’s atomic theory).
• A scientific theory models how nature is and tries to explain why nature acts a certain way.
• Theories are validated by experiments but can never be conclusively proven due to the potential for new observations to reveal flaws.

The Classification of Matter

• Matter is anything that occupies space and has mass.
• Examples of matter include textbooks, desks, chairs, and bodies.
• Matter can be classified by its state (physical form) and composition (basic components).
• The state of matter changes from solid to liquid to gas with increasing temperature.

The Classification of Matter

• In solid matter, atoms or molecules pack closely in fixed locations, vibrating but not moving past each other.
• Solids have a fixed volume and rigid shape; examples include ice, aluminum, and diamond.
• Solid matter can be crystalline (atoms in long-range, repeating order, e.g., table salt and diamond) or amorphous (no long-range order, e.g., glass and plastic).

The Classification of Matter

• In liquid matter, atoms or molecules pack closely but can move relative to each other.
• Liquids have a fixed volume but not a fixed shape, allowing them to flow and assume the shape of their container.
• Examples include water, alcohol, and gasoline at room temperature.
• In gaseous matter, atoms or molecules have a lot of space between them and can move freely, making gases compressible.

The Classification of Matter

• Matter can be classified by its composition into elements, compounds, and mixtures.

The Classification of Matter

• A pure substance has only one component, and its composition is invariant.
• A mixture is composed of two or more components in varying proportions.
• A compound can be separated into simpler substances (e.g., water, sugar, butane, acetone).
• An element cannot be separated into simpler substances (e.g., gold, iron, oxygen).
• Heterogeneous mixtures have identifiable and/or unevenly distributed components (e.g., some salad dressings, seawater with sand).
• Homogeneous mixtures are uniformly distributed and not easily identified (e.g., coffee, tea, mayo, seawater).

The Classification of Matter

• Example: Identifying a pure substance from images of atoms of different elements.

Separating Mixtures

• Mixtures are separable because their components have different physical or chemical properties.
• A mixture of sand and water can be separated by decanting (pouring off the water).

Separating Mixtures

• A mixture of an insoluble solid and a liquid can be separated by filtration, using filter paper in a funnel.
• Example: Sand filters at water treatment plants.

Separating Mixtures

• Distillation involves heating a mixture of liquids with different boiling points, where the most volatile components boil first and are then cooled and collected as a pure liquid.

Physical and Chemical Changes

• Physical changes alter the state or appearance of a substance without changing its composition.
• The atoms or molecules composing the substance do not change their identity.
• Example: Melting metal, represented as $Sn(s) \rightarrow Sn(l)$.

Physical and Chemical Changes

• Chemical changes alter the composition of matter.
• Atoms rearrange, transforming the original substances into different substances.
• Example: Rusting of iron and the reaction $Pb(NO<em>3)</em>2(aq) + 2NaCl(aq) \rightarrow PbCl<em>2(s) + 2NaNO</em>3(aq)$.

Physical and Chemical Properties

• A physical property is displayed by a substance without changing its composition (e.g., smell of gasoline, odor, taste, color, melting point, boiling point, density).
• A chemical property is displayed only by changing its composition via a chemical change (or reaction) (e.g., flammability of gasoline, corrosiveness, acidity, toxicity).
• An intensive property does not depend on the amount of substance (e.g., boiling point, color, density, temperature).
• An extensive property depends on the amount of substance (e.g., weight, volume, moles of substance, entropy).

Energy: A Currency of Chemistry

• Energy is the capacity to do work.
• Work is defined as the action of a force through a distance (F=ma).
• Doing work involves pushing a box across the floor or pedaling a bicycle.

Energy

• Kinetic energy is the energy associated with the motion of an object.
• Potential energy is the energy associated with the position or composition of an object.
• Chemical energy (stored in bonds) is a form of potential energy.
• Burning methane releases thermal energy, forming more stable products.
• Thermal energy is the energy associated with the temperature of an object and is a type of kinetic energy arising from the motion of individual atoms or molecules.

Energy

• Energy is always conserved in a physical or chemical change (law of conservation of energy).
• Systems with high potential energy tend to change in a direction that lowers their potential energy, releasing energy into the surroundings.

The Units of Measurement

• Units are standard quantities used to specify measurements.
• Scientists use the International System of Units (SI), based on the metric system.
• Selected SI base units include:
  • Length: Meter (m)
  • Mass: Kilogram (kg)
  • Time: Second (s)
  • Temperature: Kelvin (K)
  • Amount of substance: Mole (mol)
  • Electric current: Ampere (A)
  • Luminous intensity: Candela (cd)

The Units of Measurement

• The meter was originally defined as 1/10,000,000 of the distance from the equator to the North Pole (through Paris).
• Now defined as the distance light travels through a vacuum in 1/299,792,458 s (c = 299,792,458 m/s).
• The second is defined as the duration of 9,192,631,770 periods of radiation emitted from a certain transition in a 133Cs atom.
• $h = 6.62607015 \times 10^{-34} kg \cdot m^2 \cdot s^{-1}$

The Units of Measurement

• Mass measures the quantity of matter within an object; the SI unit is the kilogram (kg).
• Weight measures the gravitational pull on matter; weight can differ from mass.
• The kelvin (K) is the SI unit of temperature, measuring the average kinetic energy of atoms or molecules.
• Temperature determines the direction of thermal energy transfer (heat).
• The Kelvin scale (absolute scale) assigns 0 K (absolute zero) to −273.15 °C.
• $h = 6.62607015 \times 10^{-34} kg \cdot m^2 \cdot s^{-1}$

A Measure of Temperature

• The Fahrenheit degree is five-ninths (5/9 or 1.8) the size of a Celsius degree.
• The Celsius degree and the kelvin degree are the same size (1 K = 1 °C).
• Temperature scale conversion formulas:
  • $^{\circ}F = (1.8 \times ^{\circ}C) + 32$
  • $^{\circ}C = (^{\circ}F - 32) \times \frac{5}{9}$
  • $K = ^{\circ}C + 273.15$

A Measure of Temperature

• Example 01.01: Convert typical human body temperature (36.6 °C) to Fahrenheit and kelvins.
• Example 01.02: Convert the melting point of tungsten (6,192 °F) to kelvins.

Prefix Multipliers

• The International System of Units uses prefix multipliers with standard units to change the value by powers of 10.
• Prefixes and their multipliers include:
  • exa (E): $10^{18}$
  • peta (P): $10^{15}$
  • tera (T): $10^{12}$
  • giga (G): $10^9$
  • mega (M): $10^6$
  • kilo (k): $10^3$
  • deci (d): $10^{-1}$
  • centi (c): $10^{-2}$
  • milli (m): $10^{-3}$
  • micro (µ): $10^{-6}$
  • nano (n): $10^{-9}$
  • pico (p): $10^{-12}$
  • femto (f): $10^{-15}$
  • atto (a): $10^{-18}$

Derived Units

• A derived unit is a combination of other units.
• Volume: typically $cm^3$ or calculated as $V = L \times W \times H$.
• Density: ratio of mass to volume (e.g., g/mL, lbs/gal).
• Other combined units: speed (distance/time), flow (volume/time), price/unit.
• Energy: $1 J = kg \cdot m^2 \cdot s^{-2}$, Pressure: $1 Pa = kg \cdot m^{-1} \cdot s^{-2}$, Voltage: $V = J/C = kg \cdot m^2 \cdot s^{-3} \cdot A^{-1}$.

Significant Figures

• Scientific measurements are reported with every digit certain except the last, which is estimated.
• Significant figures indicate precision; precision depends on the instrument used.
• Preserve precision during calculations using significant figures.
• Rule of thumb: Read the device to 1/5th of the smallest unit.

Significant Figures

• The greater the number of significant figures, the greater the certainty of the measurement.
• Rules for significant figures:
  • All nonzero digits are significant (e.g., 1356.45, 127, 0.005360).
  • Zeroes between nonzero digits are significant (e.g., 120.03, 0.0503, 102.030).
  • Leading zeroes are not significant (e.g., 0.000350, 0.00721, 0.0684).
  • Trailing zeroes after a decimal point are always significant (e.g., 1.000, 1300.00, 170.002300).
  • Trailing zeroes before a decimal point (after a nonzero number) are always significant (e.g., 1200., 173000., 20.).
  • Trailing zeroes before an implied decimal point are ambiguous; use scientific notation to avoid ambiguity (e.g., 1200, 173000).

Significant Figures

• To avoid ambiguity with trailing zeroes before an implied decimal point, use scientific notation.
  • 173000 (3 sig. figs.). Tailing zeros are consider insignificant unless there is a decimal point at the end.
  • 173000. (6 sig. figs.) dec. pt.
• But it can be: 173000 (4 s.f.), 173000 (5 s.f.)
• Examples:
  • 173000 (4 s.f.) = $1.730 \times 10^5$
  • 173000 (5 s.f.) = $1.7300 \times 10^5$
  • 173000 (6 s.f.) = $1.73000 \times 10^5$

Scientific Notation

• Scientific notation expresses very large or very small numbers using only significant figures and an exponent.
• Format: $first \ nonzero \ digit \cdot (decimal \ point) \cdot remaining \ sig. \ figs \times 10^{multiplier}$.
• Examples:
  • 175689000 = $1.75689 \times 10^8$
  • 0.00023 = $2.3 \times 10^{-4}$
  • 1700.3 = $1.7003 \times 10^3$
• Numbers less than 1 have a negative exponent.

Scientific Notation

• Using scientific notation on calculators: (e.g., 6.0221x1023 can be entered as 6.0221E23).
• Examples:
  • $1.2 \times 10^2 + 2.5 \times 10^5 = 250120$
  • $3.70 \times 10^2 \times 1.50 \times 10^{-5} = 5.55 \times 10^{-3}$
  • $2.33 \times 10^2 \div 1.25 \times 10^2 = 1.864$

Exact Numbers

• Exact numbers have an unlimited number of significant figures.
• Include accurate counting of discrete objects, defined quantities, and integral numbers in equations.
• Conversion factors can be defined (exact) or measured values (significant figures).
• Examples of exact numbers:
  • 1 m = 100 cm
  • 1 h = 60 min = 3600 s
  • 1 yd = 3 ft = 12 in
  • 1 dozen = 12
  • 100 % (def)
  • 17 students
• Examples of counted (measured) values:
  • $c = 2.99792 \times 10^8 m/s$
  • 1 lb = 454 g
  • 36.6°C
  • 1 yr = 365 days
  • $1.023 g/cm^3$
  • 34.3214 g

Rules for Rounding

• General rule: Identify the place value to round to, and then:
  • Round up if the next digit is >5.
  • Leave unchanged if the next digit is <5.
  • If the next digit = 5…, apply the even/odd rule.
• Even/Odd Rule: If 5 is preceded by an even number, drop it; if by an odd number, round to the next digit.
  • 12.735 rounds to 12.74 (odd)
  • 11.085 rounds to 11.08 (even)

Significant Figures: Rules for Calculations

• Addition and Subtraction Rule: The result carries the same number of decimal places as the quantity with the fewest decimal places.
  • Example: 12.3744 + 1.45321 + 1285.24 = 1299.06761 (rounds to 1299.07 considering sig figs)
• Multiplication and Division Rule: The result carries the same number of significant figures as the factor with the fewest significant figures.
  • Example: 7.04536 ÷ 2.03 = 3.470620 (rounds to 3.47).
  • Example: 1024 x 2.8 = 2867.2 (rounds to 2900 or $2.9 \times 10^3$
• Antilogs and Logs Rule: The amount of sig. figs with respect to mantissa
• Example: $10^{-1.345} = 0.0452$, (mantissa : 3 s.f. so the answer need to have 3 s.f.)
• Example: $Ln \; 2.347 = 0.8531$, (4 s.f. so the answer need to have 4 s.f.)

Rounding in Multistep Calculations

• To avoid rounding errors, round only the final answer; do not round intermediate steps.
• If writing down intermediate answers, underline the least significant digit to keep track.
• Example 01.03: Determine the correct number of significant figures in the final answer after calculations $\frac{23 \ln 3.45}{(1.3412-1.21)0.0211} \cdot \frac{6.0221 \times 10^{23}}{8.314}$

Precision and Accuracy

• Accuracy refers to how close the measured value is to the actual value.
• Precision refers to how close a series of measurements are to one another (reproducibility).

Examples

• Example 01.04: Determine the number of significant figures in the measured value 73.150 (Answer: 5).
• Example 01.05: Calculate 352.94 – 36.0342 and report the best answer (Answer: 316.91).

Solving Chemical Problems

• Many problems are unit conversion problems.
• Using units as a guide is called dimensional analysis.
• Always include units in calculations; multiply, divide, and cancel them like algebraic quantities.
• Example:
  • $\frac{21.52 g}{1 mol H<em>2O} \times 1.19456 mol \; H</em>2O = 25.7 g$ $\rightarrow$ $\frac{mol \; H<em>2O}{g} \times g = mol \; H</em>2O$

Solving Chemical Problems

• $1 in = 2.54 cm$
• Dimensional Analysis: A unit equation states two equivalent quantities.
• A conversion factor is a fractional quantity of a unit equation with the units converting from on the bottom and the units converting to on the top.
• General form: Information given × conversion factor(s) = information sought.
• Formula : $Given \; unit \times \frac{desired \; unit}{given \; unit} = desired \; unit$
• Example: Convert 78.6 in to cm.
• $78.6 \; in \times \frac{2.54 \; cm}{1 \; in} = 200 \; cm$
• Other conversion factors:
  • 1 m = 100 cm
  • 1 cm = 10 mm
  • 1 L = 1000 mL

Solving Chemical Problems

• Identify the starting point (given information) and the end point (what must be found).
• Devise a conceptual plan to move from the starting point to the end point using known information.
• Steps: sort information, strategize via conceptual plan, solve, and check the answer.
• Example 01.06: How many cents are in $5.00?
• Example 01.07: How many inches in 3.50 yrd?

Examples

• Example 01.08: Convert the width of an American football field (53.33 yrd) to nm.

Examples

• Example 01.09: Convert the maximum speed of a TIE Fighter (333 m/s) to mph (1 mile = 1.609 km).

Examples

• Example 01.10: Calculate the volume in liters of a 91 in × 24 in × 32 in Han Solo replica in carbonite.

Examples

• Example 01.11: Convert a room area of 90.0 $ft^2$ to square inches.
• Example 01.12: Calculate the volume in liters of a cylinder with a radius of 15.50 ft and a height of 8.5 yd.

Interpreting Data

• Analyzing results from water decomposition experiments:
  • The sum of the masses of oxygen and hydrogen always equals the mass of the water sample.
  • The ratio of oxygen mass to hydrogen mass is approximately 8:1, with small variations due to experimental error.

Interpreting Graphs

• Examine the x and y axes to understand their representations and numerical ranges.
• Note if the y-axis begins at a value other than zero to highlight changes.
• Understand how the graph's appearance changes if the y-axis starts at zero.
• Recognize non-constant increases and changes in the rate of increase (slope of the line).
• Example 01.10: Determine the average rate of increase in carbon dioxide concentration between 1880 and 1920.