Unit 1: Matter and Measurement Comprehensive Study Guide

Classification and Types of Matter

• Pure Substances

  • Pure substances cannot be separated by physical means.

  • Elements

    • These are pure substances composed of only one kind of atom.

    • Examples: Oxygen, Carbon.

    • Diatomic Molecules: These are elements that form two-atom molecules in their natural form at Standard Temperature and Pressure (STP). They can be remembered using the phrase ‘HOFBrINCl’:

      • $H_2$

      • $O_2$

      • $F_2$

      • $Br_2$

      • $I_2$

      • $N_2$

      • $Cl_2$

  • Compounds

    • These are chemically bonded substances.

    • They contain two or more types of atoms combined in whole-number ratios.

    • Binary Compounds: Substances made up of exactly two kinds of atoms.

      • Examples: Water ($H_2O$), Ammonia ($NH_3$), Carbon Dioxide ($CO_2$).

• Mixtures

  • Mixtures can be separated by physical means.

  • Homogeneous Mixtures

    • These are uniform throughout; particles are evenly distributed.

    • They are categorized the same as Solutions.

    • Examples: Salt dissolved in water, oxygen dissolved in nitrogen, salt water, and atmospheric air.

  • Heterogeneous Mixtures

    • These have discernable components and a non-uniform distribution (they are not uniform throughout).

    • Examples: Chocolate-chip cookies, vegetable soup, soil, and muddy water.

Changes and States of Matter

• Physical Changes

  • These do not result in the formation of new substances.

  • They merely change the appearance of the original material.

  • Example: The melting of ice.

  • Example: Tearing a piece of paper.

• Chemical Changes

  • These result in the formation of new substances.

  • Example: The burning of hydrogen gas to produce water vapor.

  • Example: Cooking an egg.

  • Tip: To distinguish between them, ask if the change can be reversed. If the answer is no, the change is chemical.

• Physical States of Matter

  • Solid

    • Structure: Rigid.

    • Shape: Fixed.

    • Volume: Fixed.

  • Liquid

    • Structure: Not rigid.

    • Shape: No fixed shape.

    • Volume: Fixed.

  • Gas

    • Structure: Not rigid.

    • Shape: No fixed shape.

    • Volume: No fixed volume.

Temperature and Measurement Standards

• Temperature Conversions

  • The formula found in Table T is: $K = C + 273$.

  • Celsius ($^{\circ}C$) usage: Phase changes, heat questions, and temperatures measured directly in the laboratory.

  • Kelvin ($K$) usage: Gas laws.

• Key Measurement Concepts

  • Significant Digits: Specific rules used for rounding based on the precision of tools.

  • Density: An intensive property that relates mass and volume.

  • Percent Error: A calculation used to determine how far off a student's data point is from the actual or accepted measurement.

Significant Figure Rules

• The Pacific/Atlantic Rule

  • Pacific (Decimal is Present): Start on the left (Pacific) side of the number. Move toward the right and start counting at the first non-zero number. That number and all numbers after it are significant.

    • Example: $0.0050830$ has 5 significant figures ($5$, $0$, $8$, $3$, and the trailing $0$).

  • Atlantic (Decimal is Absent): Start on the right (Atlantic) side of the number. Move toward the left and start counting at the first non-zero number. That number and all numbers after it (to the left) are significant.

• Practice Examples for Significant Figures

  1. $3.0800$

  2. $0.00418$

  3. $7.09 \times 10^{-5}$

  4. $91,600$

  5. $0.003005$

  6. $3.200 \times 10^9$

  7. $250$

  8. $750,000,000$

  9. $0.0101$

  10. $0.00800$

Density Calculations

• Definition: Density is defined as mass per unit of volume.

• Formula: $d = \frac{m}{V}$

• General Rule of Density (Increasing Density): Gases are generally less dense than liquids, and liquids are generally less dense than solids.

• Method A: Direct Calculation

  • Question: What is the density of a substance with a mass of $10\,g$ and a volume of $5\,ml$?

  • Calculation: $D = \frac{10\,g}{5\,ml} = 2\,g/ml$

• Method B: Water Displacement Method

  • Used to find the volume of irregular objects.

  • Data provided:

    • Mass ($M$) = $51.842\,g$

    • Initial volume = $17.1\,mL$

    • Final volume = $19.8\,mL$

  • Volume ($V$) = $19.8\,mL - 17.1\,mL = 2.7\,mL$

  • Density calculation: $D = \frac{51.842\,g}{2.7\,mL}$

Percent Error

• Definition: Percent error is the absolute value of the difference between the experimental (measured) value and the theoretical (accepted) value, divided by the accepted value, and multiplied by 100\%.

• Formula:     $\%\text{ Error} = \frac{|\text{experimental value} - \text{accepted value}|}{|\text{accepted value}|} \times 100\%$

• Calculation Example:

  • Scenario: A student finds the density of copper to be $8.218\,g/cm^3$. The actual (accepted) density of copper is $8.960\,g/cm^3$.

  • Experimental Value ($d_m$) = $8.218\,g/cm^3$

  • Accepted Value ($d_a$) = $8.960\,g/cm^3$

  • Calculation:         $\%\text{ error} = \frac{8.218\,g/cm^3 - 8.960\,g/cm^3}{8.960\,g/cm^3} \times 100\%$

  • Result: $\%\text{ error} = -8.281\%$

  • Note: The negative sign indicates that the measured value was smaller than the accepted value.