Study Notes on Quantitative Calculations

Quantitative Calculations Study Notes

Topic I - Physical & Chemical Change

• Definition of Physical Change:

  • No new substances are formed.
  • This process is reversible.

• Definition of Chemical Change:

  • New substances are formed.
  • Matter is neither created nor destroyed; it is rearranged.
  • The particles rearrange to form new chemicals.

• Law of Conservation of Mass:

  • The total mass of the reactants is equal to the total mass of the products in a chemical reaction.

Indicators of Chemical Change

• Production of Light: e.g., flame formation.
• Effervescence: gas bubbles appear.
• Change in Smell: noticeable alteration in odor.
• Change in Colour: any alteration in the color of substances.
• Temperature Change: observable increase or decrease in temperature.
• Change in State of Matter: conversion from one state to another.

Topic I - The Three States of Matter

Solids

• Shape: Fixed shape.
• Ease of flow: Solids do not flow.
• Compressibility: Cannot be compressed.
• Summary:
  • Fixed shape & volume.
  • Do not flow.
  • Incompressible.

Liquids

• Ease of flow: Liquids flow easily.
• Compressibility: Cannot be compressed.
• Summary:
  • Fixed volume but no fixed shape.
  • Flow easily.
  • Incompressible.

Gases

• Shape: No fixed volume or shape; take the shape of their container.
• Volume and Pressure Relationship:
  • Volume is inversely proportional to pressure.
  • Pressure is directly proportional to temperature.
  • Relations:
  • + temperature = + pressure.
  • - temperature = - pressure.
  • + volume = - pressure.
  • - volume = + pressure.
• Ease of flow: Gases flow easily and occupy the entire space of their container.
• Compressibility: Gases are easy to compress.
• Summary:
  • No fixed volume or shape.
  • Flow easily & occupy all available space.
  • Compressible.

Particle Movement and Kinetic Energy

• Liquid particles have more kinetic energy (K.E.) than solids and can move in various directions over short distances.
• Solid particles vibrate; the more K.E. they gain, the faster they vibrate.
• Gas particles have the highest K.E., moving randomly and independently at high speeds, filling all available space.

Forces of Attraction Between Particles

• Strong forces of attraction in solids result in tightly packed particles.
• Weaker forces in liquids allow for some movement among particles.
• Very weak forces in gases are negligible, allowing particles to be far apart with large interstitial spaces.

Topic II - Changes of State

• Melting:

  • Occurs when solid particles are heated to their melting point, leading to the loss of orderly arrangement, transforming them into a liquid.

• Evaporation:

  • Liquid particles from the surface become gas at any temperature.

• Boiling:

  • Occurs throughout the mass of a liquid, with gas bubbles forming; happens at a fixed temperature if the liquid is pure.

• Condensation:

  • Gas particles cool down, leading to closer forces of attraction that form a liquid.

• Freezing:

  • Occurs when a liquid reaches the freezing point, with particles losing energy to join in a strong, ordered arrangement.

• Sublimation:

  • Solid turns directly into gas upon heating, with particles gaining sufficient K.E. to skip the liquid phase.
  • Example: ext{CO}_2 (s)
    ightarrow ext{CO}_2 (g).

• Deposition:

  • Gas particles lose energy and form a solid directly.
  • Examples:
  • ext{CO}_2 (g)
    ightarrow ext{CO}_2 (s).
  • ext{I}_2 (g)
    ightarrow ext{I}_2 (s).

• Melting and Freezing Point of Pure Water:

  • $0°C$

• Boiling Point of Pure Water:

  • $100°C$

Topic III - Heating & Cooling Curves

• Heating Curve:

  • A graphical representation of the stages in which a solid turns into a liquid and subsequently into a gas.

• Cooling Curve:

  • A graphical representation of the stages in which a gas becomes a liquid and then a solid.

• Sublimation Heating Curve:

  • Illustrates a substance bypassing the liquid stage upon heating.

Topic IV - Predicting the Physical State of a Substance

• If given temperature < melting point:

  • State of the substance: Solid.

• If melting point < given temperature < boiling point:

  • State of the substance: Liquid.

• If given temperature > boiling point:

  • State of the substance: Gas.

Subtopic: Pressure in Gases

• Definition of Pressure in Gases:
  • Caused by collisions of gas particles with container walls.

Factors Affecting Gas Pressure

• Change in Temperature:

  • Pressure is directly proportional to temperature (volume constant).

• Change in Volume:

  • Pressure is inversely proportional to volume (temperature constant).

• Mathematical Relationships:

  1. Given that volume is constant:
     T
     ightarrow P (directly proportional)
  2. Given that temperature is constant:
     V
     ightarrow P (inversely proportional)

Subtopic: Diffusion

• Definition of Diffusion:
  • The movement of particles from high concentration to low concentration regions until evenly distributed.

Topic V - Quantitative Calculations

Empirical & Molecular Formulae

• Empirical Formula:

  • Simplified formula representing the simplest whole-number ratio of elements in a compound.

• Molecular Formula:

  • Representation of the actual number of atoms of each element in a molecule.

Constructing Molecular Formula from Empirical Formula

• Formula:
  $ext{RMM of molecular formula} ext{ / RMM of the empirical formula} = ext{Whole number multiplier}$.

• Example:

  • Given empirical formula: $ext{CH}_2$
  • RMM calculation:
  • $12 + (1 imes 2) = 14$.
  • Given Molecular RMM:
  • $84$.
  • Calculation:
  • $84 / 14 = 6$.
  • Final Molecular Formula:
  • $ext{C}<em>6 ext{H}</em>{12}$.

Experimental Determination of Empirical Formulae

Metal Oxide and Hydrated Salt

• Experiment Steps for Metal Oxide Determination.
• Experiment Steps for Hydrated Salt Determination:
  • A salt with water of crystallization.

Stoichiometry

• Definition and Reference:
  Refer to page 22 (Quantitative Calculations).

Avogadro's Law

• Statement:

  • 1 mole of any gas occupies $22.4 ext{ dm}^3$ at STP (Standard Temperature and Pressure).

• Conversions:

  • $1 ext{ dm}^3 = 1000 ext{ cm}^3$.
  • $22.4 ext{ dm}^3 = 22400 ext{ cm}^3$.

Percentage Yield Calculation

• Formula:
  ext{Percentage yield} = rac{ ext{actual mass obtained}}{ ext{theoretical mass}} imes 100 ext{ \}

Mass Calculations Procedure

• For questions, utilize formulas:
  • Bottom/top ratio or given/theoretical ratio.
  • Example Procedure:
  • Mass of crucible + hydrated $ext{MgSO}_4$ - mass of crucible = mass of hydrated $ext{MgSO}_4$.
  • Mass of crucible + anhydrous $ext{MgSO}_4$ - mass of crucible = mass of anhydrous $ext{MgSO}_4$.
  • Mass of hydrated $ext{MgSO}_4$ - mass of anhydrous $ext{MgSO}_4$ = water removed.

Common States of Matter and Particles

Arrangement and Movement of Particles

Common Polyatomic Ions

• NH₄: Ammonium
• CO₃²⁻: Carbonate
• HCO₃⁻: Hydrogen carbonate (bicarbonate)
• NO₂⁻: Nitrite
• NO₃⁻: Nitrate
• SO₃²⁻: Sulfite
• SO₄²⁻: Sulfate
• CIO-ClO₃⁻: Chlorate
• OH⁻: Hydroxide
• C₂H₃O₂⁻: Acetate
• CN⁻: Cyanide
• PO₄³⁻: Phosphate

Formulas of Common Acids and Bases

Temperature and State of Substance

• If given temperature < melting point:
  • Substance is Solid.
• If the temperature is between melting and boiling point:
  • Substance is Liquid.
• If the temperature > boiling point:
  • Substance is Gas.