Chemistry Ch. 16

Reaction Mechanisms and the Rate-Law Expression

Most reactions occur by a series of steps. The experimental rate-law is used to postulate a molecular mechanism. The slowest step in a reaction mechanism is the rate determining step. The reaction order is determined by this rate determining step.

Transition State Theory

Transition state theory postulates that reactants form a high energy intermediate, the transition state, which then falls apart into the products. For a reaction to occur, the reactants must acquire sufficient energy to form the transition state. This energy is called the activation energy or Ea The distribution of molecules possessing different energies at a given temperature is represented below. Increasing the temperature increases the number of molecules with sufficient energy for reaction.

Integrated Rate Equation: 2nd Order Reaction

1/[A] - 1/[Ao] = akt

Order of Reaction

3 NO (g) → N2O (g) + NO2 (g) Rate = k[NO]2 This reaction is second order in NO and second order overall. H2O2 (aq) + 3 I- (aq) + H+ (aq) → 2 H2O (l) + I3- (aq) Rate = k[H2O2][I-] This reaction is first order in H2O2, first order I-, zero order in H+, and second order overall.

Temperature: The Arrhenius Equation

Arrhenius developed a relationship among (1) the temperature (T), (2) the activation energy (Ea), and (3) the specific rate constant (k). lnK = lnA - Ea/RT Write the Arrhenius equation for two temperatures, T2 and T1, then subtract these two equations. Notice that ln A cancels out. ln(K2/K1) = Ea/R (1/T1 - 1/T2)

Catalysts

Catalysts change reaction rates by providing an alternative reaction pathway with a different activation energy. Catalysts increase the rate of reaction. Catalysts do not change the overall ΔE for a reaction. Catalysts are not changed in the reaction. Catalysts can be either solid phase (heterogeneous) or liquid phase (homogeneous) Catalysts change reaction rates by providing an alternative reaction pathway with a different activation energy

Collision Theory of Reaction Rates

Collisions between reacting species must occur for a chemical reaction to take place. However, not all collisions are effective. The colliding molecules must have the proper orientation Colliding molecules must have sufficient energy to react (e.g. more effective collisions at higher temperatures)

The Rate of Reaction

Consider the hypothetical reaction, aA(g) + bB(g) cC(g) + dD(g) reactants A and B will be consumed when products C and D are formed

Review: Kinetic Molecular Theory for Gases

Gas molecules are relatively far apart and do not interact with each other. Gas molecules travel in straight line motion with varying velocities Gas molecules have elastic collisions with other molecules and the container. Energy is conserved in these collisions. The kinetic energy of the molecule is proportional to absolute temperature.

Rate Law Expression

Rate Law Expressions must be determined experimentally. The rate law cannot be determined from the balanced chemical equation. The balanced chemical equation cannot be used to determine the rate law because most chemical reactions are not one-step reactions. The rate law expression is also called the rate law.

Rate Constant, k

Rate constants and reaction order are determined from experimental data. The value of k is for a specific reaction. The units of k depend on the overall order of the reaction. The value of k does not change with changes in concentrations. The value of k does not change with time. The value of k is dependent on temperature. The value of k is changed by presence of a catalyst.

Interpreting the Rate Law

Rate= k[A][B]^2 If the initial concentration of A is doubled, the initial rate of reaction is doubled (first order in A). If the initial concentration of A is halved the initial rate of reaction is cut in half. If the initial concentration of B is doubled, the initial rate of reaction is quadrupled (second order in B). If the initial concentration of C is doubled the initial rate of reaction is unchanged (zero order in C).

Experimental Determination of the Rate Law

The method of initial rates is used to deduce the rate law from a set of experimental data with concentrations of the reactants and the initial rate of formation of the product. Use two experiments where only one reactant concentration is changing. Compare how the changing reactant changes the initial rate of product formation. This gives you the order for that reactant. Rate ratio = (ratio [A])x (solve using logs)

Nature of Reactants

The physical state of reacting substances can affect reaction rate. Mixing dry solids may provide very slow rates, while solutions of the same compounds might react quickly. The extent of subdivision (surface area) of solids can affect rates (e.g. finely divided metals). The chemical identity of elements and compounds affect rates. For example, sodium reacts with water explosively at room temperature to liberate hydrogen and form sodium hydroxide, while calcium reacts very slowly with water.

Rate Law and the Order of Reaction

The rate law provides the order of a reaction, which can be expressed in terms of either: each reactant in the reaction or the overall reaction. Order for the overall reaction is the sum of the orders for each reactant in the rate law equation.

Reaction Mechanisms

The reaction orders for an elementary step are equal to coefficients for that step. Experimentally determined reaction orders indicate the number of molecules involved in: the slow step only, or the slow step and the equilibrium steps preceding the slow step. Mechanisms involving bimolecular collisions or unimolecular decomposition are more favorable. Most third order and higher reactions involve both an equilibrium and a slow step

Reactant Concentration and the Rate Law Expression

The reaction rate changes as the reactant concentrations change. The rate law expression for a reaction describes how the reaction rate depends on concentration.

Integrated Rate Equation: Zero Order Reaction

[A] = [A0] - akt

Heterogeneous catalysts

exist in different phases than the reactants.

Homogeneous catalysts

exist in same phase as the reactants.

Integrated Rate Equation: 1st Order Reaction

ln([A0]/[A]) = akt

reaction rate

the increase in concentration of a product per unit time or decrease in concentration of a reactant per unit time.

reaction mechanism

the series of molecular steps by which a reaction occurs.

Kinetics

the study of rates of chemical reactions and the mechanisms by which they occur. determines how quickly a reaction occurs. Some reactions that are thermodynamically feasible are kinetically so slow as to be imperceptible.