The Yukawa-Tsuno parameter r^+has been measured for several...

The Yukawa-Tsuno parameter $r^{+}$has been measured for several solvolysis reactions. What relationship do you see among the properties of the reactants, the likely nature of the transition structures, and the observed value of $r^{+}$? a. Solvolysis of benzyl tosylates in acetic acid; $r^{+}=1.3$ compared to solvolysis of 1 -aryl-2,2,2-trifluoroethyl tosylates in $80 \%$ aqueous acetone; $r^{+}=1.39$ b. Aryl-assisted solvolysis of 2 -aryl-2-(trifluoromethyl)ethyl $m$-nitrobenzoates in $80 \%$ aqueous trifluoroethanol; $r^{+}=0.77$ compared to aryl-assisted solvolyis of 2 -arylethyl tosylates; $r^{+}=0.6$

The Yukawa-Tsuno parameter $r^{+}$has been measured for several solvolysis reactions. What relationship do you see among the properties of the reactants, the likely nature of the transition structures, and the observed value of $r^{+}$?
a. Solvolysis of benzyl tosylates in acetic acid; $r^{+}=1.3$ compared to solvolysis of 1 -aryl-2,2,2-trifluoroethyl tosylates in $80 \%$ aqueous acetone; $r^{+}=1.39$
b. Aryl-assisted solvolysis of 2 -aryl-2-(trifluoromethyl)ethyl $m$-nitrobenzoates in $80 \%$ aqueous trifluoroethanol; $r^{+}=0.77$ compared to aryl-assisted solvolyis of 2 -arylethyl tosylates; $r^{+}=0.6$

Key Concepts

Yukawa-Tsuno Parameter

This parameter is a quantitative measure used to refine Hammett correlations by incorporating the influence of resonance as well as inductive effects on reaction rates. It helps explain deviations in expected reactivity patterns when electron-donating or withdrawing substituents are present and provides insight into the level of charge delocalization occurring in the transition state.

Solvolysis Reaction Mechanism

Solvolysis reactions involve the replacement of a leaving group by a nucleophile that is typically the solvent. They often proceed via a carbocation intermediate or a related transition state character that is significantly influenced by the substrate's electronic structure, making the study of such reactions crucial for understanding substitution mechanisms.

Transition State Structure

The nature of the transition state in a chemical reaction determines the reaction rate and the distribution of charge. In processes like solvolysis, the degree of charge delocalization, stabilization by substituents, and the developing structure of the carbocation all play critical roles. Analysis of the transition state can reveal whether resonance stabilization or inductive effects are dominant.

Electronic Substituent Effects

Substituents on the reactant molecule can alter the electronic distribution through inductive or resonance effects. Their ability to stabilize or destabilize a developing positive charge directly influences the reaction kinetics. Understanding these effects is essential for interpreting variations in observed parameters such as r+ in different reaction scenarios.

Aromatic Participation in Reaction Mechanisms

Aromatic groups often participate in stabilizing transition states or intermediates through resonance donation. Their ability to delocalize positive charge can enhance reaction rates in solvolysis processes, and comparing the extent of this participation helps clarify the role of substituent structure on the overall reaction mechanism.

Transcript

00:01 This question is very similar to many of the previous questions.

00:05 It is a method of initial rates question where given the rates of reactions, the initial rate, with the initial concentrations of the reactants, you should be able to determine the order of the reaction with respect to each individual reactant.

00:24 Then knowing the order of the reaction with respect to each individual reactant, you can determine the overall order by simply summing up the orders of each specific reactant.

00:37 Then, after you know that, you could write the rate law, and from the rate law determine the rate constant with the data found for one of the experiments.

00:47 And then last of all, see whether or not a mechanism is plausible or come up with your own.

00:54 In this particular problem, they have provided a mechanism, and you simply want to verify whether or not it is plausible.

01:02 So let's look at the data that has been provided.

01:05 First, we'll look at experiment 1.

01:09 In experiment 1, we see that compared to experiment 2, we see that the ch3, co -ch3, concentration stays constant, and the h -plus concentration stays constant.

01:25 The only concentration that is changing between experiments 1 and 2 is the bromine concentration.

01:32 It goes from 0 .05 molar in experiment 1 to 0 .1 molar in experiment 2.

01:39 Therefore, the bromine concentration is the only thing that is doubled between experiments 1 and 2.

01:45 When the bromine concentration is doubled, we see that there is no change to the initial rate of the reaction.

01:53 Therefore, we can predict that the rate of the reaction is independent of the bromine concentration or the order of the reaction with respect to bromine is zero.

02:06 Now let's look at experiments 1 and 3.

02:08 In experiments 1 and 3, we see that the only change in concentration is for the hydrogen ion.

02:15 It goes from 0 .05 in experiment 1 to 0 .1 in experiment 3.

02:24 But the concentration of ch3 coch3 stays constant at 0 .3, and the concentration of bromine stays constant at 0 .05.

02:36 So with a doubling of the h plus concentration, we see that the rate has doubled.

02:43 It goes from 0 .05 times 10 to negative 5 to 1 .2 times 10 to negative 4, which is essentially double the rate.

02:53 So if what we do to the concentration happens to the rate, namely we double the concentration, we double the rate, this is first order.

03:01 So now let's look at experiments 1 and 4.

03:04 In experiments 1 in 4, we see that the bromine concentration is staying constant at 0 .05 and the, well actually this would be 1 in 5, 1 in 4, or whatever it is in your textbook.

03:27 We've got the bromine concentration and the hydrogen ion concentration at 0 .05 in one experiment and in the other experiment.

03:39 Everything is 0 .05 except for the ch3, coch3.

03:44 That goes from 0 .3 to 0 .4.

03:48 So if it goes from 0 .3 to 0 .4, we have increased it, but it's not obvious by how much.

03:56 It's not like a doubling or a tripling or something like that.

04:00 So the best way to determine the order with respect to this reactant is to do a ratio of the rate laws.

04:09 The rate is going to be equal to the rate constant, multiplied by the concentration of everything raised to their order.

04:18 Well, we know that bromine is zero, so this ends up canceling, but we know that the hydrogen is first order...

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