Ib chemistry – Reactivity 2

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IB Chemistry: Reactivity 2 Mastery
IB Chemistry Course Companion

REACTIVITY 2

How Much, How Fast & How Far?

Ea

Mole Ratio • Collision Theory • Le Châtelier • Rates • Equilibrium

CORE

2.1 How Much? (Stoichiometry)

1. The Mole Ratio

Chemical equations are recipes. The coefficients tell you the ratio of moles, not grams.

Avogadro's Law (Gases)

At the same temperature and pressure, Mole ratio = Volume ratio.

N2(g) + 3H2(g) → 2NH3(g)
10 dm3 N2 reacts with 30 dm3 H2

2. Yields & Limiting Reactant

Limiting Reactant

Examiner Tip: Calculate $\frac{\text{Moles}}{\text{Coefficient}}$ for each reactant. The smallest number is the limiting reactant.

Percentage Yield
$\frac{\text{Experimental Mass}}{\text{Theoretical Mass}} \times 100$

Measures Reaction Efficiency

3. Atom Economy (Green Chemistry)

Measures waste, not just yield.

$\text{Atom Economy} = \left( \frac{\text{Molar Mass of Desired Product}}{\text{Total Molar Mass of Reactants}} \right) \times 100$
CORE

2.2 How Fast? (Kinetics)

1. Collision Theory

For a reaction to occur, particles must collide with:

1. Energy $\ge E_a$
2. Correct Orientation

2. Maxwell-Boltzmann Distribution

Shows the distribution of kinetic energy among particles.

Kinetic Energy # Particles Low T High T Ea
Effect of Higher Temperature
  • Curve flattens and peak shifts right.
  • Total Area stays constant (same number of particles).
  • Key Result: Significant increase in the area past $E_a$ (more successful collisions).

3. Factors Affecting Rate

Factor Microscopic Explanation
ConcentrationMore particles per unit volume $\rightarrow$ collision frequency $\uparrow$
Surface AreaMore particles exposed $\rightarrow$ collision frequency $\uparrow$
TemperatureMajor: More particles have $E \ge E_a$.
Minor: Particles move faster (frequency $\uparrow$).
CatalystProvides an alternative pathway with Lower $E_a$.
CORE

2.3 How Far? (Equilibrium)

1. Dynamic Equilibrium

Examiner Definition
  1. Rate of Forward reaction = Rate of Backward reaction.
  2. Concentrations of reactants and products remain constant (not necessarily equal).
  3. Occurs in a Closed System.

2. The Equilibrium Law ($K_c$)

$$ K_c = \frac{[Products]^{coef}}{[Reactants]^{coef}} $$
$K_c$ is ONLY changed by Temperature.

3. Le Châtelier's Principle

When a system at equilibrium is subjected to a change, it will shift to minimize that change.

Change Shift Direction Value of $K_c$
Add ReactantRight (Make Product)No Change
Increase PressureTo side with fewer gas molesNo Change
Add CatalystNone (Rates increase equally)No Change
Increase T (Exo)Left (Absorb Heat)Decreases
Increase T (Endo)Right (Absorb Heat)Increases
Trap Alert

Do not confuse Rate with Yield.
Increasing T in an Exothermic reaction increases Rate (faster) but decreases Yield (less product).

⛔️ STOP HERE IF YOU ARE SL

Advanced Theory

The following section is for HL Students ONLY.
Rate Laws • Mechanisms • Arrhenius • Gibbs Energy

AHL

Rate Expressions

1. The Rate Law

The rate law is derived experimentally, NOT from the balanced equation.

Rate $= k [A]^m [B]^n$
Zero Order Rate independent of $[A]$
First Order Rate $\propto [A]$
Second Order Rate $\propto [A]^2$
Cheat Code: Units of k

$mol^{1-\text{order}} dm^{3(\text{order}-1)} s^{-1}$

Example (Order 3): $mol^{-2} dm^6 s^{-1}$

2. Mechanisms & RDS

  • RDS (Rate Determining Step): The Slowest Step. The reaction bottleneck.
  • The Rate Law depends only on species involved in the RDS (and any prior steps).
  • Complex Case: If Step 1 is a fast equilibrium before the RDS, substitute intermediate concentration using $K_{eq}$.
AHL

The Arrhenius Equation

Quantifies exactly how the Rate Constant ($k$) changes with Temperature.

$\ln k = -\frac{E_a}{R} \left( \frac{1}{T} \right) + \ln A$
1/T ln k Gradient = -Ea/R
Graphical Analysis
  • Y-axis: $\ln k$
  • X-axis: $1/T$ (Kelvin)
  • Gradient ($m$): $-E_a/R$
Trap Alert: $R = 8.31 J$. Exam questions usually ask for $E_a$ in kJ. Don't forget to divide by 1000!
AHL

Gibbs Energy & Equilibrium

1. Reaction Quotient ($Q$)

Ratio of concentrations at any time, not just equilibrium.

$Q < K$
Shift Right $\rightarrow$
$Q = K$
Equilibrium
$Q > K$
$\leftarrow$ Shift Left

2. Relating $\Delta G$ and $K$

$\Delta G^{\ominus} = -RT \ln K$

This equation links Spontaneity to Equilibrium Position.

  • If $\Delta G$ is negative, $\ln K$ is positive $\rightarrow K > 1$ (Products Favored).
  • If $\Delta G$ is positive, $\ln K$ is negative $\rightarrow K < 1$ (Reactants Favored).

The Examiner's Vault

Strictly assessed on Reactivity 2 content.

1. Limiting Reactant Logic CORE

Reaction: N2 + 3H2 → 2NH3.
Mixed: 2.0 mol N2 and 3.0 mol H2. What is the max NH3 produced?

2. Le Châtelier (Haber Process) CORE

N2(g) + 3H2(g) ↔ 2NH3(g)   $\Delta H = -92 kJ$.
Which change increases the value of $K_c$?

HL
3. Rate Constant Units

Rate doubles when [A] doubles. Quadruples when [B] doubles. What are the units of $k$?

4. Maxwell-Boltzmann Sketch

Sketch curves for T1 and higher temp T2. Explain rate increase.

HL
5. Mechanism Analysis

Step 1: NO + Cl2 ↔ NOCl2 (Fast Eq)
Step 2: NOCl2 + NO → 2NOCl (Slow)
Deduce Rate Law.

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