Chapter 1: Matter, Measurement, and Problem Solving
Chapter 1: Matter, Measurement, and Problem Solving
1.1 Matter and Its Properties
Definition of Matter: Anything that occupies space (i.e., volume) and has mass.
Properties of Matter: Determined by the properties of the atoms and molecules within the matter.
Example: Water molecules (H2O) and hydrogen peroxide molecules (H2O_2) consist of the same elements (hydrogen and oxygen) but in different proportions and arrangements, leading to distinct properties.
Core Definitions
Atom:
The smallest particle of an element.
Retains its unique chemical characteristics.
Considered the building blocks of all matter.
Molecule:
A collection of two or more atoms chemically bonded together.
Atoms are present in fixed proportions and a fixed arrangement.
Chemistry: The science that seeks to understand the behavior of matter by studying the behavior of atoms and molecules.
1.2 The Scientific Approach
Observations: The starting point, often leading to questions.
Hypothesis: A tentative explanation for a set of observations. It is testable and falsifiable.
Experiments: Designed to test hypotheses, observations, laws, or theories.
Scientific Law:
A statement that summarizes past observations and predicts future ones.
Describes what happens but does not explain why it happens.
Can be confirmed or revised through experiments.
Scientific Theory:
A general explanation of widely observed phenomena that has been extensively tested.
Explains why phenomena occur.
Can be confirmed or revised through experiments.
Example: Law vs. Theory
Law of Conservation of Mass (Lavoisier):
What: In a chemical reaction, matter is neither created nor destroyed. The total mass stays constant.
Dalton's Atomic Theory:
Why: Matter is composed of small, indestructible particles called atoms. During a chemical reaction, these particles are merely rearranged (not created or destroyed). This rearrangement explains why the total mass remains constant.
Practice Question Review (Slide 6)
Incorrect Statement Analysis: The statement "Once a scientific theory has been proven, it cannot be modified" is incorrect.
Scientific theories are extensively tested and highly supported explanations, but they are not immutable. As new evidence emerges or new scientific approaches develop, theories can be refined, modified, or even replaced (though this is rare for well-established theories).
1.3 States of Matter
Solid:
Fixed shape and fixed volume.
Particles are tightly packed in a fixed arrangement.
Liquid:
Fixed volume but changeable shape (takes the shape of its container).
Particles are close together but can move past one another.
Gas:
Both shape and volume are variable (expands to fill its container).
Particles are far apart and move randomly and rapidly.
Important Note: Changes between states of matter (e.g., melting, boiling) do not involve breaking chemical bonds; they are physical changes.
Types of Solids
Crystalline Solid: Atoms or molecules are arranged in patterns with a long-range, repeating order.
Examples: Diamond (carbon), salt (NaCl), sugar (C{12}H{22}O_{11}).
Amorphous Solid: No long-range, repeating order of its atoms or molecules.
Examples: Glass, most plastics.
1.4 Classes of Matter
1. Pure Substance
Consists of only one type of chemical substance.
Has a fixed composition and properties.
Element: The simplest form of matter; composed of only one kind of atom (represented by a single symbol from the Periodic Table).
Examples: Helium (He), Copper (Cu).
Compound: Two or more elements chemically bonded together in a fixed composition and fixed arrangement.
Examples: Water (H2O), Methane (CH4), Glucose (C6H{12}O_6).
2. Mixture
Consists of two or more chemicals that are physically mixed but not chemically bonded.
Has a variable composition.
Can be separated by physical means.
Homogeneous Mixture: Uniform composition throughout (appears as a single substance).
Examples: Pure water (in the context of being a pure substance, not a mixture, slide 10 example seems to contradict, but it's important to distinguish pure water as a compound from, say, salt water which is a homogeneous mixture), tea with sugar, black coffee, air in a room (assuming uniform composition).
Heterogeneous Mixture: Non-uniform composition; visibly distinguishable components.
Examples: Wet sand, a pencil (wood, graphite, rubber, metal), tea with ice cubes (if components are visibly distinct).
Flowchart for Classifying Matter (Visual Aid from Slide 10)
Matter
Variable Composition?
No ightarrow Pure Substance
Decomposable (separable into simpler substances)?
No
ightarrow Element (e.g., Helium)Yes
ightarrow Compound (e.g., Pure water)
Yes ightarrow Mixture
Uniform Throughout?
No
ightarrow Heterogeneous (e.g., Wet sand)Yes
ightarrow Homogeneous (e.g., Tea with sugar)
Separating Mixtures
Methods are based on differences in physical properties of the components.
Key Principle: No chemical bonds are broken during separation.
Techniques:
Gravity Filtration: Separates an insoluble solid from a liquid (e.g., sand from water) based on particle size and solubility.
Mixture poured through filter paper; solid is trapped, liquid (filtrate) passes through.
Distillation: Separates a mixture of liquids (or a dissolved solid from a liquid) based on differences in boiling points.
The mixture is heated, the component with the lower boiling point vaporizes first, the vapor is cooled and condensed into a purer liquid.
Paper Chromatography: Separates components based on their differential preference for a stationary phase (e.g., paper) versus a mobile phase (e.g., solvent).
Practice Question Review (Slide 14)
Incorrect Classification: "The air in a room = heterogeneous mixture" is incorrect.
Air is a mixture of gases (nitrogen, oxygen, argon, etc.), and these gases are uniformly mixed at a given atmospheric pressure and temperature without distinct layers or visible boundaries. Therefore, air is a homogeneous mixture.
1.5 Physical vs. Chemical Properties
Physical Properties: Characteristics that can be observed or measured without changing the chemical identity of the substance (no chemical bonds broken).
Examples: Hardness, color, melting point, boiling point, density, solubility, odor, state of matter.
Chemical Properties: The tendency of a substance to undergo a chemical reaction with another substance, resulting in the formation of new substances (involves the breaking and/or forming of chemical bonds).
Examples: Flammability (reacts with oxygen to produce heat and light), reactivity with acids/bases, oxidation (e.g., iron reacting with oxygen to form rust).
Practice Identifying Properties (Slide 16)
Description of Property | Category |
|---|---|
Diamond is a very hard substance. | Physical |
Mercury is a liquid at room temperature. | Physical |
Unlike silver, gold does not tarnish. | Chemical |
Glass shatters when dropped. | Physical |
Aspirin can be used to treat headaches and pain. | Chemical |
Perfume has a pleasant odor. | Physical |
Gasoline is flammable. | Chemical |
Salt dissolves in water. | Physical |
1.6 Energy
Energy: The capacity to do work.
Work: Force acting through distance.
ext{Work} = ext{Force} imes ext{Distance}
Types of Energy
Kinetic Energy: Energy associated with motion.
Any object in motion possesses kinetic energy.
Thermal Energy: Energy associated with the temperature of an object. It represents the total kinetic energy of all the random motions of particles (atoms and molecules) within a substance.
Potential Energy: Energy associated with position or composition.
Positional Potential Energy: Energy due to an object's height or position in a force field (e.g., a weight held high above the ground).
Compositional/Chemical Potential Energy: Energy stored in the chemical bonds of a substance (e.g., in gasoline, food, or a charged battery).
The Law of Conservation of Energy (First Law of Thermodynamics)
Statement: Energy can be converted from one form to another, but it cannot be created or destroyed. The total amount of energy in a closed system remains constant.
Examples:
A weight on top of a building has high potential energy. When dropped, its potential energy is converted into kinetic energy. When it hits the ground, this kinetic energy is converted into thermal and sound energy.
Molecules in gasoline initially have high chemical potential energy. When burned in an engine, this potential energy is converted to thermal energy and kinetic energy, which causes the car to move.
Important Ideas About Energy
Energy is always conserved in any physical or chemical change.
Systems with high potential energy tend to change in a direction that lowers their potential energy, releasing energy into the surroundings. This principle drives many natural processes and chemical reactions.
1.7 Measurements and Units
Importance: Accurate measurements are essential for reliable scientific experimentation and data sharing.
Standardized Units: The use of internationally agreed-upon units (SI units) is crucial for consistency.
Error Analysis: Proper analysis of experimental measurements and their associated errors is fundamental to scientific rigor.
SI Base Units
Quantity | Unit Name | Unit Symbol |
|---|---|---|
Length | Meter | m |
Mass | Kilogram | kg |
Time | Second | s |
Temperature | Kelvin | K |
Energy | Joule | J |
Amount of Substance | Mole | mol |
Electrical Current | Ampere | A |
Luminosity | Candela | cd |
Prefixes for SI Units
Prefixes are used to denote multiples or submultiples of base units, based on powers of 10.
Multiplier | Name | Symbol | Exponential |
|---|---|---|---|
10^{12} | tera | T | |
10^9 | giga | G | |
10^6 | mega | M | |
10^3 | kilo | k | |
10^{-1} | deci | d | |
10^{-2} | centi | c | |
10^{-3} | milli | m | |
10^{-6} | micro | \mu | |
10^{-9} | nano | n | |
10^{-12} | pico | p |
Temperature Scales
Based on Water: Our common temperature scales (Fahrenheit, Celsius) use the freezing and boiling points of water as reference points.
Absolute Zero: The theoretical temperature at which all particle motion stops (0 ext{ K} or -273.15 ext{ °C} or -459.67 ext{ °F}).
Changing Temperature Scales (Linear Relationships)
Celsius (TC) to Fahrenheit (TF):
TF = rac{9}{5} TC + 32 or TF = 1.8 TC + 32
Derivation: Using freezing point (0 ext{ °C}, 32 ext{ °F}) and boiling point (100 ext{ °C}, 212 ext{ °F}).
Slope (m) = rac{212 - 32}{100 - 0} = rac{180}{100} = 1.8
Intercept (b) = 32
Celsius (TC) to Kelvin (TK):
TK = TC + 273.15
Practice Question Review (Slide 25)
Incorrect Statement: "Absolute zero is defined as the temperature at which water freezes" is incorrect.
Absolute zero is the theoretical temperature where all particle motion ceases (0 ext{ K}). Water freezes at 0 ext{ °C} (273.15 ext{ K}), which is well above absolute zero.
English-Metric Conversions (Important Equivalencies)
Length: 1 ext{ in} = 2.54 ext{ cm} (exact conversion)
Mass: 1 ext{ lb} = 453.592 ext{ g}
Volume: 1 ext{ gal} = 3.7854 ext{ L}
Definition: 1 ext{ mL} = 1 ext{ cm}^3
Derived Units: Volume & Density
Volume: A unit of length cubed (e.g., m^3, cm^3).
Density (d): The mass of a substance per unit volume of the substance.
Formula: d = rac{ ext{mass}}{ ext{volume}} = rac{m}{V}
Density can be used as a conversion factor between mass and volume.
Extensive vs. Intensive Properties
Extensive Property: A characteristic that varies with the amount of substance.
Examples: Length, mass, volume.
Intensive Property: A characteristic that is independent of the amount of substance.
Examples: Color, density, melting point, boiling point, temperature.
1.8 Precision and Accuracy
Precision: The repeatability of a set of measurements and the extent to which they agree with each other.
Accuracy: The agreement between an experimental value and the true (or accepted) value.
Visual Examples (from Slide 29):
Student A: Inaccurate and Imprecise (measurements scattered, far from true value).
Student B: Inaccurate but Precise (measurements clustered together, but far from true value).
Student C: Accurate and Precise (measurements clustered together, close to true value).
Sources of Error
Random Errors:
Result from the limitations of reading the scale of an instrument (e.g., fluctuation in the last estimated digit).
Associated with precision.
Can be minimized by taking multiple measurements and averaging.
Systematic Errors:
Result from faulty instrumentation (e.g., a thermometer that always reads 2 ext{ °C} too low, an improperly calibrated balance) or flawed experimental design (e.g., consistently losing some precipitate during filtration).
Associated with accuracy.
Affect all measurements in the same way (consistently high or consistently low).
1.9 Significant Figures in Measurements
Uncertainty in Measurements: Every measurement has some degree of uncertainty (or error).
The last digit recorded in a measurement is always estimated and is considered uncertain (or doubtful).
When reporting measurements, include all certain digits plus one uncertain (estimated) digit.
Example: For a meniscus between 4.5 and 4.6 ext{ mL}, an estimate like 4.56 ext{ mL} would be reported, where the '6' is the uncertain digit.
Rules for Counting Significant Figures (SF)
Nonzero Integers: All nonzero digits are significant.
Example: 4.5 ext{ g} (2 SF), 122.35 ext{ m} (5 SF)
Zeros:
Leading Zeros: Zeros to the left of the first nonzero digit are not significant (they only locate the decimal point).
Example: 0.0004 ext{ lb} (1 SF), 0.075 ext{ m} (2 SF)
Interior Zeros: Zeros between nonzero digits are significant.
Example: 205 ext{ m} (3 SF), 5.082 ext{ kg} (4 SF)
Trailing Zeros:
Zeros at the end of a number with a decimal point are significant.
Example: 50. ext{ L} (2 SF), 25.0 ext{ °C} (3 SF), 16.00 ext{ g} (4 SF)
Zeros at the end of a number without a decimal point are not significant (ambiguous, assume they are placeholders unless specified).
Example: 850,000 ext{ m} (2 SF), 1,250,000 ext{ g} (3 SF)
Scientific Notation: All digits in the coefficient of a number written in scientific notation are significant.
Example: 4.0 imes 10^5 ext{ m} (2 SF), 5.70 imes 10^{-3} ext{ g} (3 SF)
Practice Question Review (Slide 34)
Incorrect Labeled SF: "100 ext{ lb} (3 SF)" is incorrect.
According to the rules, trailing zeros in a number without a decimal point are generally not significant. Thus, 100 ext{ lb} has only 1 significant figure (the '1'). To make it 3 SF, it would have to be written as 100. ext{ lb}. If it were intended to specify precision, it would be written in scientific notation such as 1.00 imes 10^2 ext{ lb}. The other options are correctly labeled.
Exact Numbers
Definition: Exact numbers have an infinite number of significant figures.
Sources:
Definitions (e.g., 1 ext{ inch} = 2.54 ext{ cm} exactly, 1 ext{ km} = 1000 ext{ m} exactly, 1 ext{ dozen} = 12 ext{ items} exactly, 1 ext{ hour} = 60 ext{ minutes} exactly).
Counting individual items (e.g., 1 ext{ H}_2 ext{O} molecule = 2 ext{ H} atoms).
Significant Figures: Rules for Arithmetic Operations
Addition and Subtraction:
Round off the answer to the first column (from left to right) that has an uncertain digit (i.e., the largest absolute error).
Example:
226 g (uncertain digit in ones place) 33.5 g (uncertain digit in tenths place) 589 g (uncertain digit in ones place) 11.88 g (uncertain digit in hundredths place) --------- 860.38 g (raw sum)
The least precise measurement is in the ones place (from 226 ext{ g} and 589 ext{ g}). Therefore, the sum is rounded to the ones place:
860.38 ext{ g}
ightarrow 860 ext{ g} ext{ or } 8.60 imes 10^2 ext{ g}
Multiplication and Division:
Round off the answer to the same number of significant figures as the factor with the smallest number of significant figures.
Example: What is the volume of a cube that is 34.49 ext{ cm} long, 23.0 ext{ cm} wide, & 15 ext{ cm} high?
Length = 34.49 ext{ cm} (4 SF)
Width = 23.0 ext{ cm} (3 SF)
Height = 15 ext{ cm} (2 SF)
ext{Volume} = ext{Length} imes ext{Width} imes ext{Height}
ext{Volume} = 34.49 ext{ cm} imes 23.0 ext{ cm} imes 15 ext{ cm} = 11,899.05 ext{ cm}^3
Since 15 ext{ cm} has the fewest SF (2 SF), the volume must be rounded to 2 significant figures:
11,899.05 ext{ cm}^3
ightarrow 12,000 ext{ cm}^3 ext{ or } 1.2 imes 10^4 ext{ cm}^3
Practice Calculations (Slide 38)
A. Addition: 8.6 ext{ cm} + 3.3 ext{ cm} + 5.1 ext{ cm} = 17.0 ext{ cm}
All numbers have uncertainty in the tenths place. The result maintains this precision.
B. Subtraction: 104.13 ext{ g} - 103.92 ext{ g} = 0.21 ext{ g}
Both numbers have uncertainty in the hundredths place. The result maintains this precision.
C. Multiplication: 15.68 ext{ g} imes 2.94 imes 10^3 ext{ g} = 4.61 imes 10^4 ext{ g}^2
15.68 (4 SF), 2.94 imes 10^3 (3 SF). The answer is rounded to 3 SF.
D. Division: rac{1.23 ext{ g} - 0.524 ext{ g}}{0.3452 ext{ mL}}
First, perform subtraction in the numerator: 1.23 ext{ g} - 0.524 ext{ g} = 0.71 ext{ g}
(Rounded to the hundredths place, as 1.23 is precise to hundredths).
Now, perform division: rac{0.71 ext{ g}}{0.3452 ext{ mL}} = 2.0567… rac{ ext{g}}{ ext{mL}}
0.71 (2 SF), 0.3452 (4 SF). The answer is rounded to 2 SF.
2.1 rac{ ext{g}}{ ext{mL}}
1.10 Dimensional Analysis (Units Conversion)
Conversion Factor: A fraction expressing an accepted fixed relationship where the numerator and denominator are equivalent quantities but in different units.
Example: 1 ext{ kg} = 1000 ext{ g}
Conversion factors can be written as rac{1000 ext{ g}}{1 ext{ kg}} or rac{1 ext{ kg}}{1000 ext{ g}}
Methodology: Many chemistry calculations can be solved by using conversion factors to change units or compare measurements.
Key Principle: Write the conversion factor so that the starting units (usually in the numerator) cancel with the same units in the conversion factor (placed in the denominator).
Example: Hamburger Patties (Slide 41)
How many 8.0 ext{ oz} patties can be made from 3.2 ext{ lbs} of hamburger?
Given: 3.2 ext{ lbs} of hamburger.
Conversion Factors: 1 ext{ lb} = 16 ext{ oz}, 1 ext{ patty} = 8.0 ext{ oz}
Calculation:
3.2 ext{ lbs} imes rac{16 ext{ oz}}{1 ext{ lb}} imes rac{1 ext{ patty}}{8.0 ext{ oz}} = 6.4 ext{ patties}Note: Start the calculation with the quantity that cannot be expressed as a conversion factor.
Example: Mass of Lead Cube (Slide 42)
What is the mass of a cube of lead which is 1.0 ext{ inch} on edge if the density of lead is 11.34 ext{ g/mL}?
Given: Edge length = 1.0 ext{ in}, Density (d) = 11.34 ext{ g/mL}
Required Conversions: inches to centimeters, cubic inches to cubic centimeters, cubic centimeters to milliliters, milliliters to grams.
Step 1: Calculate Volume in cubic inches:
ext{Volume} = (1.0 ext{ in})^3 = 1.0 ext{ in}^3Step 2: Convert Volume and then to mass:
1.0 ext{ in}^3 imes igg( rac{2.54 ext{ cm}}{1 ext{ in}}igg)^3 imes rac{1 ext{ mL}}{1 ext{ cm}^3} imes rac{11.34 ext{ g}}{1 ext{ mL}}
= 1.0 ext{ in}^3 imes rac{16.387 ext{ cm}^3}{1 ext{ in}^3} imes rac{1 ext{ mL}}{1 ext{ cm}^3} imes rac{11.34 ext{ g}}{1 ext{ mL}}
= 186.0 ext{ g}Significant Figures: The initial edge length (1.0 ext{ in}) has 2 SF. The calculated mass should be rounded to 2 SF.
186.0 ext{ g}
ightarrow 190 ext{ g} ext{ or } 1.9 imes 10^2 ext{ g}
Mass % as a Conversion Factor
Definition: Composition is often reported in mass percent (or "% by mass"), indicating the mass of a component per 100 units of mass of the total substance.
Creating Conversion Factors: If a ring contains 32.5 ext{ mass % Au}, this means there are 32.5 ext{ g} of Gold for every 100 ext{ g} of the ring.
rac{32.5 ext{ g Au}}{100 ext{ g ring}} or rac{100 ext{ g ring}}{32.5 ext{ g Au}}
These factors can be used with any consistent mass units (e.g., 32.5 ext{ kg Au} per 100 ext{ kg ring}).
Practice Problem: Bronze Alloy (Slide 44)
A bronze alloy contains 78 ext{ % by mass Cu}. If the density of the bronze alloy is 8.52 ext{ g/mL}, what volume of bronze would contain 13.46 ext{ g} of Cu?
Identify Conversion Factors:
Mass % Cu: rac{78 ext{ g Cu}}{100 ext{ g bronze}} or rac{100 ext{ g bronze}}{78 ext{ g Cu}}
Density of bronze: rac{8.52 ext{ g bronze}}{1 ext{ mL bronze}} or rac{1 ext{ mL bronze}}{8.52 ext{ g bronze}}
Calculation (Start with 13.46 ext{ g Cu}):
13.46 ext{ g Cu} imes rac{100 ext{ g bronze}}{78 ext{ g Cu}} imes rac{1 ext{ mL bronze}}{8.52 ext{ g bronze}}
= 13.46 imes rac{100}{78} imes rac{1}{8.52} ext{ mL bronze}
= 2.022… ext{ mL bronze}Significant Figures: 13.46 ext{ g} (4 SF), 78 ext{ %} (2 SF), 8.52 ext{ g/mL} (3 SF). The limiting factor is 78 ext{ %} with 2 SF.
Result (rounded to 2 SF): 2.0 ext{ mL bronze}
1.11 Interpreting Graphs
Purpose: Graphs visually represent the relationship between two variables, typically plotted as "Y" vs. "X".
Reading (X,Y) Pair: To find a specific value, select a value on either the X-axis (independent variable) or Y-axis (dependent variable) and read the corresponding value from the graph.
Slope (m): Represents the "rate" of change of the Y-variable with respect to the X-variable.
ext{Slope} = rac{ ext{change in Y}}{ ext{change in X}} = rac{ ext{ΔY}}{ ext{ΔX}}
When the X-axis is time, the steepness of the graph represents the rate (change in value per unit time).
Example (Atmospheric CO_2 vs. Time): The slope indicates the rate of change of atmospheric carbon dioxide concentration per year.