The object is to study the kinetics of the reaction between peroxodisulfate
and iodide ions.
$$\begin{aligned}
&\text { (a) } \mathrm{S}_{2} \mathrm{O}_{8}^{2-}(\mathrm{aq})+3
\mathrm{I}^{-}(\mathrm{aq}) \longrightarrow 2
\mathrm{SO}_{4}^{2-}(\mathrm{aq})+\mathrm{I}_{3}^{-}(\mathrm{aq})
\end{aligned}$$
The \(I_{3}^{-}\) formed in reaction (a) is actually a complex of iodine,
\(\mathrm{I}_{2},\) and iodide ion, \(\mathrm{I}^{-}\). Thiosulfate ion,
\(\mathrm{S}_{2} \mathrm{O}_{3}^{2-}\) also present in the reaction mixture,
reacts with \(\mathrm{I}_{3}^{-}\) just as fast as it is formed.
$$\text { (b) } 2 \mathrm{S}_{2}
\mathrm{O}_{3}^{2-}(\mathrm{aq})+\mathrm{I}_{3}^{-}(\mathrm{aq})
\longrightarrow \mathrm{S}_{4} \mathrm{O}_{6}^{2-}+3
\mathrm{I}^{-}(\mathrm{aq})$$
When all of the thiosulfate ion present initially has been consumed by
reaction (b), a third reaction occurs between
\(\mathrm{I}_{3}^{-}(\mathrm{aq})\) and starch, which is also present in the
reaction mixture.
$$\text { (c) } \mathrm{I}_{3}^{-}(\mathrm{aq})+\operatorname{starch}
\longrightarrow \text { blue complex }$$
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 s). Tables I and II list some actual student data
obtained in this study.
$$\begin{array}{l}
\hline\text { TABLE I } \\
\text { Reaction conditions at } 24^{\circ} \mathrm{C}: 25.0 \mathrm{mL} \text
{ of the } \\
\left(\mathrm{NH}_{4}\right)_{2} \mathrm{S}_{2} \mathrm{O}_{8}(\text { aq)
listed, } 25.0 \mathrm{mL} \text { of the } \mathrm{KI}(\mathrm{aq}) \\
\text { listed, } 10.0 \mathrm{mL} \text { of } 0.010 \mathrm{M}
\mathrm{Na}_{2} \mathrm{S}_{2} \mathrm{O}_{3}(\mathrm{aq}), \text { and } 5.0
\mathrm{mL} \\
\text { starch solution are mixed. The time is that of the } \\
\text { first appearance of the starch-iodine complex. } \\
\hline & \text { Initial Concentrations, } \mathrm{M} \\
\hline \text { Experiment } & \left(\mathrm{NH}_{4}\right)_{2} \mathrm{S}_{2}
\mathrm{O}_{8} & \mathrm{KI} & \text { Time, s } \\
\hline 1 & 0.20 & 0.20 & 21 \\
2 & 0.10 & 0.20 & 42 \\
3 & 0.050 & 0.20 & 81 \\
4 & 0.20 & 0.10 & 42 \\
5 & 0.20 & 0.050 & 79 \\
\hline
\end{array}$$
$$\begin{array}{l}
\hline \text { TABLE II } \\
\text { Reaction conditions: those listed in Table I for } \\
\text { Experiment } 4, \text { but at the temperatures listed. } \\
\hline \text { Experiment } & \text { Temperature, }^{\circ} \mathrm{C} &
\text { Time, } \mathrm{s} \\
\hline 6 & 3 & 189 \\
7 & 13 & 88 \\
8 & 24 & 42 \\
9 & 33 & 21 \\
\hline
\end{array}$$
(a) Use the data in Table I to establish the order of reaction (a) with
respect to \(\mathrm{S}_{2} \mathrm{O}_{8}^{2-}\) and to I \(^{-}\). 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
\(\mathrm{M} \mathrm{s}^{-1} .\) [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 \((a),(b), \text { and }(c) .]\)
(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, \(E_{\mathrm{a}}\), 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.
$$\begin{array}{c}
\mathrm{I}^{-}+\mathrm{S}_{2} \mathrm{O}_{8}^{2-} \longrightarrow
\mathrm{IS}_{2} \mathrm{O}_{8}^{3-} \\
\mathrm{IS}_{2} \mathrm{O}_{8}^{3-} \longrightarrow 2
\mathrm{SO}_{4}^{2-}+\mathrm{I}^{+} \\
\mathrm{I}^{+}+\mathrm{I}^{-} \longrightarrow \mathrm{I}_{2} \\
\mathrm{I}_{2}+\mathrm{I}^{-} \longrightarrow \mathrm{I}_{3}^{-}
\end{array}$$
Show that this mechanism is consistent with both the stoichiometry and the
rate law of reaction (a). Explain why it is reasonable to expect the first
step in the mechanism to be slower than the others.
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