Question

The reaction ${\mathbf{H}}_{\mathbf{2}}{\mathbf{SeO}}_{\mathbf{3}}\mathbf{\left(}\mathbf{aq}\mathbf{\right)}\mathbf{+}\mathbf{6}{\mathbf{I}}^{\mathbf{-}}\mathbf{\left(}\mathbf{aq}\mathbf{\right)}\mathbf{+}\mathbf{4}{\mathbf{H}}^{\mathbf{+}}\mathbf{\left(}\mathbf{aq}\mathbf{\right)}\mathbf{\to }\mathbf{Se}\mathbf{\left(}\mathbf{s}\mathbf{\right)}\mathbf{+}\mathbf{2}{{\mathbf{I}}_{\mathbf{3}}}^{\mathbf{-}}\mathbf{\left(}\mathbf{aq}\mathbf{\right)}\mathbf{+}\mathbf{3}{\mathbf{H}}_{\mathbf{2}}\mathbf{O}\mathbf{\left(}\mathbf{l}\mathbf{\right)}$was studied at ${\mathbf{0}}^{\mathbf{°}}\mathbf{C}$, and the following data were obtained:

$\mathbf{[}{\mathbf{H}}_{\mathbf{2}}\mathbf{SeO}{\mathbf{]}}_{\mathbf{0}}\left(\mathrm{mol}/L\right)$	$\mathbf{[}{\mathbf{H}}^{\mathbf{+}}{\mathbf{]}}_{\mathbf{0}}\left(\mathrm{mol}/L\right)$	$\mathbf{\left[}{\mathbf{I}}^{\mathbf{-}}\mathbf{\right]}\left(\mathrm{mol}/L\right)$	$\mathbf{Initial}\mathbf{}\mathbf{Rate}\left({\mathrm{molL}}^{-1}{s}^{-1}\right)$
localid="1663839197909" $\mathbf{1}\mathbf{.}\mathbf{0}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{4}}$	localid="1663839994858" $\mathbf{2}\mathbf{.}\mathbf{0}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{2}}$	localid="1663840803384" $\mathbf{2}\mathbf{.}\mathbf{0}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{2}}$	role="math" localid="1663841146761" $\mathbf{1}\mathbf{.}\mathbf{66}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{7}}$
$\mathbf{2}\mathbf{.}\mathbf{0}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{4}}$	localid="1663840000906" $\mathbf{2}\mathbf{.}\mathbf{0}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{2}}$	$\mathbf{2}\mathbf{.}\mathbf{0}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{2}}$	$\mathbf{3}\mathbf{.}\mathbf{33}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{7}}$
$\mathbf{3}\mathbf{.}\mathbf{0}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{4}}$	localid="1663840007628" $\mathbf{2}\mathbf{.}\mathbf{0}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{2}}$	$\mathbf{2}\mathbf{.}\mathbf{0}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{2}}$	$\mathbf{4}\mathbf{.}\mathbf{99}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{7}}$
$\mathbf{1}\mathbf{.}\mathbf{0}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{4}}$	localid="1663840013722" $\mathbf{4}\mathbf{.}\mathbf{0}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{2}}$	$\mathbf{2}\mathbf{.}\mathbf{0}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{2}}$	$\mathbf{6}\mathbf{.}\mathbf{66}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{7}}$
$\mathbf{1}\mathbf{.}\mathbf{0}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{4}}$	localid="1663840021033" $\mathbf{1}\mathbf{.}\mathbf{0}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{2}}$	$\mathbf{2}\mathbf{.}\mathbf{0}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{2}}$	$\mathbf{0}\mathbf{.}\mathbf{42}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{7}}$
$\mathbf{1}\mathbf{.}\mathbf{0}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{4}}$	localid="1663840026824" $\mathbf{2}\mathbf{.}\mathbf{0}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{2}}$	$\mathbf{4}\mathbf{.}\mathbf{0}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{2}}$	$\mathbf{13}\mathbf{.}\mathbf{2}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{7}}$
$\mathbf{1}\mathbf{.}\mathbf{0}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{4}}$	localid="1663840033291" $\mathbf{1}\mathbf{.}\mathbf{0}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{2}}$	$\mathbf{4}\mathbf{.}\mathbf{0}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{2}}$	$\mathbf{3}\mathbf{.}\mathbf{36}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{7}}$

The relationships hold only if there is an insignificant amount of ${{\mathbf{I}}_{\mathbf{3}}}^{\mathbf{-}}$ present. What is the rate law and the value of the rate constant?

$\left(\mathrm{Assume}\mathrm{that}\mathrm{rate}=-\frac{d\left[H_2{\mathrm{SeO}}_3\right]}{\mathrm{dt}}.\right)$

Short answer

$\mathrm{Rate}=\mathrm{k}\left[{\mathrm{H}}_2{\mathrm{SeO}}_3\right][{\mathrm{H}}^{+}{]}^2[{\mathrm{I}}^{-}{]}^3$ and $\mathrm{k}=5.19\mathrm{x}{10}^5{\mathrm{mol}}^{-5}{\mathrm{L}}^5{\mathrm{s}}^{-1}$

Step-by-step solution

Finding the order w.r.t. all reactants separately

According to the question,$\mathrm{Rate}=\mathrm{k}[{\mathrm{H}}_2{\mathrm{SeO}}_3{]}^{\mathrm{a}}[{\mathrm{H}}^{+}{]}^{\mathrm{b}}[{\mathrm{I}}^{-}{]}^{\mathrm{c}}$

The rate equation for the 1^st column gives, $1.66\times {10}^{-7}=k[1\times {10}^{-2}{]}^1[2\times {10}^{-2}{]}^2[2\times {10}^{-2}{]}^3$... eq. ( i )

The rate equation for the 2^nd column gives, $3.33\times {10}^{-7}=k[2\times {10}^{-2}{]}^a[2\times {10}^{-2}{]}^b[2\times {10}^{-2}{]}^c$... eq. ( ii )

Dividing eq. ( i ) by eq. ( ii ), we get a = 1

The rate equation for the 6^th column gives, $3.34\times {10}^{-7}=k[1\times {10}^{-2}{]}^a[1\times {10}^{-2}{]}^b[4\times {10}^{-2}{]}^c$ ... eq. ( iii )

The rate equation for the 7^th column gives, $3.34\times {10}^{-7}=k[1\times {10}^{-2}{]}^a[1\times {10}^{-2}{]}^b[4\times {10}^{-2}{]}^c$... eq. ( iv )

Dividing eq. ( iii ) by eq. ( iv ), we get b = 2

The rate equation for the 5^th column gives, $0.42\times {10}^{-7}=k[1\times {10}^{-2}{]}^a[1\times {10}^{-2}{]}^b[2\times {10}^{-2}{]}^c$ ...eq. ( v )

Dividing eq. ( v ) by eq. ( iii ) and substituting the values of a and b, we get c = 3

Calculating value of k

Taking any equation, let’s say eq. ( i ) and putting the value of a, b, and c, we get

$1.66\times {10}^{-7}=k[1\times {10}^{-2}{]}^1[2\times {10}^{-2}{]}^2[2\times {10}^{-2}{]}^3$

We get the value of k, i.e. $5.19x{10}^5$.