Atkins & de Paula Atkins & de Paula: Elements of Physical Chemistry 6e Chapter 10: Chemical kinetics: the rates of reactions ©Oxford University Press, 2013. All rights reserved. Chemically relevant questions. What can we say about chemical reactions? • Reactants mix and products form. • A balanced equation is essential quantitative tool for calculating product yields from reaction amounts. What about the dynamics of chemical reactions? Useful questions that require answers include: • Will the reaction proceed by itself and release energy, or will it require energy to proceed? Thermodynamics (free energy) and thermochemistry. • What will the reactant and product concentrations be when the reaction is Complete? Thermodynamics and chemical equilibrium. • How fast is the chemical reaction proceeding at a given moment? Chemical kinetics. An essential concept in chemical kinetics is that of chemical reaction rate. This is defined in terms of the change in species concentration (amount per unit volume, i.e. mol/L) with respect to time (s). Atkins & de Paula: Elements of Physical Chemistry 6e Spectrophotometry Atkins & de Paula: Elements of Physical Chemistry 6e Experimental Technique Atkins & de Paula: Elements of Physical Chemistry 6e Experimental Technique Atkins & de Paula: Elements of Physical Chemistry 6e Timescales in Chemical Kinetics Atkins & de Paula: Elements of Physical Chemistry 6e Timescales in Chemical Kinetics Atkins & de Paula: Elements of Physical Chemistry 6e Direction of a Reaction Q. A reaction: A + B C + D. Will it proceed in the direction indicated? Is there a general way to know reaction direction? → A. We can tell from the change of Gibbs free energy in a reaction, G ∆ ° < reaction can proceed (we don’t know how fast it will be!) for a reaction at GT 0 Δ constant T, P, ∆GT ° = 0 reaction at equilibrium (no change in system - ‘dead’ state) we have ∆GT ° > 0 reaction will NOT proceed (or can proceed backward!) The 2nd Law of Thermodynamics - Processes occur in a direction of decreasing quality of energy. We need to study reaction system in terms of energies and their changes • The energies associated with a reaction system – Many energy terms, a, U, H, G, - all depend on 4 basic parameters: P, T, V, S – Usually P, T, V are specified by given reaction conditions. S is related to the substances in the reaction (reactants/products) and reaction conditions (P, T, V) – Knowing P, T, V and S, all other energy terms can be determined. The most important ones in relation to chemical reactions are H and G. Atkins & de Paula: Elements of Physical Chemistry 6e Basic ideas in reaction kinetics. • Chemical reaction kinetics deals with the rate of velocity of chemical reactions. • We wish to quantify . The velocity at which reactants are transformed to products. The detailed molecular pathway by which a reaction proceeds (the reaction mechanism) . • These objectives are accomplished using experimental measurements. • We are also interested in developing theoretical models by which the underlying basis of chemical reactions can be understood at a microscopic molecular level. • Chemical reactions are said to be activated processes : energy (usually thermal (heat) energy) must be introduced into the system so that chemical transformation can occur. Hence chemical reactions occur more rapidly when the temperature of the system is increased. • In simple terms an activation energy barrier must be overcome before reactants can be transformed into products. Atkins & de Paula: Elements of Physical Chemistry 6e Reaction rate : definition What do we mean by the term reaction rate? • The term rate implies that something changes with respect to something else. • How may reaction rates be determined ? • The reaction rate is quantified in terms of the change in concentration of a reactant or product species with respect to time. d[product] / dt • This requires an experimental measurement of the manner in which the concentration changes with time of reaction. We can monitor either the concentration change d[product] / dt directly, or monitor changes in some physical quantity which is directly proportional to the concentration. Atkins & de Paula: Elements of Physical Chemistry 6e Reaction rate : definition • The reactant concentration decreases with increasing time, and the product concentration increases with increasing time. • The rate of a chemical reaction depends on the concentration of each of the participating reactant species. • The manner in which the rate changes in magnitude with changes in the magnitude of each of the participating reactants is termed the reaction order. Atkins & de Paula: Elements of Physical Chemistry 6e Chemical Reaction - The Equilibrium Consider a reaction of the form νAA + νBB → νCC + νDD. When GT° =0, we say the reaction is in chemical reaction equilibrium. • What is a chemical reaction equilibrium? NH4 + - Example 1: NH3(aq)+H2O(l) NH4 (l)+OH (aq) At constant T and p, when t → ∞ ⇄ NH3 = + − t 4 Example 2: 2NO(g) + O (g) 2NO (g) 23 2 2 At constant T and p, when t → ∞ NO2 ⇄ NO = O2 2 2 t 2 • The concentration of a gas is usually2 measured as partial pressure • At an equilibrium the reaction quotient becomes constant Atkins & de Paula: Elements of Physical Chemistry 6e Chemical Reaction - The Equilibrium Chemical reaction equilibrium : νAA + νBB → νCC + νDD. • An equilibrium is a state at which no further change is possible under that specific set of reaction system parameters • An equilibrium is a dynamic process, meaning that the rate of forward reaction is equal to that of reverse • At equilibrium = 0 : = 0 = 0 = , , , , 0 0 ∆ 0 0 0 • ∆Any change∑ of reaction − ∑ parameters will redefine⟹ ∑ a system leading∑ to a new equilibrium, which may not be the same as that before the change • Kp indicates only the relation between the partial pressures of reactants and products at equilibrium, how fast a reaction proceed is controlled by reaction kinetics. Atkins & de Paula: Elements of Physical Chemistry 6e Definition of Rate Consider a reaction of the form νAA + νBB → νCC + νDD. A unique rate of reaction, , can be defined as the rate of change of the extent of reaction, ξ: 1 1ν 1 1 = = = = = −1 (Remember that ν is negative for reactants and positive for products). i For a homogeneous system these expression are often divided by the (constant) volume of the system, and the reaction rate expressed in terms of concentrations: 1 1 = = −3 −1 For heterogeneous reactions division by the surface area of the species i leads to 1 = −2 −1 where σ is the surface density of i. i Atkins & de Paula: Elements of Physical Chemistry 6e Rate laws, rate constants, and reaction order In virtually all chemical reactions that have been studied experimentally, the reaction rate depends on the concentration of one or more of the reactants. In general, the rate may be expressed as a function of these concentrations: = f ([A], [B], … ). The most frequently encountered functional dependence is the rate's being ν proportional to a product of algebraic powers of the individual concentrations, i.e., ∝ [A]a[B]b The exponents a and b may be integer, fractional, or negative. This ν proportionality can be converted to an equation by inserting a proportionality constant k, thus: = k [A]a[B]b This equation is called a rate law, rate equation or rate expression. The ν exponent a is the order of the reaction with respect to reactant A, and b is the order with respect to reactant B. The proportionality constant k is called the rate constant. The overall order of the reaction is simply p = a + b. Atkins & de Paula: Elements of Physical Chemistry 6e Rate laws, rate constants, and reaction order The rate law of a reaction is determined experimentally, and cannot in general be inferred from the chemical equation of the reaction. The reaction of hydrogen and bromine, for example, has a very simple stoichiometry, H2(g) + Br2(g) → 2 HBr(g), but its law is complicated: = 1⁄2 �1+2 � 2 In certain cases the rate law does reflect푘 the stoichiometry of the reaction; 2 but that is either a coincidence or reflects a feature of the underlying reaction mechanism. Atkins & de Paula: Elements of Physical Chemistry 6e Elementary reactions and molecularity Most reactions occur in a sequence of steps called elementary reactions, each of which involves only a small number of atoms, molecules or ions. An elementary reaction itself proceeds in a single step. The molecularity of an elementary reaction is the number of molecules coming together to react in it. Common are unimolecular reactions, in which a molecule shakes itself apart or its atoms in a new arrangement, as in the isomerization of cyclopropene to propene. In a bimolecular reaction, a pair of molecules collide and exchange energy, atoms, or groups of atoms, or undergo some other kind of change (e.g. F + H2 → HF + H). Three reactants that come together to form products constitute a termolecular reaction. Reactions with four, five, etc. reactants involved in an elementary reaction have not been encountered in nature. Atkins & de Paula: Elements of Physical Chemistry 6e Elementary reactions and molecularity It is important to distinguish molecularity from order: reaction order is an empirical quantity, and obtained from the experimental rate law; molecularity refers to an elementary reaction proposed as an individual step in a mechanism. Molecularity and overall order of an elementary reaction are the same! If the elementary steps of a complex mechanism are known, the overall rate law can be deduced! Isomerization as a typical unimolecular elementary reaction. Atkins & de Paula: Elements of Physical Chemistry 6e Atkins & de Paula: Elements of Physical Chemistry 6e Atkins & de Paula: Elements of Physical Chemistry 6e Atkins & de Paula: Elements of Physical Chemistry 6e Atkins & de Paula: Elements of Physical Chemistry 6e Atkins & de Paula: Elements of Physical Chemistry 6e Atkins & de Paula: Elements of Physical Chemistry 6e Atkins & de Paula: Elements of Physical Chemistry 6e Atkins & de Paula: Elements of Physical Chemistry 6e Atkins & de Paula: Elements of Physical Chemistry 6e Simple integrated rate laws First-order reactions, half-lives and time constants e.g.