Chapter 20, Problem 97FP

The object is to study the kinetics of the reaction between perioxodisulfate and iodide ions.

1. ${\text{S}}_2{O}_8^{2-}\left(\text{aq}\right)+3{\text{I}}^{\text{-}}\left(\text{aq}\right)\to 2{\text{SO}}_{\text{4}}^{\text{2-}}\left(\text{aq}\right)+3{\text{I}}^{-}\left(\text{aq}\right)$
   The ${\text{I}}_3^{-}$ formed in reaction (a) is actually a complex of iodine, ${\text{I}}_2$, and iodide ion, ${\text{I}}^{-}$ Thiosulfateion, ${\text{S}}_{\text{2}}{\text{O}}_{\text{3}}^{\text{2-}}$?, also present in the reaction mixture reacts with l just as fast as it is formed
2. ${\text{2S}}_{\text{2}}{\text{O}}_{\text{3}}^{\text{2-}}\left(\text{aq}\right)+{\text{I}}_{\text{3}}^{\text{-}}\left(\text{aq}\right)\to 3{\text{I}}^{\text{-}}\left(\text{aq}\right)$
   When all of the thiosulfate ion present initially has been consumed by reaction (b), a third reaction occurs between l (aq) and starch, which is also present in the reaction mixture
3. ${\text{I}}_{\text{3}}^{\text{-}}\left(\text{aq}\right)+\text{starch}\to \text{blue complex}$The rate of reaction (a) is inversely related to the time required for the blue color of the starch-iodine complex to appear That is, the faster reaction (a) proceeds, the more quickly the thiosulfate ion is consumed in reaction (b), and the sooner the blue color appears in reaction (C). One of the photographs shows the initial colorless solution and an electronic timer set at t = 0; the other photograph shows the very first appearance of the blue complex (after 49 89 5). Tables I and II list some actual student data obtained in this study.

Table I Reaction conditions at $24°\text{C}$ L 25.0 mL of $\left({\text{NH}}_{\text{4}}\right){\text{S}}_{\text{2}}{\text{O}}_{\text{4}}\left(\text{aq}\right)$ listed, 25.0 mL of the KI(aq) listed, 10.0mL of 0.010M ${\text{Na}}_{\text{2}}{\text{S}}_{\text{2}}{\text{O}}_{\text{2}}$ (a), and 5.0 mL starch solution are mixed. The time is time is that of the first appearance of the starch-iodine complex.

Table II Reaction conditions: those listed in Table I for Experiment 4, but at the temperature listed.

a. Use the data in Table I to establish the order of reaction (a) with respect to ${\text{S}}_2{O}_2^{2-}$ and to ${\text{I}}^{\text{-}}$ . What is the overall reaction order? [Hint: How are the times required for the blue complex to appear related to the actual rates of reaction?]
b. Calculate the initial rate of reaction in Experiment 1, expressed in M s"1. [Hint: You must take into account the dilution that occurs when the various solutions are mixed, as well as the reaction stoichiometry indicated by equations (a], (b)_; and (c).]
c. Calculate the value of the rate constant k based on experiments 1 and 2 d Calculate the rate constant, k, for the four different temperatures in Table II
e. Determine the activation energy, E_a; of the peroxodisulfate-iodide ion reaction.
f. The following mechanism has been proposed for reaction (a). The first step is slow, and the others are fast.
   $\begin{array}{l}{\text{I}}^{-}+{\text{S}}_{\text{2}}{\text{O}}_{\text{8}}^{\text{3-}}\to {\text{IS}}_{\text{2}}{\text{O}}_8^{3-}\\ {\text{IS}}_{\text{2}}{\text{O}}_{\text{8}}^{\text{3-}}\to {\text{2SO}}_{\text{4}}^{\text{2-}}{\text{+I}}^{\text{-}}\\ {\text{I}}^{\text{+}}+{\text{I}}^{\text{-}}\to {\text{I}}_{\text{2}}\\ {\text{I}}_{\text{2}}+{\text{I}}^{\text{-}}\to I_3^{-}\end{array}$

Show that this meachanism is consistent with both the stoichimetry and the rate law of reaction (a). Explain why it is reasonable to expect the first step in the meachanism than the others.