Chapter E: Essentials – Units, Measurement, and Problem Solving

Scientific Method

The scientific method is a systematic approach to understanding the natural world through observation and experimentation. It is foundational to all scientific inquiry.

• Observation: Gathering information using the senses or instruments. Observations can be qualitative (descriptive) or quantitative (measured).

• Experiment: A controlled procedure carried out to test a hypothesis or demonstrate a known fact.

• Hypothesis: A tentative explanation for an observation, which can be tested by further investigation.

• Theory: A well-substantiated explanation of some aspect of the natural world, based on a body of evidence and repeatedly confirmed through observation and experiment.

Key Point: The main difference between a hypothesis and a theory is that a hypothesis is a proposed explanation, while a theory is a thoroughly tested and confirmed explanation.

SI Units and Prefixes

The International System of Units (SI) is the standard for scientific measurements. Each physical quantity has a base unit.

• Mass: kilogram (kg)

• Length: meter (m)

• Temperature: kelvin (K)

• Amount of substance: mole (mol)

• Time: second (s)

SI prefixes are used to indicate multiples or fractions of units:

Example: 1 km = m; 1 mg = g

Key Skill: Be able to convert between prefixed units and base units, or between two prefixed units, using the appropriate conversion factors.

Temperature Conversions

Temperature can be measured in Celsius (°C), Fahrenheit (°F), or Kelvin (K). Know how to convert between these scales.

• Celsius to Kelvin:

• Celsius to Fahrenheit:

• Fahrenheit to Celsius:

Example: Convert 25°C to K: K

Volume Units and Conversions

Volume is the amount of space an object occupies. It can be expressed in cubic units or liters.

• Key Relationships:

  • 1 dm3 = 1 L

  • 1 cm3 = 1 mL

  • 1 m3 = 1000 L

• Volume of a cube: (where is the length of a side)

Example: Convert 250 mL to L:

Density

Density is the mass per unit volume of a substance.

• Formula:

• Units: g/cm3, kg/m3, etc.

• Density can be used as a conversion factor between mass and volume.

Example: If a liquid has a density of 0.789 g/mL, what is the mass of 50.0 mL?

Solution:

Kinetic Energy

Kinetic energy is the energy of motion.

• Formula:

• 1 Joule (J) = 1 kg·m2/s2

• Mass must be in kilograms (kg), velocity in meters per second (m/s).

Example: Calculate the kinetic energy of a 2.0 kg object moving at 3.0 m/s.

Solution:

Significant Figures

Significant figures reflect the precision of a measured value. They are important for reporting scientific data accurately.

• All nonzero digits are significant.

• Zeros between nonzero digits are significant.

• Leading zeros are not significant.

• Trailing zeros are significant only if there is a decimal point.

Key Skill: Be able to determine the number of significant figures in a value and apply the correct rules when performing calculations.

Example: 0.00450 has three significant figures.

Chapter 1: Atoms

Law of Conservation of Mass

The Law of Conservation of Mass states that mass is neither created nor destroyed in a chemical reaction.

• Total mass of reactants = total mass of products.

Example: If 10.0 g of hydrogen reacts with 80.0 g of oxygen, the total mass of water produced is 90.0 g.

Atomic Structure

Atoms are composed of three main subatomic particles:

• Protons: Positively charged particles found in the nucleus.

• Neutrons: Neutral particles found in the nucleus.

• Electrons: Negatively charged particles found outside the nucleus.

Key terms:

• Atomic number (Z): Number of protons in the nucleus; defines the element.

• Mass number (A): Total number of protons and neutrons in the nucleus.

• Charge: Determined by the difference between the number of protons and electrons.

Isotopes are atoms of the same element with different numbers of neutrons (and thus different mass numbers).

Example: Carbon-12 and Carbon-14 are isotopes of carbon.

Average Atomic Mass and Isotopic Calculations

The average atomic mass of an element is the weighted average of the masses of its naturally occurring isotopes.

• Formula:

Example: If chlorine has two isotopes, Cl (75.78%, mass = 34.969 amu) and Cl (24.22%, mass = 36.966 amu):

amu

• You may also be asked to calculate the mass or abundance of an isotope given the average mass and the other isotope's data.

Avogadro’s Number and the Mole

Avogadro’s number () is the number of particles in one mole of a substance.

• particles/mol

• Used to convert between number of atoms/molecules and moles.

Example: How many atoms are in 2.00 mol of carbon?

Solution:

Molar Mass

Molar mass is the mass of one mole of a substance, usually expressed in g/mol.

• It serves as a conversion factor between mass and moles.

• Formula:

Example: How many moles are in 18.0 g of water (molar mass = 18.0 g/mol)?

Solution:

Additional info: Students should be prepared to perform all calculations without provided conversion factors or equations, except for those explicitly noted above.