Chemical Kinetics: Reaction Rates and Rate Laws

• Chemical kinetics studies reaction rates, how rates change with conditions, and reaction mechanisms.

Reaction Rate

• For a reaction $aA + bB \rightarrow cC + dD$, the rate is expressed as: $rate = -\frac{1}{a}\frac{d[A]}{dt} = -\frac{1}{b}\frac{d[B]}{dt} = \frac{1}{c}\frac{d[C]}{dt} = \frac{1}{d}\frac{d[D]}{dt}$

Factors Affecting Reaction Rate

• Reactant concentration: Increased concentration usually increases reaction rate.
• Temperature: Increased temperature usually increases reaction rates.
• Surface area: Increased surface area (for solids) increases reaction rate.
• Catalysts: Speed up reactions via alternate pathways with lower activation energy.
• Pressure: Increased pressure (for gaseous reactions) can increase the reaction rate.

Rate Law

• Expresses the relationship between reaction rate and reactant concentrations
• For a general reaction $aA + bB \rightarrow cC + dD$, the rate law is typically: $rate = k[A]^m[B]^n$
• k: rate constant
• m: reaction order with respect to A
• n: reaction order with respect to B
• Overall reaction order: m + n

Integrated Rate Laws

• Relate reactant concentration to time
• Zero-Order: $rate = k$, $[A]_t = -kt + [A]_0$
• First-Order: $rate = k[A]$, $ln[A]_t = -kt + ln[A]_0$
• Second-Order: $rate = k[A]^2$, $\frac{1}{[A]_t} = kt + \frac{1}{[A]_0}$
• $[A]_t$: concentration of A at time t
• $[A]_0$: initial concentration of A

Half-Life ($t_{1/2}$)

• Time for reactant concentration to halve
• Zero-Order: $t_{1/2} = \frac{[A]_0}{2k}$
• First-Order: $t_{1/2} = \frac{0.693}{k}$
• Second-Order: $t_{1/2} = \frac{1}{k[A]_0}$

Collision Theory

• For a reaction to occur:
• Reactant molecules must collide
• Molecules must collide with sufficient energy (activation energy)
• Molecules must collide with proper orientation

Arrhenius Equation

• Describes temperature dependence of reaction rates
• $k = Ae^{-\frac{E_a}{RT}}$
• k: rate constant
• A: pre-exponential factor
• $E_a$: activation energy
• R: gas constant (8.314 J/mol·K)
• T: absolute temperature (Kelvin)

Reaction Mechanisms

• Step-by-step sequence of elementary reactions for overall chemical change
• Elementary Step: Single step in a reaction mechanism
• Rate-Determining Step: Slowest step, determines overall reaction rate
• Intermediate: Species produced in one step, consumed in a subsequent step

Catalysis

• A catalyst speeds up a chemical reaction without being consumed.

Types of Catalysis

• Homogeneous Catalysis: Catalyst in the same phase as reactants
• Heterogeneous Catalysis: Catalyst in a different phase from reactants
• Enzyme Catalysis: Biological catalysts for biochemical reactions

Catalytic Mechanism

• Catalysts provide an alternative pathway with lower activation energy, increasing reaction rate.

Explore chemical kinetics, focusing on reaction rates and the factors influencing them. Understand how reactant concentration, temperature, surface area, catalysts, and pressure affect reaction speeds. Learn about rate laws and how they relate reaction rates to reactant concentrations.