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In an investigation of the kinetics of the reaction
\( \mathrm{MnO}_{4}^{-}+\mathrm{Cr}^{3+} \longrightarrow \mathrm{CrO}_{4}^{2-}+\mathrm{Mn}^{4+} \) at \( 25^{\circ} \mathrm{C} \) Fales and Roller
measured the times required to carry the reaction to various
\( \mathrm{P} \) degrees of completion, first as a function of \( \mathrm{MnO}_{4}^{-} \)concentration

W and then as a function of \( \mathrm{Cr}^{3+} \) concentration.
In each case after definite intervals of time, \( 25 \mathrm{ml} \) aliquots (sample) of the reaction mixture were removed and added rapidly to a solution containing \( 60 \mathrm{ml} \) of \( 1.2 \mathrm{M} \mathrm{H}_{2} \mathrm{SO}_{4} \) and \( 25 \mathrm{ml} \) of \( 0.5 \mathrm{M} \) \( \mathrm{KBr} \) to occur the following reaction \( 2 \mathrm{MnO}_{4}^{-}+10 \mathrm{Br}^{2}+16 \mathrm{H}^{-} \longrightarrow 2 \mathrm{Mn}^{2+}+5 \mathrm{Br}_{2}+8 \mathrm{H}_{2} \mathrm{O} \)
Free bromine was instantly liberated was extracted by \( \mathrm{CS}_{\gamma} \). The \( \mathrm{Cr}_{2} \mathrm{O}_{7}^{-2} \) that had been formed by the reaction \( 2 \mathrm{CrO}_{4}^{-}+2 \mathrm{H}^{-} \) \( \longrightarrow \mathrm{Cr}_{2} \mathrm{O}_{7}{ }^{2-}+\mathrm{H}_{2} \mathrm{O} \)
was titrated with \( 0.01 \mathrm{~N} \mathrm{FeSO}_{4} \) in the reaction
\( \mathrm{Cr}_{2} \mathrm{O}_{4}^{2-}+6 \mathrm{Fe}^{2}+16 \mathrm{H}^{+}+2 \mathrm{SO}_{4}^{2-} \longrightarrow 2 \mathrm{Cr}^{3+}+6 \mathrm{Fe}^{3+}+2 \mathrm{HSO}_{4}^{-}+ \) \( \mathrm{TH}_{2} \mathrm{O} \).

The number of milli liters of \( 0.01 \mathrm{~N} \mathrm{Cr}_{2} \mathrm{O}_{7}^{2-} \) present in the mixture at the indicated reaction time is given in the table. In a set of three experiments, the results were as follows
\( \begin{array}{llll}\text { Experiment No. } & \text { I } & \text { II } & \text { III } \\ {\left[\mathrm{MnO}_{4}^{-}\right](\mathrm{mol} / \mathrm{lt})} & 1 & 2 & 1 \\ {\left[\mathrm{Cr}^{3-}\right](\mathrm{mol} / \mathrm{t})} & 1 & 1 & 0.5 \\ \text { Volume of } \mathrm{Cr}_{2} \mathrm{O}_{7}^{2-} & & & \\ (0.01 \mathrm{~N}) \text { present }(\mathrm{ml}) & & \\ 0.122 \mathrm{~min} & 11 \mathrm{~min} & 45 \mathrm{~min} \\ 0.236 \mathrm{~min} & 18 \mathrm{~min} & 72 \mathrm{~min} \\ 0.460 \mathrm{~min} & 30 \mathrm{~min} & 121 \mathrm{~min} \\ 0.680 \mathrm{~min} & 40 \mathrm{~min} & 162 \mathrm{~min}\end{array} \)
What is the order of reaction with respect to \( \left[\mathrm{Cr}^{3+}\right] \)
(a) 1
(b) 2
(c) \( 1.5 \)
(d) \( 0.5 \)
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