Rates Of Reactions PDF

The Rates Of Reactions 20 Physical chemistry II - CHEM 343 (a) The definition of rate Consider a reaction of the form A + 2B →3C + D The molar concentration of a participant J is [J] the volume of the system is constant. The instantaneous rate of consumption of one of...

The Rates Of Reactions 20 Physical chemistry II - CHEM 343 (a) The definition of rate Consider a reaction of the form A + 2B →3C + D The molar concentration of a participant J is [J] the volume of the system is constant. The instantaneous rate of consumption of one of the reactants at a given time is -d[R]/dt, where R is A or B This rate is a positive quantity (Fig.). 21 Physical chemistry II - CHEM 343 The rate of formation of one of the products (C or D, which we denote P) is d[P]/dR (note the difference in sign). This rate is also positive. It follows from the stoichiometry for the reaction A + 2B → 3C + D that 𝐝𝐃 𝟏𝐝 𝐂 𝐝𝐀 𝟏𝐝𝐁 = =− =− 𝐝𝒕 𝟑 𝐝𝒕 𝐝𝒕 𝟐 𝐝𝒕 So, there are several rates connected with the reaction. 22 Physical chemistry II - CHEM 343 If the rate of formation of NO in the reaction 2NOBr(g) → 2NO(g) + Br2(g) Is reported as 0.16 mmol dm-3 s-1, We use stoichiometry of NO = +2 Because stoichiometry of NOBr = -2 it follows that d[NOBr]/dt = - 0.16 mmol dm-3s-I. The rate of consumption of NOBr is therefore 0.16 mmol dm-3s-1, or 9.6 x 1016 molecules cm-3s-I. 23 Physical chemistry II - CHEM 343 Self-test The rate of change of molar concentration of CH3 radicals in the reaction 2 CH3(g) → CH3CH3(g) was reported as d[CH3]/dt = -1.2 mol dm-3s-1 under particular conditions. What is (a) the rate of reaction and (b) the rate of formation of CH3CH3? Answer [(a) 0.60 mol dm-3s-1, (b) 0.60 mol dm-3s-l] 24 Physical chemistry II - CHEM 343 Note some rxs, when written in ionic form show that some ions don’t change concentration. eg. Mg(s) + 2HCl(aq) → H2(g) + MgCl2(aq) NOTE: To write an equation in ionic form, dissociate all the aqueous (aq) compounds: ionic form : Mg(s) + 2H+(aq) + 2Cl-(aq) → H2(g) + Mg2+(aq) + 2Cl-(aq) (use ion chart) [Cl -] does not change as rx. proceeds (spectator ion) 25 Physical chemistry II - CHEM 343 (b) Rate laws and rate constants: aA + bB → cC + Dd General form of rate law: [A], [B] – conc. in M or P rate = k[A]m[B]n k – rate constant; units vary m, n – reaction orders Reaction orders and, thus, rate laws must be determined EXPERIMENTALLY!!! Note: m ≠ a and n ≠ b Overall order = sum of individual orders Rate constant is independent of concentration. 26 Physical chemistry II - CHEM 343 (c) Reaction order: Many reactions are found to have rate laws of the form v = k[A]a[B]b The power to which the concentration of a species (a product or a reactant) is raised in a rate law of this kind is the order of the reaction with respect to that species. A reaction with the rate law in above equation is first - order in A and first -order in B. The overall order of a reaction with a rate law like that in equation is the sum of the individual orders, a + b +.... 27 Physical chemistry II - CHEM 343 The rate law in above equation is therefore second-order overall. A reaction need not have an integral order, and many gas- phase reactions do not. For example, a reaction having the rate law v = k[A]1/2[B] is half-order in A, first-order in B, and three-halves-order overall. Some reactions obey a zero-order rate law, and therefore have a rate that is independent of the concentration of the reactant (so long as some is present). 28 Physical chemistry II - CHEM 343  Thus, the catalytic decomposition of phosphine (PH3) on hot tungsten at high pressures has the rate law v=k (d) The determination of the rate law: The determination of a rate law is simplified by the isolation method in which the concentrations of all the reactants except one are in large excess. If B is in large excess, for example, then to a good approximation its concentration is constant throughout the reaction. 29 Physical chemistry II - CHEM 343 Although the true rate law might be v = k[A] [B], we can approximate [B] by [B]o ,its initial value, and write v = k`[A]→k` = k [B]o which has the form of a first-order rate law. Because the true rate law has been forced into first-order form by assuming that the concentration of B is constant, above equation is called a pseudo first-order rate law. In the method of initial rates, which is often used in conjunction with the isolation method, the rate is measured at the beginning of the reaction for several different initial concentrations of reactants. 30 Physical chemistry II - CHEM 343 We shall suppose that the rate law for a reaction with A isolated is v = k[A]a; then its initial rate, vo , is given by the initial values of the concentration of A, and we write vo = k[A]oa Taking logarithms gives: Log vo = log k + a log[A]o For a series of initial concentrations, a plot of the logarithms of the initial rates against the logarithms of the initial concentrations of A should be a straight line with slope a. 31 Physical chemistry II - CHEM 343 Example The recombination of iodine atoms in the gas phase in the presence of argon was investigated and the order of the reaction was determined by the method of initial rate. The initial rates of reaction of 2I(g)+ Ar(g) → I2(g) +Ar(g) were as follows: [I]0/(10-5 mol dm-3) 1.0 2.0 4.0 6.0 (a) 8.70 x 10-4 3.48 x 10-3 1.39 x 10-2 3.13 x 10-2 Vo/ (mol dm-3 s-1) (b) 4.35 x 10-3 1.74 x 10-2 6.96 x 10-2 1.57 x 10-1 (c) 8.69 x 10-3 3.47 x 10-2 1.38 x 10-1 3.13 x 10-1 The Ar concentrations are (a) 1.0 mmol dm-3, (b) 5.0 mmol dm-3 , and (c) 10.0 mmol dm-3. Determine the orders of reaction with respect to the I and Ar atom concentrations and the rate constant. 32 Physical chemistry II - CHEM 343 Method: Plot the logarithm of the initial rate, log vo against log [I]o for a given concentration of Ar, and, separately, against log [Ar]o, for a given concentration of I. The slopes of the two lines are the orders of reaction with respect to I and Ar , respectively. The intercepts with the vertical axis give log k. 33 Physical chemistry II - CHEM 343 The plot of log vo against (a) log [I]o for a given [Ar]o., and (b) log [Ar]o, for a given [I] o Answer :The plots are shown in Fig. The slopes are 2 and 1, respectively, so the (initial) rate law is vo = k[I]o2 [Ar]o This rate law signifies that the reaction is second-order in [I], first-order in [Ar], and third-order overall. The intercept corresponds to k = 9 x 109 mol-2dm3s-I. 34 Physical chemistry II - CHEM 343 The units of k come automatically from the calculation and are always such as to convert the product of concentrations to a rate in concentration/time (for example, mol dm-3 S-1). Self-test The initial rate of a reaction depended on concentration of a substance J as follows: [J]0 /(mmol dm-3) 5.0 8.2 17 30 3.6 9.6 41 130 Vo /(10-7 mol dm-3 s-1) Determine the order of the reaction with respect to J and calculate the rate constant. [ 2.14 x 10-2 dm3 mol-1 s-1] 35 Physical chemistry II - CHEM 343