## **1. Reaction Rates**
**Definition:** Reaction rate is the change in concentration of a reactant or product per unit time.
**Rate Expression:** Rate = Δ[concentration] / Δtime
**Key Points:**
- Rates are always positive (we use absolute values)
- For a given reaction, the rate of consumption of reactants equals the rate of formation of
products (when stoichiometry is considered)
- Rates can be measured in M/s, M/min, or other time units
**Example:** For the reaction 2A → B, if [A] decreases by 0.4 M in 2 seconds, the rate of
consumption of A is 0.2 M/s, and the rate of formation of B is 0.1 M/s.
--## **2. Rate Laws and Reaction Order**
**Rate Law:** An equation that relates the rate of a reaction to the concentrations of reactants.
**General Form:** Rate = k[A]^m[B]^n
- k = rate constant (depends on temperature)
- m, n = reaction orders (determined experimentally, NOT from stoichiometry)
- Overall order = m + n
**Reaction Orders:**
- **Zero Order:** Rate = k (rate is independent of concentration)
- **First Order:** Rate = k[A] (doubling [A] doubles the rate)
- **Second Order:** Rate = k[A]² or Rate = k[A][B] (doubling [A] quadruples the rate for Rate =
k[A]²)
--## **3. Integrated Rate Laws**
- **Zero Order:** [A] = [A]₀ - kt | Half-life: t₁/₂ = [A]₀ / 2k
- **First Order:** ln[A] = ln[A]₀ - kt | Half-life: t₁/₂ = 0.693 / k
- **Second Order:** 1/[A] = 1/[A]₀ + kt | Half-life: t₁/₂ = 1 / (k[A]₀)
**Key Insight:** The integrated rate law allows you to find concentration at any time or
determine the rate constant.
--## **4. Half-Life**
**Definition:** The time required for the concentration of a reactant to decrease to half its initial
value.
**Important Patterns:**
- **First Order:** Half-life is constant (independent of initial concentration)
- **Zero and Second Order:** Half-life depends on initial concentration
--## **5. Activation Energy and Temperature Dependence**
**Activation Energy (E_a):** The minimum energy required for reactants to form products.
**Arrhenius Equation:** k = Ae^(-E_a/RT)
- A = frequency factor (pre-exponential factor)
- E_a = activation energy (J/mol)
- R = gas constant (8.314 J/mol·K)
- T = absolute temperature (K)
**Two-Temperature Form:** ln(k₂/k₁) = (E_a/R)(1/T₁ - 1/T₂)
**Key Points:**
- Higher temperature → higher rate constant → faster reaction
- Lower activation energy → faster reaction
- A 10°C increase typically doubles or triples the reaction rate
--## **6. Reaction Mechanisms**
**Definition:** A series of elementary steps that add up to the overall reaction.
**Elementary Step:** A single molecular event; the order of an elementary step matches its
stoichiometry.
**Intermediate:** A species produced in one step and consumed in another (does not appear in
overall reaction).
**Rate-Determining Step (RDS):** The slowest step in the mechanism; it determines the overall
reaction rate.
**Example Mechanism:**
- Step 1 (slow): A + B → C
- Step 2 (fast): C + D → E + F
- Overall: A + B + D → E + F
**Key Points:**
- The rate law for the overall reaction is determined by the RDS and any pre-equilibrium steps
- Intermediates cancel out when elementary steps are added
- The mechanism must be consistent with the experimental rate law
--## **7. Catalysts**
**Definition:** A substance that increases reaction rate without being consumed.
**How Catalysts Work:**
- Provide an alternative reaction pathway with lower activation energy
- Do not change ΔG or ΔH of the reaction
- Appear in the mechanism but not in the overall equation
- Do not shift equilibrium position
**Types:**
- **Homogeneous Catalyst:** Same phase as reactants (e.g., H⁺ in aqueous solution)
- **Heterogeneous Catalyst:** Different phase from reactants (e.g., Pt surface in gas-phase
reaction)
--## **8. Collision Theory**
**Key Principles:**
- Reactions occur when reactant molecules collide with sufficient energy and proper orientation
- The fraction of collisions with energy ≥ E_a increases exponentially with temperature
- Proper orientation is crucial for effective collisions
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