Reaction Rate and Rate Law

Reaction Rate

• Depicts how fast reactants turn into products.
• Measures the change in the amount of reactants or products over time.

Rate Law

• Expresses the speed of a reaction by linking it to the amounts of substances involved.
• For $aA + bB \longrightarrow cC + dD$, the rate law is $rate = k[A]^m[B]^n$.
• $k$ signifies the rate constant, indicating reaction speed.
• $[A]$ and $[B]$ represent the concentration.
• $m$ and $n$ are the reaction orders with respect to $A$ and $B$.

Order of Reaction

• The sum of the exponents in the rate law, where $order = m + n$.
• Zero order reaction: rate is independent of reactant concentrations.
• First order reaction: rate is directly proportional to the concentration of one reactant.
• Second order reaction: rate is proportional to the square of one reactant, or the product of two.

Elementary Reactions

• Reactions occurring in a single step.
• Rate law can be derived from reaction stoichiometry.
• For $A + B \longrightarrow C$, the rate law is $rate = k[A][B]$.

Complex Reactions

• Reactions that proceed through multiple steps.
• Require experimental data to determine their rate law.

Factors Affecting Reaction Rate

• Temperature: Higher temperatures usually speed up reactions by increasing molecule kinetic energy.
• Concentration: Increased reactant concentration typically boosts reaction rate due to more frequent collisions.
• Catalyst: A substance that accelerates a reaction without being consumed, by lowering its activation energy.

Rate Constant

• Relates reaction rate to reactant concentrations.

Arrhenius Equation

• Formula connecting rate constant, temperature, and activation energy.
• $k = Ae^{-E_a/RT}$, where each symbol represents rate constant ($k$), frequency factor ($A$), activation energy ($E_a$), gas constant ($R$), and temperature in Kelvin ($T$).

Activation Energy

• The minimum energy needed for a reaction to occur.

Reaction Mechanisms

• Detail the sequence of steps in a reaction at a molecular level.

Rate-Determining Step

• The slowest step in a reaction mechanism, dictating the overall reaction rate.

Half-Life

• The time needed for a reactant's concentration to halve from its initial amount.

First-Order Reactions

• Exhibit a half-life independent of initial reactant concentration.
• $t_{1/2} = \frac{0.693}{k}$, with $t_{1/2}$ as half-life and $k$ as the rate constant.

Catalysis

• Speeds up reactions, and can be divided into two main types.
• Homogeneous Catalysis: Catalyst exists in the same phase as reactants.
• Heterogeneous Catalysis: Catalyst is in a different phase from the reactants.