Unit 1: Matter & Measurement (class notes)

Domain and Methods of Science

• A way of seeing and understanding.

• Requires an agreed-upon method.

• Relies on observation.

• Quantitative measurements are preferred (numerical).

• Involves moving from observation to understanding through a two-stage process.

Stage 1: Discovery Cycle

• Experiment: An action or process carried out to test a hypothesis or theory.

• Natural Law: A statement of what occurs without exception.

• Theory: A logical model explaining why things occur.

  • Examples: Gravity, Conservation of Mass, Life begets Life.

  • Not static; testable by experiment.

  • Modified incrementally via the cycle of understanding.

  • Examples include geocentric theory.

Stage 2: Understanding Cycle

• Prediction: an expected outcome based on a theory. For example:

  • Theory 1: Less massive gases than nitrogen rise in air because their gravitational attraction is less.

    • Prediction: Hydrogen should rise, Helium should not.

  • Theory 2: Gases that form stable compounds with oxygen burn.

    • Prediction: Helium should not burn, Argon should not burn.

• Experiment: Testing predictions, leading to modification of theories.

Chemistry

• Definition: The branch of science that deals with the identification of the substances of which matter is composed; the investigation of their properties and the ways in which they interact, combine, and change; and the use of these processes to form new substances.

• Study of matter, properties, composition, structure, interactions, and changes.

• Examples: Graphite and Diamond (different structures, same composition).

Branches of Chemistry

• Physical Chemistry: Studies the physics, matter, and energy of chemicals at an atomic and molecular level.

• Analytical Chemistry: Utilizes different methods, instruments, and techniques to study and quantify different matter.

• Biochemistry: Studies chemical reactions and processes in living things.

• Organic Chemistry: Studies the structure, synthesis, and properties of organic compounds (containing carbon).

• Inorganic Chemistry: Studies the structure, synthesis, and properties of inorganic compounds (containing metals).

• Theoretical Chemistry: Studies key chemistry concepts and the theories behind them.

• Materials Chemistry: Studies and creates different materials for a specific function.

Matter Classification

What is Matter?

• Anything that has mass and occupies space.

Physical States

• Solid: Fixed shape, fixed volume.

• Liquid: No fixed shape, fixed volume.

• Gas: No fixed shape, no fixed volume.

Fundamental Composition

• Elements: Composed of atoms; cannot be broken down into smaller pieces.

  • Need to know the first four rows of the periodic table along with Rb, Cs, Sr, Ba, Pd, Ag, Cd, Sn, I, Xe, Pt, Au, Hg, and Pb.

• Compounds: Composed of more than one atom in fixed proportions.

• Mixtures: Can be separated into elements, compounds, or both.

  • Homogeneous: Uniform.

  • Heterogeneous: Non-uniform.

Example 1

• Classify the following:

  1. Sweet Tea: Homogeneous mixture

  2. Copper: Element

  3. Blood: Heterogeneous mixture

  4. Glucose: Compound

  5. Diamond: Element

Calculations

• Error in measurements must always be considered.

• Error can be in accuracy (agreement with true value) or in precision (agreement of the values with each other).

Types of Error

• Determinate (Systematic): Associated with poor accuracy; values are off in one direction.

• Indeterminate (Random): Associated with poor precision; values are high and low.

Significant Figures

• All non-zero digits are significant (1, 2, 3, …, 9).

• All captive zeros are significant (105, 3507, 14025).

• Leading zeros are not significant (0.0035, 0.0589, 0.0701).

• Trailing zeros before a decimal point are significant if specified in the problem (350.24, 3500., 3500).

• Trailing zeros after a decimal point are significant (35.0, 37.230, 97.000).

• Conversion factors have infinite significant figures and are ignored.

Example 2

• How many significant figures?

  • A. 2730.78 m: 6

  • B. 0.0076 mL: 2

  • C. 3400 kg: 2

  • D. 3400.0 m$^2$: 5

Math with Significant Digits

Multiplication/Division

• Limited by the number of significant digits.

• Example: $\frac{278 \, mm}{11.70 \, g} = 23.8 \, mm/g$

Addition/Subtraction

• Limited by the number of decimal places.

• Example: $3.18 \, L + 0.01315 \, L = 3.19 \, L$

3 significant figures / 3 significant figures --> 3 significant figures
2 decimal places / 5 decimal places --> 2 decimal places

• Example:
  $(57.890 \, cc + 73.2 \, cc) / 0.37 \, cc = 131.09 \, cc / 0.37 \, cc = 354.297 \, cc = 350 \, cc$
  3 decimal places + 1 decimal place --> Keep 1 decimal place
  4 significant digits / 2 significant digits -->Round to 2 significant digits

Example 3

• Solve and round to the correct number of significant digits:
  $\frac{3.478 * 1.164}{2.00} + \frac{0.354}{15.415 - 14.515} + 3.465 + 0.0402597$

Units of Measurement

International System of Units (SI)

SI Base Units

SI Prefixes

SI Derived Units

Example 1

• 1 micrometer (µm) = 0.000001 ($1 \times 10^{-6}$) meters (m) OR 1,000,000 ($1 \times 10^6$) micrometers = 1 meter (m)

• The average width of human hair is 53 µm. What is this measurement in meters?
  $53 \, µm * \frac{1 \times 10^{-6} m}{1 \, µm} = 5.3 \times 10^{-5} m$
  $53 \, µm * \frac{1 \, m}{1 \times 10^{6} µm} = 5.3 \times 10^{-5} m$

Unit Cancellation

• Unit Cancellation helps to direct the calculation toward the correct answer with the correct units.

• What is the speed of light in mi/hr and how many times does light circle the globe at the equator every second?

• Given Information: Equator = 24901 miles | Speed of light = $2.998 \times 10^8$ m/s | 1.609 km = 1 mile

$2.998 \times 10^8 \frac{m}{s} * \frac{1 \, km}{1 \times 10^3 \, m} * \frac{1 \, mile}{1.609 \, km} * \frac{3600 \, s}{1 \, hr} = 6.708 \times 10^7 \, mi/hr$
$2.998 \times 10^8 \frac{m}{s} * \frac{1 \, km}{1 \times 10^3 \, m} * \frac{1 \, mile}{1.609 \, km} * \frac{1 \, s}{24901 \, mile} = 7.483 \, loops$

Temperature

• Measure of average kinetic energy and therefore available energy.

• Formulas:

  • $°F = 1.8 * (°C) + 32$

  • $°C = 0.55 * (°F – 32)$

  • $K = °C + 273.15$

Example 4

• The melting point of mercury is 235 K. What is this in degrees Celsius?

• The surface temperature of the sun is $1 \times 10^4$ °F (compared to the core temperature of $2.7 \times 10^7$ °F). What is the surface temperature in Kelvin?

Unit 1 Review – What to Know

• Natural Law versus Theory

• How to classify matter based on its physical state or composition

• Memorize the first four rows of the periodic table (name and symbol) along with Rb, Cs, Sr, Ba, Pd, Ag, Cd, Sn, I, Xe, Pt, Au, Hg, and Pb

• Systematic versus Random error

• Determination of significant digits

• SI prefixes (base 10 conversions) listed on Memorization Sheet

• How to solve problems using unit cancellation

• Temperature units and their conversions

Domain and Methods of Science

• A way of seeing and understanding.

  • Science provides a framework for observing, experimenting, and interpreting the world around us.

• Requires an agreed-upon method.

  • The scientific method ensures consistency and reliability in scientific investigations.

• Relies on observation.

  • Empirical evidence is crucial for supporting scientific claims.

• Quantitative measurements are preferred (numerical).

  • Numerical data allows for precise analysis and comparison.

• Involves moving from observation to understanding through a two-stage process.

  • This process includes forming hypotheses, testing them, and refining theories based on evidence.

Stage 1: Discovery Cycle

• Experiment: An action or process carried out to test a hypothesis or theory.

  • Experiments involve manipulating variables and observing outcomes to draw conclusions.

• Natural Law: A statement of what occurs without exception.

  • Natural laws describe consistent patterns observed in nature.

• Theory: A logical model explaining why things occur.

  • Theories provide comprehensive explanations for observed phenomena.

  • Examples: Gravity, Conservation of Mass, Life begets Life.

  • Not static; testable by experiment.

    • Scientific theories are continuously tested and refined through experimentation.

  • Modified incrementally via the cycle of understanding.

    • Theories evolve as new evidence emerges and understanding deepens.

  • Examples include geocentric theory.

    • The geocentric theory was an early model of the universe that was later replaced by the heliocentric theory.

Stage 2: Understanding Cycle

• Prediction: an expected outcome based on a theory. For example:

  • Predictions are derived from theories and tested through experimentation.

  • Theory 1: Less massive gases than nitrogen rise in air because their gravitational attraction is less.

    • This theory suggests that buoyancy is related to the gravitational attraction of gases.

    • Prediction: Hydrogen should rise, Helium should not.

    • Testing this prediction helps validate or refine the theory.

  • Theory 2: Gases that form stable compounds with oxygen burn.

    • This theory connects the reactivity of gases with their ability to form stable compounds.

    • Prediction: Helium should not burn, Argon should not burn.

    • Observing whether these gases burn provides evidence for or against the theory.

• Experiment: Testing predictions, leading to modification of theories.

  • Experiments provide empirical data that either supports or contradicts theoretical predictions.

Chemistry

• Definition: The branch of science that deals with the identification of the substances of which matter is composed; the investigation of their properties and the ways in which they interact, combine, and change; and the use of these processes to form new substances.

  • Chemistry is concerned with understanding the composition, structure, properties, and reactions of matter.

• Study of matter, properties, composition, structure, interactions, and changes.

  • These aspects are fundamental to understanding chemical systems and processes.

• Examples: Graphite and Diamond (different structures, same composition).

  • These allotropes illustrate how different arrangements of atoms can result in distinct properties.

Branches of Chemistry

• Physical Chemistry: Studies the physics, matter, and energy of chemicals at an atomic and molecular level.

  • This branch applies principles of physics to understand chemical phenomena.

• Analytical Chemistry: Utilizes different methods, instruments, and techniques to study and quantify different matter.

  • Analytical chemistry focuses on measuring and characterizing chemical substances.

• Biochemistry: Studies chemical reactions and processes in living things.

  • Biochemistry explores the chemical basis of life processes.

• Organic Chemistry: Studies the structure, synthesis, and properties of organic compounds (containing carbon).

  • Organic chemistry is concerned with compounds containing carbon, which are essential to life.

• Inorganic Chemistry: Studies the structure, synthesis, and properties of inorganic compounds (containing metals).

  • Inorganic chemistry focuses on compounds that do not primarily contain carbon.

• Theoretical Chemistry: Studies key chemistry concepts and the theories behind them.

  • Theoretical chemistry uses mathematical models to understand and predict chemical behavior.

• Materials Chemistry: Studies and creates different materials for a specific function.

  • Materials chemistry designs and synthesizes new materials with specific properties.

Matter Classification

What is Matter?

• Anything that has mass and occupies space.

  • Matter is the substance that makes up the physical universe.

Physical States

• Solid: Fixed shape, fixed volume.

  • Solids maintain their shape and volume.

• Liquid: No fixed shape, fixed volume.

  • Liquids take the shape of their container but maintain a constant volume.

• Gas: No fixed shape, no fixed volume.

  • Gases expand to fill the available space.

Fundamental Composition

• Elements: Composed of atoms; cannot be broken down into smaller pieces.

  • Elements are the simplest form of matter and cannot be decomposed by chemical means.

  • Need to know the first four rows of the periodic table along with Rb, Cs, Sr, Ba, Pd, Ag, Cd, Sn, I, Xe, Pt, Au, Hg, and Pb.

  • Familiarity with these elements is essential for understanding chemical reactions and compounds.

• Compounds: Composed of more than one atom in fixed proportions.

  • Compounds are formed when atoms of different elements combine chemically.

• Mixtures: Can be separated into elements, compounds, or both.

  • Mixtures are combinations of substances that are not chemically bonded.

  • Homogeneous: Uniform.

  • Homogeneous mixtures have a consistent composition throughout.

  • Heterogeneous: Non-uniform.

  • Heterogeneous mixtures have varying composition in different regions.

Example 1

• Classify the following:

  1. Sweet Tea: Homogeneous mixture

  • Sweet tea has a uniform composition throughout.

  1. Copper: Element

  • Copper is a pure substance that cannot be broken down further.

  1. Blood: Heterogeneous mixture

  • Blood contains various components, such as cells and plasma, that are not uniformly distributed.

  1. Glucose: Compound

  • Glucose is a molecule composed of carbon, hydrogen, and oxygen atoms in a fixed ratio.

  1. Diamond: Element

  • Diamond is a pure form of carbon.

Calculations

• Error in measurements must always be considered.

  • No measurement is perfect, and errors can affect the accuracy and precision of results.

• Error can be in accuracy (agreement with true value) or in precision (agreement of the values with each other).

  • Accurate measurements are close to the true value, while precise measurements are reproducible.

Types of Error

• Determinate (Systematic): Associated with poor accuracy; values are off in one direction.

  • Systematic errors can be identified and corrected.

• Indeterminate (Random): Associated with poor precision; values are high and low.

  • Random errors are unpredictable and can be minimized by taking multiple measurements.

Significant Figures

• All non-zero digits are significant (1, 2, 3, …, 9).

  • Non-zero digits always contribute to the precision of a measurement.

• All captive zeros are significant (105, 3507, 14025).

  • Captive zeros are between non-zero digits.

• Leading zeros are not significant (0.0035, 0.0589, 0.0701).

  • Leading zeros only indicate the position of the decimal point.

• Trailing zeros before a decimal point are significant if specified in the problem (350.24, 3500., 3500).

  • Trailing zeros can indicate the precision of the measurement if explicitly stated.

• Trailing zeros after a decimal point are significant (35.0, 37.230, 97.000).

  • Trailing zeros after the decimal point indicate the precision of the measurement.

• Conversion factors have infinite significant figures and are ignored.

  • Conversion factors are exact and do not limit the number of significant figures in a calculation.

Example 2

• How many significant figures?

  • A. 2730.78 m: 6

  • All digits are significant.

  • B. 0.0076 mL: 2

  • Only the 7 and 6 are significant.

  • C. 3400 kg: 2

  • Only the 3 and 4 are significant.

  • D. 3400.0 m$^2$: 5

  • All digits, including the trailing zeros after the decimal point, are significant.

Math with Significant Digits

Multiplication/Division

• Limited by the number of significant digits.

  • The result should have the same number of significant digits as the factor with the fewest significant digits.

• Example: $\frac{278 \, mm}{11.70 \, g} = 23.8 \, mm/g$

  • 278 has 3 significant digits, and 11.70 has 4 significant digits, so the answer is rounded to 3 significant digits.

Addition/Subtraction

• Limited by the number of decimal places.

  • The result should have the same number of decimal places as the number with the fewest decimal places.

• Example: $3.18 \, L + 0.01315 \, L = 3.19 \, L$

  • 3.18 has 2 decimal places, and 0.01315 has 5 decimal places, so the answer is rounded to 2 decimal places.

3 significant figures / 3 significant figures --> 3 significant figures

2 decimal places / 5 decimal places --> 2 decimal places

• Example:
  $(57.890 \, cc + 73.2 \, cc) / 0.37 \, cc = 131.09 \, cc / 0.37 \, cc = 354.297 \, cc = 350 \, cc$

  • First, add 57.890 and 73.2, which gives 131.09. Since 73.2 has only one decimal place, round 131.09 to 131.1.

  • Then, divide 131.1 by 0.37, which gives 354.324. Since 0.37 has two significant figures, round 354.324 to 350.

3 decimal places + 1 decimal place --> Keep 1 decimal place

4 significant digits / 2 significant digits -->Round to 2 significant digits

Example 3

• Solve and round to the correct number of significant digits:
  
  $\frac{3.478 * 1.164}{2.00} + \frac{0.354}{15.415 - 14.515} + 3.465 + 0.0402597$

Units of Measurement

International System of Units (SI)

SI Base Units

SI Prefixes

SI Derived Units

Example 1

• 1 micrometer (µm) = 0.000001 ($1 \times 10^{-6}$) meters (m) OR 1,000,000 ($1 \times 10^6$) micrometers = 1 meter (m)

• The average width of human hair is 53 µm. What is this measurement in meters?
  
  $53 \, µm * \frac{1 \times 10^{-6} m}{1 \, µm} = 5.3 \times 10^{-5} m$
  
  $53 \, µm * \frac{1 \, m}{1 \times 10^{6} µm} = 5.3 \times 10^{-5} m$

Unit Cancellation

• Unit Cancellation helps to direct the calculation toward the correct answer with the correct units.

  • By tracking units through a calculation, you can ensure that the final answer has the correct units.

• What is the speed of light in mi/hr and how many times does light circle the globe at the equator every second?

  • These problems illustrate how unit cancellation can be used to convert between different units.

• Given Information: Equator = 24901 miles | Speed of light = $2.998 \times 10^8$ m/s | 1.609 km = 1 mile

$2.998 \times 10^8 \frac{m}{s} * \frac{1 \, km}{1 \times 10^3 \, m} * \frac{1 \, mile}{1.609 \, km} * \frac{3600 \, s}{1 \, hr} = 6.708 \times 10^7 \, mi/hr$

$2.998 \times 10^8 \frac{m}{s} * \frac{1 \, km}{1 \times 10^3 \, m} * \frac{1 \, mile}{1.609 \, km} * \frac{1 \, s}{24901 \, mile} = 7.483 \, loops$

Temperature

• Measure of average kinetic energy and therefore available energy.

  • Temperature is directly proportional to the average kinetic energy of the particles in a substance.

• Formulas:

  • $°F = 1.8 * (°C) + 32$

  • This formula converts degrees Celsius to degrees Fahrenheit.

  • $°C = 0.55 * (°F – 32)$

  • This formula converts degrees Fahrenheit to degrees Celsius.

  • $K = °C + 273.15$

  • This formula converts degrees Celsius to Kelvin.

Example 4

• The melting point of mercury is 235 K. What is this in degrees Celsius?

  • Use the formula $K = °C + 273.15$ to find °C. Rearrange the formula to $°C = K - 273.15$. Substitute 235 K to the new formula, $°C = 235 - 273.15$. Therefore, the melting point is -38.15 °C.

• The surface temperature of the sun is $1 \times 10^4$ °F (compared to the core temperature of $2.7 \times 10^7$ °F). What is the surface temperature in Kelvin?

  • Use the formula $°F = 1.8 * (°C) + 32$ to find °C. Rearrange the formula to $°C = 0.55 * (°F – 32)$. Substitute $1 \times 10^4$ °F to the new formula, $°C = 0.55 * (1 \times 10^4 – 32)$. Therefore, the surface temperature is 5521.6 °C. Then use the formula $K = °C + 273.15$ to find K. Substitute 5521.6 °C to the formula, therefore, the surface temperature of the sun is 5794.8 K.

Unit 1 Review – What to Know

• Natural Law versus Theory

  • Understand the difference between descriptive natural laws and explanatory theories.

• How to classify matter based on its physical state or composition

  • Be able to identify matter as solid, liquid, or gas and as element, compound, or mixture.

• Memorize the first four rows of the periodic table (name and symbol) along with Rb, Cs, Sr, Ba, Pd, Ag, Cd, Sn, I, Xe, Pt, Au, Hg, and Pb

  • Knowing these elements will help in understanding chemical formulas and reactions.

• Systematic versus Random error

  • Know the causes and effects of each type of error.

• Determination of significant digits

  • Be able to count significant digits in a measurement and apply the rules for calculations.

• SI prefixes (base 10 conversions) listed on Memorization Sheet

  • Familiarize yourself with common prefixes like kilo-, centi-, and milli-.

• How to solve problems using unit cancellation

  • Practice converting between different units using the factor-label method.

• Temperature units and their conversions

  • Be able to convert between Celsius, Fahrenheit, and Kelvin.