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Study Summary - Chemical Kinetics Summary
Summary of Chapter 26: Chemical Kinetics 1 – Rate Laws This chapter introduces chemical kinetics , focusing on the rate laws that describe how chemical reactions change over time. Key topics include rate laws, experimental determination of reaction rates, integrated rate equations, temperature dependence of rate constants, and reversible reactions.
1. Rate Laws and Time Dependence of Chemical
Reactions
A rate law expresses the rate of reaction in terms of reactant concentrations:
where: is the rate constant , and are reaction orders , determined experimentally. Extent of reaction (ξ) is introduced to relate concentration changes to stoichiometry:
where is the initial amount of reactant A. Reaction rate definitions :
2. Determining Rate Laws Experimentally
Method of Initial Rates : Measure reaction rate at different concentrations, then compare:
v = k [ A ] m^ [ B ] n
k m n
n (^) A ( t ) = n (^) A (0) − v (^) Aξ ( t ) n (^) A (0)
v = − (^) v^1 Ad dt [ A ]^ =− (^) v^1 Bd dt [ B ]= v^1 Y d dt [ Y^ ]
Logarithmic transformation is used to solve for and. Method of Isolation : Keep one reactant in large excess so its concentration remains constant, reducing the rate law to a pseudo-first-order form. Example: The reaction follows the rate law:
3. Integrated Rate Laws for First- and Second-Order
Reactions
First-Order Reaction:
Half-life: Second-Order Reaction:
Half-life: Example: Uranyl nitrate decomposition follows first-order kinetics, with data used to determine at different temperatures.
4. Temperature Dependence of Rate Constants –
Arrhenius Equation
The rate constant follows the Arrhenius equation :
where:
v^ v 21 =(^ [^ [ AA ]] 21 )
mA ( (^) [^ [ BB ]] 21 )
mB
mA mB
N O 2 + F 2 → N O 2 F
v = k [ N O (^) 2 ][ F (^) 2 ]
ln[ A ] = ln[ A ] 0 − kt t (^) 1/2 =^ 0.693 k
[ A^1 ]^ = [ A^1 ]^0 + kt t (^) 1/2 = k [ A^1 ] 0
k
k = Ae − E^ a / RT
Solve for equilibrium extents of reactions.
Conclusion This chapter provides a foundation in chemical kinetics , focusing on rate laws , experimental determination, mathematical integration of rate equations, and temperature dependence. Understanding these concepts is essential for analyzing reaction dynamics in chemical systems.
Summary of Chapter 27: Chemical Kinetics II – Reaction Mechanisms This chapter focuses on reaction mechanisms , which describe the steps by which reactants are converted into products. It introduces elementary reactions, complex reactions, rate laws, kinetic approximations, and catalysis.
1. Elementary Reactions and Molecularity
Elementary reactions occur in a single step. The rate law for an elementary reaction is derived directly from its balanced equation: Unimolecular reaction ( products): Bimolecular reaction ( products): Termolecular reaction ( products): Example 27-1: Deduce rate laws for different reactions.
2. Principle of Detailed Balance
In equilibrium, the forward and reverse reaction rates are equal for each step in a reaction mechanism. For a reversible elementary reaction:
A → v = k [ A ] A + B → v = k [ A ][ B ] A + B + C → v = k [ A ][ B ][ C ]
Forward rate: Reverse rate: At equilibrium: Example 27-2 & 27-3: Show equilibrium constant derivations.
3. Distinguishing Single-Step vs. Consecutive Reactions
Some reactions occur via multiple steps rather than a single-step process. If one step is much slower than the others, it is the rate-determining step. Example 27-4: How to distinguish mechanisms when the second step is rate- determining.
4. Steady-State Approximation
Assumes that the concentration of intermediates remains constant during the reaction. For a two-step mechanism:
If the second step is fast, we set. Example: Decomposition of ozone ( ). Example 27-5: Apply steady-state approximation to ozone decomposition.
5. Rate Law and Mechanism Relationship
A given rate law does not uniquely determine the mechanism.
A + B ⇌ C + D
v (^) 1 = k (^) 1 [ A ][ B ] v (^) −1 = k (^) −1[ C ][ D ] K (^) c = k^ k −1^1
A → I → P
d [ I ]/ dt = 0 O 3
8. Catalysis
Catalysts lower activation energy but do not change equilibrium. Types of Catalysis: Homogeneous catalysis (same phase as reactants): Example – Ce catalyzes oxidation of Tl. Heterogeneous catalysis (different phase): Example – Iron catalyzes ammonia synthesis. Biological catalysis (enzymes) : Example – Hexokinase catalyzing glucose conversion. Example 27-9: Enzyme kinetics and the Michaelis-Menten mechanism :
Rate law:
At low [S] : First-order, at high [S] : Zero-order.
Conclusion This chapter explores how chemical reactions proceed via mechanisms , discussing elementary reactions, complex reactions, rate-determining steps, steady-state approximations, and catalysis. Understanding these principles is crucial for predicting and controlling reaction rates in chemistry and biochemistry.
E + S ⇌ ES → E + P
v = (^) K (^) m^ k [+ [ S ] S ]
