The loss of water from the complexes [Ru(NH3)5 H2 O] X3 (where X=Cl^-, Br^-, I^-, or NO3^-) has

The loss of water from the complexes [Ru(NH3)5 H2 O] X3...

The loss of water from the complexes $\left[\mathrm{Ru}\left(\mathrm{NH}_3\right)_5 \mathrm{H}_2 \mathrm{O}\right] \mathrm{X}_3$ (where $\mathrm{X}=\mathrm{Cl}^{-}, \mathrm{Br}^{-}, \mathrm{I}^{-}$, or $\mathrm{NO}_3^{-}$) has activation energies of $95.0,97.9$, 112 , and $80.8 \mathrm{~kJ} / \mathrm{mol}$, respectively. The values for the entropy of activation are $-7.1,-5.2,5.8$, and -15.5 e.u., respectively. In light of the kinetic parameters, discuss the mechanism of dehydration of the complexes.

Key Concepts

Dissociative versus Associative Mechanisms

In coordination chemistry, the pathway by which a ligand is lost or replaced can be classified as either dissociative or associative. A dissociative mechanism involves the initial loss of a ligand to form a less coordinated intermediate, typically accompanied by a positive or less negative entropy of activation due to the increased disorder. An associative mechanism involves a new ligand attacking the complex, forming a more ordered intermediate, and is indicated by a more negative entropy of activation due to the formation of a tighter, more organized transition state.

Transition State Theory

Transition state theory describes how reactants pass through a high-energy intermediate state (the transition state) before becoming products. It provides a framework to interpret both the activation energy and the entropy of activation, linking these kinetic parameters to the structural and energetic features of the transition state in a reaction mechanism.

Activation Energy

Activation energy is the minimum energy barrier that must be overcome for a chemical reaction to occur. In the context of reaction mechanisms, comparing activation energies can help determine the kinetics of bond-breaking or bond-formation steps. A higher activation energy indicates a less favorable or slower process, while a lower activation energy suggests a reaction that can more readily proceed under given conditions.

Entropy of Activation

Entropy of activation reflects the change in disorder from reactants to the transition state. A negative entropy of activation implies that the transition state is more ordered than the reactants, which is often associated with mechanisms involving a highly organized or associative pathway. Conversely, a positive entropy of activation indicates an increase in disorder, which can be characteristic of dissociative mechanisms where components become less organized.

Transcript

00:01 We're given quite a bit of information and the equation that we're looking at is right here.

00:08 Okay, we are told that our slow step is, and our fast step is, okay, so let's predict the rate law based on our reaction mechanisms.

01:50 So i'm going to say that the rate law will be first order, k times, i'm just going to write trans.

02:28 Okay, that's what i'll say will be my rate law for the first one.

02:45 There we go.

02:47 And for b, as the reaction proceeds, blah, blah, blah, blah, blah, color changes from green to red with a gray intermediate stage.

03:30 The gray color is reached at the same time, no matter what concentrations initially.

04:02 How does this show the reaction is first order? if it was zero order, let me see, if it were zero order, then it would take a longer time for the gray intermediate to form.

05:25 So it's not zero order.

05:27 If it was second order, the rate would be dependent on the square of the concentration.

05:53 This is not true.

05:59 So that justifies the first order classification.

06:15 Okay, then c, we have to plot, plot the ln of k versus one over t.

06:34 And k equals negative one over t times the ln of r over r zero.

06:57 The time is a measure of k, use the data below.

07:02 So we have data, temp in degrees c is 56, 60, 65, and 70.

07:12 Then i'm going to go over here, the time is 156.

07:18 This is all in seconds, 114, 88, and 47.

07:28 Okay, so we're going to add 273 and one over x...