Meditaliano IMAT Chemistry

Lesson 14: Chemical Kinetics, Equilibrium, Acids & Bases, and Redox (Extended)

Unit 1: Solutions & Solubility

The core of this unit is understanding how the number of particles affects physical properties (Colligative properties) and how to prepare solutions accurately. Solvation is the interaction of a solute with the solvent, which leads to stabilization of the solute species in the solution.

1. Basics of Solutions

Visualizing Solvation (NaCl in Water)

Na+ Cl-

Hydration: Water molecules orient themselves based on charge. Oxygen ($\delta-$) faces Cations, Hydrogens ($\delta+$) face Anions.

Visualizing Solvation of NaCl (Hydration Process)

Solvation of NaCl

This diagram shows how water molecules surround Na+ and Cl- ions. The oxygen atoms ($\delta-$) orient towards the sodium cation, while the hydrogen atoms ($\delta+$) face the chloride anion.

  • Solute: The substance being dissolved (e.g., Salt).
  • Solvent: The liquid doing the dissolving (e.g., Water).
  • Solution: Homogeneous mixture of Solute + Solvent.

Concentration Units: The Critical Distinction

Unit Symbol Formula Temp Dependent? Use Case
Molarity $M$ $M = \frac{\text{moles solute}}{\text{Liters solution}}$ YES Stoichiometry, Titrations.
Volume changes with temp.
Molality $m$ $m = \frac{\text{moles solute}}{\text{kg solvent}}$ NO Colligative Properties ($T_f, T_b$).
Mass is invariant.

2. Colligative Properties

Properties that depend only on the number of particles, not their identity. This means 1 mole of glucose and 1 mole of urea have the same effect, but 1 mole of NaCl has double the effect due to dissociation.

A. Vapor Pressure Lowering (Raoult's Law)

Solute particles block the surface, preventing solvent evaporation. Vapor pressure decreases. The more solute particles present, the harder it is for solvent molecules to escape into the gas phase.

Pure Solvent Solution > Vapor Pressure
B. Boiling Point Elevation & Freezing Point Depression

Because vapor pressure lowers, the liquid must be heated higher to boil, and cooled lower to freeze.

$$\Delta T_b = i \cdot K_b \cdot m$$ $$\Delta T_f = i \cdot K_f \cdot m$$
CRITICAL CONCEPT: The Van't Hoff Factor ($i$)
You must multiply by the number of particles formed in solution.
  • Glucose (Non-electrolyte): Does not split. $i = 1$
  • $NaCl$ (Electrolyte): Splits into $Na^+ + Cl^-$. $i = 2$
  • $CaCl_2$ (Electrolyte): Splits into $Ca^{2+} + 2Cl^-$. $i = 3$

3. Solution Preparation & Lab

A. Dilution Formula

Used to make a specific concentration from a stock solution. The key principle is that the moles of solute remain constant before and after dilution.

$$M_1 V_1 = M_2 V_2$$

B. Lab Equipment & Safety

Volumetric Flask

Used for precise concentrations. Read the Meniscus at eye level. The bottom of the curve must touch the line.

(Eye Level) --- ‿ --- (Line)
Copper(II) Sulfate ($CuSO_4$)
  • Hydrated ($ \cdot 5H_2O$): Blue Crystals (Water present).
  • Anhydrous: White Powder (No water).
  • Safety: Irritant & Toxic to aquatic life. Dispose in specific waste containers (Heavy Metal), not the sink.
IMAT Challenge

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Question 101 Official Paper: 2018 - Q42

Which one of the following substances has the highest solubility in the specified liquid at a temperature of $298\text{ K}$ and $1\text{ atm}$ pressure?

Unit 2: Chemical Kinetics

1. Collision Theory

For a reaction to occur, molecules must collide with sufficient energy and correct orientation. Only a fraction of collisions result in a reaction.

  1. Collision: Particles must physically hit each other.
  2. Energy: Must have $E \ge E_a$ (Activation Energy). This energy is needed to break existing bonds.
  3. Orientation: Steric factor. The reactive parts of the molecules must face each other.

Maxwell-Boltzmann Distribution (Temperature Effect)

Kinetic Energy # Molecules Low Temp (T1) High Temp (T2) Ea

The shaded area shows particles with $E \ge E_a$. Increasing T flattens the curve and shifts it right, increasing the area under the curve past Ea.

Effect of Temperature on Particle Energy Distribution (Kinetics)

Reaction Kinetics

This graph illustrates the distribution of kinetic energy at low (blue) and high (red) temperatures. It highlights the activation energy (Ea) threshold and demonstrates how increasing the temperature significantly increases the fraction of molecules with energy $E \ge E_a$.

2. Rate Laws & Orders

Order Rate Law Half-Life ($t_{1/2}$) Linear Plot ($y$ vs $t$) Units of $k$
0 Rate $= k$ Decreases with time $[A]$ is linear $M \cdot s^{-1}$
1 Rate $= k[A]$ Constant ($0.693/k$) $\ln[A]$ is linear $s^{-1}$
2 Rate $= k[A]^2$ Increases with time $1/[A]$ is linear $M^{-1} \cdot s^{-1}$

Unit 3: Equilibrium & Thermodynamics

1. Thermodynamics Basics

Spontaneity is determined by Gibbs Free Energy ($\Delta G$). The equation combines enthalpy (heat content) and entropy (disorder):

$$\Delta G = \Delta H - T\Delta S$$

Conditions for Spontaneity ($\Delta G < 0$)

Enthalpy ($\Delta H$) Entropy ($\Delta S$) Result
Exothermic (-) Increase (+) Always Spontaneous
Endothermic (+) Decrease (-) Never Spontaneous
Exothermic (-) Decrease (-) Spontaneous at Low T
Endothermic (+) Increase (+) Spontaneous at High T
Connection to Equilibrium

Gibbs free energy change under standard conditions ($\Delta G^\circ$) determines the position of equilibrium, represented by the Equilibrium Constant ($K$):

$$\Delta G^\circ = -RT \ln K$$
  • If $\Delta G^\circ < 0$, then $K > 1$ (Products favored). Reaction is spontaneous forward.
  • If $\Delta G^\circ > 0$, then $K < 1$ (Reactants favored). Reaction is non-spontaneous forward.
  • If $\Delta G^\circ = 0$, then $K = 1$. The system is at equilibrium.

2. Dynamic Equilibrium ($K_c$ vs $Q$)

Concept: Equilibrium is not static. It is "dynamic" because the forward and reverse reactions are still happening, but at the same rate. Imagine walking up a "down" escalator at the exact same speed it moves down; you are moving, but your position doesn't change.

Rate vs Time (Reaching Equilibrium)

Time Reaction Rate Forward Rate Reverse Rate Equilibrium Reached Rates become equal

Dynamic Equilibrium and Le Chatelier's Adjustments (System Shifts)

Le Chatelier's Principle

This diagram visualizes the state of dynamic equilibrium where the rates of the forward and reverse reactions are equal. It also shows how the system shifts in response to external stresses (concentration, pressure, temperature) according to Le Chatelier's Principle.

The Law of Mass Action

For a general reaction $aA + bB \rightleftharpoons cC + dD$:

$$K_c = \frac{[C]^c [D]^d}{[A]^a [B]^b}$$
  • Heterogeneous Equilibrium: Pure solids ($s$) and liquids ($l$) have constant concentration, so they are excluded from the expression. Only gases ($g$) and aqueous solutions ($aq$) are included.
  • $K_p$ vs $K_c$: For gases, we use partial pressures. $K_p = K_c(RT)^{\Delta n}$, where $\Delta n = \text{moles gas products} - \text{moles gas reactants}$.

The Reaction Quotient ($Q$)

$K$ tells you where you want to be. $Q$ tells you where you are right now. Calculated exactly like $K$, but using current concentrations.

  • $Q < K$: The numerator (products) is too small. The system must shift RIGHT ($\rightarrow$) to make more products.
  • $Q > K$: The numerator is too big. The system must shift LEFT ($\leftarrow$) to consume products.
  • $Q = K$: The system is at equilibrium. No net change.

Le Chatelier's Principle: Detailed Analysis

If a stress is applied to a system at equilibrium, the system shifts to relieve that stress.

Disturbance Shift Logic Effect on $K$
Add Reactant System consumes excess reactant. Shifts RIGHT. No Change
Remove Product System tries to replace missing product. Shifts RIGHT. No Change
Increase Pressure
(Decrease Volume)		 System wants to reduce pressure. Shifts to side with FEWER moles of gas. No Change
Increase Temp
(Exothermic $\Delta H < 0$)		 Heat is a product ($A \rightleftharpoons B + \text{Heat}$). Adding heat pushes reaction LEFT. Decreases
Increase Temp
(Endothermic $\Delta H > 0$)		 Heat is a reactant ($\text{Heat} + A \rightleftharpoons B$). Adding heat pushes reaction RIGHT. Increases
Catalyst Lowers $E_a$ for both forward and reverse equally. Equilibrium is reached faster, but position does not change. No Change
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Question 105 Official Paper: 2023 - Q40

At a given temperature, the $K$ value of a gaseous exothermic reaction is equal to $7 \times 10^{-5}\text{ dm}^{6}\text{ mol}^{-2}$. Which one of the following statements is correct?

Unit 4: Acids & Bases

1. Three Definitions of Acids

It is crucial to distinguish between the three historical definitions.

  • Arrhenius:
    Acid: Produces $H^+$ in water. Base: Produces $OH^-$ in water.
    Limitation: Only works in aqueous solutions.
  • Brønsted-Lowry (Most Common):
    Acid: Proton ($H^+$) Donor. Base: Proton ($H^+$) Acceptor.
    Example: $NH_3 + H_2O \rightleftharpoons NH_4^+ + OH^-$. Here $NH_3$ accepts a proton (Base), $H_2O$ donates it (Acid).
  • Lewis (Broadest):
    Acid: Electron Pair Acceptor (Electrophile).
    Base: Electron Pair Donor (Nucleophile).
    Example: $BF_3$ is a Lewis Acid (incomplete octet, accepts electrons).

2. Strong vs Weak

Key Concept: Determine if it's Strong (100% dissociation) or Weak (Equilibrium).

H+ A-

Strong Acid

100% Dissociated

Weak Acid

Partial Dissociation

Strong Acids/Bases

100% Dissociation ($\rightarrow$)

Acids: $HCl, HNO_3, H_2SO_4, HClO_4$

Bases: Group 1 Hydroxides ($NaOH, KOH$)

$$pH = -\log[H^+]$$
Weak Acids/Bases

Partial Dissociation ($\rightleftharpoons$)

Examples: $CH_3COOH, NH_3$

Use $K_a$ (Acid Dissociation Constant).

$$[H^+] \approx \sqrt{K_a \cdot C}$$
The Auto-ionization of Water & pH Scale

Water acts as both an acid and a base (Amphoteric).

$$2H_2O(l) \rightleftharpoons H_3O^+(aq) + OH^-(aq)$$

At 25°C, the equilibrium constant ($K_w$) is $1.0 \times 10^{-14}$.

$$K_w = [H^+][OH^-] = 10^{-14}$$ $$pK_w = pH + pOH = 14$$

This implies that if $[H^+]$ goes up (acidic), $[OH^-]$ must go down to keep the product constant.

Comparison of Acid-Base Definitions & The pH Scale

Acid-Base Concepts

This visual guide compares the three major acid-base definitions (Arrhenius, Brønsted-Lowry, and Lewis) and displays the pH scale with a color gradient from acidic to basic.

3. Titration Analysis

Titration is a technique to determine the unknown concentration of an analyte by neutralizing it with a titrant of known concentration.

Titration Curves

The shape of the pH curve depends on the strength of the acid and base.

  • Strong Acid + Strong Base:
    Starts at low pH (e.g., 1). Very flat, then huge vertical jump. Equivalence point is exactly pH 7.
  • Weak Acid + Strong Base:
    Starts higher (e.g., pH 3). Rises initially, then flattens (Buffer Region). Equivalence point is Basic (pH > 7) due to conjugate base hydrolysis.
    Half-Equivalence Point: The point where half the acid is neutralized. Here, $pH = pK_a$.
  • Strong Acid + Weak Base:
    Equivalence point is Acidic (pH < 7) due to conjugate acid hydrolysis.
Equivalence Point Theoretical point where moles Acid = moles Base.
End Point Experimental point where indicator changes color.
Phenolphthalein Acid: Colorless $\rightarrow$ Base: Pink (Range pH 8.2-10). Ideal for Weak Acid vs Strong Base.
Safety: The "AAA" Rule

Always Add Acid to Water.
Never add water to concentrated acid. It will boil instantly and splash (Exothermic).
NaOH Safety: Caustic (dissolves skin/eyes), Exothermic when dissolved, Deliquescent (absorbs water from air). Wear goggles.

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Question 116 Official Paper: 2022 - Q51

The general formula of an oxoacid is $\text{H}_{m}\text{X}\text{O}_{n}$. Which of the following expressions gives the oxidation state of element $\text{X}$?

Unit 5: Hydrolysis & Buffer Systems

1. Salt Hydrolysis Matrix

When salts dissolve, the ions can react with water to change pH. The rule of thumb: "The Stronger Parent Dominates."

Salt Parent Acid Parent Base Resulting pH Reason
$NaCl$ Strong ($HCl$) Strong ($NaOH$) Neutral (7) Neither ion reacts with water.
$CH_3COONa$ Weak Strong Basic (>7) Anion ($CH_3COO^-$) acts as a base:
$A^- + H_2O \rightarrow HA + OH^-$
$NH_4Cl$ Strong Weak Acidic (<7) Cation ($NH_4^+$) acts as an acid:
$NH_4^+ \rightarrow NH_3 + H^+$

2. Buffer Systems: The "Sponge"

A buffer is a solution that resists changes in pH upon the addition of small amounts of acid or base. It consists of a Weak Acid ($HA$) and its Conjugate Base ($A^-$).

Visual Mechanism (Common Ion Effect)

Add Acid ($H^+$)

The Base reserve ($A^-$) absorbs it:

$$A^- + H^+ \rightarrow HA$$

Strong H+ becomes weak HA.

Add Base ($OH^-$)

The Acid reserve ($HA$) neutralizes it:

$$HA + OH^- \rightarrow A^- + H_2O$$

Strong OH- becomes water.

Calculation: Henderson-Hasselbalch Equation

Used to calculate the pH of a buffer solution.

$$pH = pK_a + \log\left(\frac{[A^-]}{[HA]}\right)$$
Practical Applications
  • Buffer Capacity: The amount of acid/base a buffer can absorb before pH changes significantly. Highest when $[HA] = [A^-]$ (high concentration is better).
  • Blood Buffer System: Our blood pH (7.4) is maintained by the Carbonic Acid / Bicarbonate system:
    $$CO_2 + H_2O \rightleftharpoons H_2CO_3 \rightleftharpoons H^+ + HCO_3^-$$
    Breathing faster (Hyperventilation) removes $CO_2$, shifting equilibrium left (lowering $H^+$), causing Alkalosis.

Unit 6: Redox & Electrochemistry

1. Basics (OIL RIG)

Memory Aid OIL RIG

Oxidation Is Loss (of e-)
Reduction Is Gain (of e-)

Galvanic Cell An Ox / Red Cat

Anode = Oxidation
Reduction = Cathode

Rules for Assigning Oxidation Numbers

Follow these rules in order of priority:

  1. Elements: Free elements ($Na, O_2, Cl_2$) are always 0.
  2. Ions: Monatomic ions equal their charge ($Na^+ = +1$).
  3. Fluorine: Always -1 in compounds.
  4. Oxygen: Usually -2 (Exceptions: Peroxides $H_2O_2$ are -1, with F it is +2).
  5. Hydrogen: Usually +1 (Exception: Metal hydrides $NaH$ are -1).
  6. Sum: Sum of numbers in a neutral compound is 0. In a polyatomic ion, it equals the charge.

Oxidizing Agent: The substance getting reduced (causes oxidation).
Reducing Agent: The substance getting oxidized (causes reduction).

2. Electrochemical Cells

There are two main types of cells. It is vital to know the difference.

Feature Galvanic (Voltaic) Cell Electrolytic Cell
Spontaneity Spontaneous ($\Delta G < 0$) Non-Spontaneous ($\Delta G > 0$)
Purpose Produces Electricity (Battery) Consumes Electricity (Plating/Lysis)
Anode Charge Negative (-) (Source of e-) Positive (+) (Attached to + terminal)
Cathode Charge Positive (+) Negative (-)
Reaction Oxidation at Anode Oxidation at Anode

The Galvanic Cell (The Daniell Cell)

V e- Flow → Anode (Zn) Oxidation (-) Cathode (Cu) Reduction (+)

Salt Bridge allows ions to flow to balance charge. Electrons flow Anode $\rightarrow$ Cathode.

Mechanism of a Galvanic Cell (Daniell Cell)

Galvanic Cell

This detailed diagram of a Zn-Cu galvanic cell shows the arrangement of the anode (Zn), cathode (Cu), salt bridge, external circuit, and voltmeter. It indicates the direction of electron flow and the half-reactions occurring at each electrode.

$$E^\circ_{cell} = E^\circ_{cathode} - E^\circ_{anode}$$ Standard Reduction Potentials are used. The more positive $E^\circ$, the stronger the oxidizing agent (wants e- more).

3. pH Meter Principle

Glass Membrane H+ Sensitive Storage: KCl Soln
  • Principle: Measures potential difference caused by $[H^+]$ difference across a special glass membrane (based on Nernst Eq).
  • Calibration: Must use buffer solutions (pH 4.01, 7.00, 9.21) before use to account for temperature and electrode drift (slope).
  • Storage: Keep wet in 3M KCl solution. Never store in distilled water, as it leaches ions from the glass membrane, slowing response time.
IMAT Challenge

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Question 124 Official Paper: 2012 - Q61

In the following reactions, which substances are acting as oxidising agents?
$\text{C}(\text{s})+\text{O}_{2}(\text{g})\rightarrow \text{CO}_{2}(\text{g})$
$2\text{Fe}^{3+}(\text{aq})+2\text{I}^{-}(\text{aq})\rightarrow 2\text{Fe}^{2+}(\text{aq})+\text{I}_{2}(\text{aq})$
$\text{Mg}(\text{s})+2\text{H}^{+}(\text{aq})\rightarrow \text{Mg}^{2+}(\text{aq})+\text{H}_{2}(\text{g})$
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Question 122 Official Paper: 2014 - Q45

A battery has lead plates dipped in sulfuric acid. When charged, the positive plate is covered with $\text{PbO}_{2}$. After discharge both plates are covered with $\text{PbSO}_{4}$. Which option below correctly describes the overall change in the oxidation number of the lead involved in the chemical reaction during discharge?
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Question 118 Official Paper: 2019 - Q42

Which of the following equations represent(s) a redox reaction?
1 $4\text{LiH} + \text{AlCl}_{3} \rightarrow 3\text{LiCl} + \text{LiAlH}_{4}$
2 $\text{N}_{2}\text{O}_{3} + 3\text{H}_{2}\text{O} \rightarrow 2\text{H}_{3}\text{O}^{+} + 2\text{NO}_{2}^{-}$
3 $\text{NH}_{4}\text{NO}_{3} \rightarrow 2\text{H}_{2}\text{O} + \text{N}_{2}\text{O}$

Master Formula Sheet

Equilibrium
$$K_c = \frac{[Products]}{[Reactants]}$$
$$K_p = K_c(RT)^{\Delta n}$$
$$K_w = [H^+][OH^-] = 10^{-14}$$
$$\Delta G^\circ = -RT \ln K$$
pH & Buffers
$$pH = -\log[H^+]$$
$$[H^+]_{weak} \approx \sqrt{K_a \cdot C}$$
$$pH = pK_a + \log\frac{[A^-]}{[HA]}$$
$$E^\circ_{cell} = E^\circ_{red, cat} - E^\circ_{red, an}$$

Final Exam (20 Questions)

Comprehensive review of Units 1-6.