Matter, Measurement & Problem Solving

What Is Chemistry?

Chemistry is the scientific study of the composition, structure, properties, and transformations of matter. It sits at the intersection of nearly every other science because everything physical is made of matter undergoing chemical and physical change. Chemists traditionally divide the discipline into five major branches, each with its own focus and typical questions.

• •Organic chemistry — the study of carbon-containing compounds, especially those in living systems and synthetic materials.
• •Inorganic chemistry — the study of non-carbon-based compounds, including metals, minerals, and organometallic species.
• •Biochemistry — the study of chemical processes within living organisms (proteins, enzymes, metabolism).
• •Physical chemistry — the study of the physical principles (energy, thermodynamics, quantum mechanics) underlying chemical behavior.
• •Analytical chemistry — the study of the composition of matter and the development of tools/methods to measure it.

Classifying Matter

Matter is anything with mass that occupies space, and it can be classified along two branching decisions: is it a pure substance or a mixture, and if pure, is it an element or a compound? A pure substance has a fixed composition and fixed properties, while a mixture has variable composition made of two or more substances that retain their own identities. This classification scheme is one of the very first tools chemists use to organize the physical world.

• •Element: a pure substance that cannot be broken down into simpler substances by chemical means (e.g., gold, oxygen).
• •Compound: a pure substance composed of two or more elements chemically combined in a fixed ratio (e.g., water, NaCl).
• •Homogeneous mixture (solution): uniform composition and properties throughout (e.g., saltwater, air).
• •Heterogeneous mixture: non-uniform composition; distinct regions or phases are visible (e.g., oil and water, sand and iron filings).
• •Mixtures can be separated by physical means (filtration, distillation, evaporation); compounds require chemical reactions to separate into elements.

The Three Phases of Matter

Solids, liquids, and gases differ in how tightly their particles are packed and how freely those particles move, which in turn explains macroscopic properties like shape and compressibility. In a solid, particles are locked in fixed positions, vibrating but not translating, giving a solid a definite shape and volume. In a liquid, particles are close together but can slide past one another, giving a definite volume but no fixed shape. In a gas, particles are far apart and move independently at high speed, so gases expand to fill their container and are easily compressed.

• •Solid: definite shape, definite volume, particles vibrate in fixed positions, essentially incompressible.
• •Liquid: indefinite shape, definite volume, particles flow past each other, nearly incompressible.
• •Gas: indefinite shape, indefinite volume, particles move independently and rapidly, highly compressible.

Phase Changes

Matter converts between phases through six named transitions, each involving energy flow but no change in chemical identity. Changes toward a higher-energy, more disordered phase (melting, vaporization, sublimation) require energy input, while changes toward a lower-energy, more ordered phase (freezing, condensation, deposition) release energy. Because these are physical changes, the chemical formula of the substance never changes during a phase change.

• •Melting (fusion): solid → liquid, absorbs energy.
• •Freezing: liquid → solid, releases energy.
• •Vaporization: liquid → gas, absorbs energy.
• •Condensation: gas → liquid, releases energy.
• •Sublimation: solid → gas directly, absorbs energy (e.g., dry ice).
• •Deposition: gas → solid directly, releases energy (e.g., frost formation).

Intensive vs. Extensive Properties

An extensive property depends on the amount of matter present, such as mass, volume, or total energy content — doubling the sample doubles the property. An intensive property does not depend on the amount of matter and is therefore useful for identifying a substance, such as density, color, melting point, or concentration. Chemists prize intensive properties because they act like a chemical 'fingerprint' independent of sample size.

• •Extensive examples: mass, volume, length, total heat content.
• •Intensive examples: density, temperature, color, melting/boiling point, hardness.
• •The ratio of two extensive properties (e.g., mass/volume = density) is always intensive.

Physical vs. Chemical Properties and Changes

A physical property can be observed or measured without changing the substance's chemical identity (color, melting point, density), while a chemical property describes how a substance reacts to form a new substance (flammability, reactivity with acid). Correspondingly, a physical change alters appearance or state without changing chemical composition (melting ice, dissolving sugar), whereas a chemical change produces one or more new substances with different properties (rusting, combustion). Evidence of chemical change includes gas bubble formation, color change, precipitate formation, temperature change, and light emission.

• •Physical change: no new substance formed, generally reversible (e.g., crushing, melting, dissolving).
• •Chemical change: new substance(s) formed, often not easily reversible (e.g., burning, rusting, digesting).
• •Common evidence of a chemical reaction: color change, precipitate, gas evolution, odor, temperature/light change.

Parts of a Chemical Equation

A chemical equation is a symbolic representation of a chemical reaction, written with reactants on the left and products on the right separated by an arrow. Coefficients placed in front of formulas indicate the relative number of moles (or particles) of each substance and are required for the equation to satisfy conservation of mass. State symbols in parentheses after each formula specify the physical form of each substance under the reaction conditions.

• •Reactants: substances consumed, written to the left of the arrow.
• •Products: substances formed, written to the right of the arrow.
• •Coefficients: numbers in front of formulas showing molar ratios; a coefficient of 1 is omitted.
• •State/phase labels: (s) solid, (l) liquid, (g) gas, (aq) aqueous (dissolved in water).

Energy, the First Law, and Potential vs. Kinetic Energy

Energy is the capacity to do work or transfer heat, and it exists in two fundamental forms: kinetic energy (energy of motion, KE = ½mv²) and potential energy (stored energy due to position or composition, such as chemical bonds). The First Law of Thermodynamics states that energy cannot be created or destroyed, only converted from one form to another or transferred between a system and its surroundings — total energy of the universe is constant. Chemical and physical systems spontaneously tend to move toward arrangements of lower potential energy, releasing the difference as heat or other forms of energy, which is why exothermic reactions (like combustion) are so common and energetically favorable.

• •Kinetic energy: associated with motion; increases with temperature and speed.
• •Potential energy: stored energy from position, composition, or bonding arrangement.
• •First Law of Thermodynamics: energy is conserved; ΔE(universe) = 0.
• •Systems favor lower potential energy states, releasing excess energy to surroundings.

SI Base Units and Metric Prefixes

The International System of Units (SI) provides seven base units from which all other scientific units are derived. Because measured quantities can span enormous ranges of magnitude, metric prefixes attach to base units to represent very large or very small quantities without cumbersome numbers of zeros. Fluency converting among prefixes is essential for nearly every calculation in this course.

• •kilogram (kg) — mass; meter (m) — length; second (s) — time; kelvin (K) — temperature.
• •mole (mol) — amount of substance; ampere (A) — electric current; candela (cd) — luminous intensity.
• •Common prefixes (largest to smallest): giga- (G, 10⁹), mega- (M, 10⁶), kilo- (k, 10³), deci- (d, 10⁻¹), centi- (c, 10⁻²), milli- (m, 10⁻³), micro- (μ, 10⁻⁶), nano- (n, 10⁻⁹), pico- (p, 10⁻¹²).
• •Example conversions: 1 km = 1000 m; 1 m = 100 cm; 1 cm = 10 mm; 1 g = 1000 mg; 1 mg = 1000 μg.

Volume, Density, and Dimensional Analysis

Volume is the amount of space a substance occupies, commonly expressed in liters (L), milliliters (mL), or cubic centimeters (cm³), where 1 mL = 1 cm³ exactly. Density is the intensive ratio of mass to volume (d = m/V) and serves as a powerful conversion factor linking the mass and volume of a specific substance. Dimensional analysis (the factor-label method) uses conversion factors — ratios equal to 1 — to systematically cancel unwanted units and arrive at desired units, and it is the single most useful problem-solving technique in general chemistry.

• •Density units: g/mL or g/cm³ for liquids/solids; g/L for gases.
• •Density as a conversion factor: mass ⇌ volume using d = m/V.
• •Dimensional analysis: multiply by conversion factors so units cancel, leaving only the desired unit.
• •Equation-based problem solving (e.g., algebraically solving d = m/V) is an alternative to pure unit cancellation and both should give the same answer.

Significant Figures and Uncertainty

Every measurement carries some uncertainty, and significant figures communicate the precision of a measured (not exact) quantity. Rules govern which digits count: all nonzero digits are significant, captive zeros (between nonzero digits) are significant, leading zeros are never significant, and trailing zeros are significant only if a decimal point is present. In calculations, multiplication/division results are rounded to match the measurement with the fewest significant figures, while addition/subtraction results are rounded to match the measurement with the fewest decimal places; exact numbers (from definitions or counting) have infinite significant figures and never limit precision.

• •Nonzero digits: always significant (e.g., 342 has 3 sig figs).
• •Captive zeros: significant (e.g., 405 has 3 sig figs).
• •Leading zeros: never significant (e.g., 0.0042 has 2 sig figs).
• •Trailing zeros: significant only with a decimal point (e.g., 100. has 3 sig figs; 100 has 1).
• •Multiplication/division: round to fewest sig figs among factors; addition/subtraction: round to fewest decimal places.

Convert 2.35 kg to milligrams.

1. 1Identify the given quantity: 2.35 kg.
2. 2Recall that 1 kg = 1000 g and 1 g = 1000 mg, so 1 kg = 1,000,000 mg (10⁶ mg).
3. 3Set up dimensional analysis: 2.35 kg × (1000 g / 1 kg) × (1000 mg / 1 g).
4. 4Cancel units: kg cancels with kg, g cancels with g, leaving mg.
5. 5Multiply: 2.35 × 1000 × 1000 = 2,350,000 mg.
6. 6Report with correct sig figs (3 sig figs from 2.35): 2.35 × 10⁶ mg.

2.35 × 10⁶ mg

A metal sample has a mass of 47.5 g and a volume of 6.35 cm³. Calculate its density and identify it if aluminum has a density of 2.70 g/cm³.

1. 1Write the density formula: d = m / V.
2. 2Substitute values: d = 47.5 g / 6.35 cm³.
3. 3Divide: 47.5 ÷ 6.35 = 7.480... g/cm³.
4. 4Round to 3 sig figs (limited by both measurements): 7.48 g/cm³.
5. 5Compare to aluminum's density (2.70 g/cm³) — the sample is far denser, so it is not aluminum (it is close to zinc, ~7.14 g/cm³, or another dense metal).

7.48 g/cm³ (not aluminum)

Use density to find the volume occupied by 25.0 g of ethanol (density = 0.789 g/mL).

1. 1Write density as a conversion factor: 0.789 g/mL means 0.789 g ≡ 1 mL.
2. 2Set up dimensional analysis: 25.0 g × (1 mL / 0.789 g).
3. 3Cancel grams, leaving mL.
4. 4Divide: 25.0 ÷ 0.789 = 31.685... mL.
5. 5Round to 3 sig figs: 31.7 mL.

31.7 mL

Perform the calculation (12.11 + 18.0) × 4.256 and report the answer with correct significant figures.

1. 1First perform the addition inside parentheses: 12.11 + 18.0 = 30.11 → but 18.0 has only 1 decimal place, so round the sum to 1 decimal place: 30.1.
2. 2Now multiply: 30.1 × 4.256 = 128.1056.
3. 3For multiplication, round to the fewest sig figs among factors: 30.1 has 3 sig figs, 4.256 has 4 sig figs, so the answer gets 3 sig figs.
4. 4Round 128.1056 to 3 sig figs: 128.

128

Convert a body temperature of 37.0 °C to Kelvin and to Fahrenheit.

1. 1For Kelvin: K = °C + 273.15 = 37.0 + 273.15 = 310.15 K, round to 310.2 K (1 decimal place matching 37.0's precision).
2. 2For Fahrenheit: °F = (9/5)°C + 32.
3. 3Substitute: °F = (9/5)(37.0) + 32 = 66.6 + 32.
4. 4Add: 66.6 + 32 = 98.6 °F.

310.2 K and 98.6 °F

Q1. Which branch of chemistry primarily studies carbon-containing compounds?

Q2. Saltwater is best classified as a:

Q3. Which phase change releases energy?

Q4. Which of the following is an intensive property?

Q5. A piece of iron rusting is an example of a:

Q6. In the equation 2H₂(g) + O₂(g) → 2H₂O(l), what does the coefficient '2' in front of H₂O indicate?

Q7. According to the First Law of Thermodynamics:

Q8. Which SI base unit corresponds to amount of substance?

Q9. How many milliliters are in 3.5 liters?

Q10. A sample of liquid has a mass of 15.0 g and a volume of 12.5 mL. What is its density?

Q11. How many significant figures are in the measurement 0.004050 g?

Q12. Which statement correctly distinguishes accuracy from precision?

Q13. Which is an example of a chemical property?

Q14. Deposition is the phase change in which:

Q15. Which metric prefix represents a factor of 10⁻³?