The second-order rate constants for the reaction of a number of amines with benzyl chloride are

The second-order rate constants for the reaction of a number...

Key Concepts

Transition State Theory

Transition state theory is a framework used to understand the rates of chemical reactions by considering the distribution of energy among reactant molecules. It postulates the existence of an activated complex (or transition state) at the peak of the energy barrier, and explains how the structure and energy of this intermediate state influence the reaction rate.

Structure-Reactivity Relationship

Structure-reactivity relationships explore how variations in molecular structure, such as electronic or steric characteristics of reactants like amines, affect their chemical reactivity. Analysis of these trends allows for correlations between molecular features, like the activation enthalpy and entropy, and the experimentally observed rate constants, thereby providing insights into the underlying mechanistic aspects of the reaction.

Activation Entropy (?S‡)

Activation entropy describes the change in disorder or randomness from the reactants to the transition state. It provides information on the degree of organization in the transition state relative to the reactants, and impacts the overall activation free energy. A more negative ?S‡ indicates a more ordered transition state, whereas a positive value suggests increased disorder.

Eyring Equation

The Eyring equation is a central expression in transition state theory that relates the rate constant of a reaction to the activation free energy, temperature, and the universal constants. It enables the determination of activation parameters such as activation enthalpy and activation entropy from experimental rate data, offering insights into the energy barrier that must be overcome for the reaction to proceed.

Activation Enthalpy (?H‡)

Activation enthalpy is the energy difference between the reactants and the transition state, representing the minimum amount of energy that must be supplied to initiate a reaction. It reflects the structural reorganization and bond changes during the conversion from reactants to the activated complex, influencing how readily a reaction can occur based on the energy barrier.

Transcript

00:01 In this question, we have a reaction of c .h3 cl, reacting with three moles of cl2, producing c, cl4, and three moles of hcl.

00:17 We are given data for four experiments where concentration of the reactants are provided and the initial rate is provided, and we're asked to determine the order of the reaction with respect to each reactant so that we can, can write the rate law for the reaction and then calculate the k value.

00:40 To do this, we need to determine the order with respect to each reactant.

00:46 We notice in experiments 1 and 2, the concentration of cl2 is unchanging or staying constant, but the concentration of ch3cl is being doubled.

01:01 If we double the concentration of ch3cl, we see that the rate doubles from 0 .014 to 0 .09.

01:11 It's not an exact doubling, but it's probably because of rounding issues.

01:18 So a doubling of the concentration resulting in a doubling in the rate is indicative of first order.

01:24 So the reaction is first order with respect to ch3cl.

01:29 But then if we look at experiments 2 and 3, where the ch3 cl concentration is staying constant, and we are doubling the cl2 concentration, we're going from 0 .05 to 0 .1, we have something that is not double nor quadruple the rate.

01:55 We go from 0 .0 to 9 to 0 .0 .1.

01:58 If it were first order, doubling the concentration would double the rate, and the rate would be more like .058.

02:07 If it were second order, then doubling the concentration would quadruple the rate.

02:12 That didn't happen.

02:13 If it were zero order, then doubling the concentration would result in the rate staying constant.

02:19 So it's not one of these very common orders, zero first, or second.

02:25 It must be a fraction order to calculate the...

02:29 Order that is a fraction, we need to set up an algebraic expression where we will take the rate law and plug in the data for experiment 2, where the rate is 0 .029.

02:46 Set that equal to k, multiplied by the concentration of ch3, cl, raised to the first power, because we determined that up here, multiplied by the concentration of cl2 raised to an unknown power...

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