Question 7.FP.4: At an ionic strength of 0.100 mol dm^-3 and a temperature of......
At an ionic strength of 0.100 mol \mathrm{d}\mathrm{m}^{-3} and a temperature of 25 °C, the observed rate constant for the reaction
\mathrm{CH}_{2}\mathrm{BrCOO}^{-}({\mathrm{aq}})+\mathrm{S}_{2}\mathrm{O}_{3}^{2-}({\mathrm{aq}})\to\mathrm{CH}_{2}\mathrm{S}_{2}\mathrm{O}_{3}\mathrm{COO}^{2-}({\mathrm{aq}})+\mathrm{Br}^{-}({\mathrm{aq}})
is 1.07\times10^{-2}\,\mathrm{mol}^{-1}\,\mathrm{d}\mathrm{m}^{3}\,\mathrm{s}^{-1}, while that for a reaction of the type
\mathrm{Ptdien}X^{+}(\mathrm{aq})+Y^{-}(\mathrm{aq})\longrightarrow\mathrm{Ptdien}Y^{+}(\mathrm{aq})+X^{-}(\mathrm{aq})
{\mathrm{is~}}3.6\times10^{-3}\mathrm{~mol}^{-1}\ {\mathrm{dm}}^{3}\ s^{-1}. Comment on these values.
Estimate the values of the rate constants for zero ionic strength, and comment on the relative values and compare with the values at I=0.100\mathrm{~mol~dm}^{-3}.
- \mathrm{At}\,I=0.100\,\mathrm{mol}^{-1}\,\mathrm{dm}^{3}, the reaction of \mathrm{CH}_{2}\mathrm{BrCOO}^{-}({\mathrm{aq}})\mathrm{~with ~S_{2}O_{3}^{2-}({\mathrm{aq}})} has a larger rate constant than that for \mathrm{Ptdien}X^{+}(\mathrm{aq})\,+\,\mathrm{Y}^{-}(\mathrm{aq}).
- \mathrm{CH}_{2}\mathrm{BrCOO}^{-}({\mathrm{aq}})+\mathrm{S}_{2}\mathrm{O}_{3}^{2-}({\mathrm{aq}})\to
{{z}}_{\mathrm{A}}{{z}}_{\mathrm{B}}=(-1)\times(-2)=2
\log_{10}k=\log_{10}k_{0}+2\times2\times0.510{\frac{\sqrt{0.100}}{1+{\sqrt{0.100}}}}
\mathrm{log}_{10}~k_{0}=\mathrm{log}_{10}(1.07\times10^{-2}\,\mathrm{mol}^{-1}\,\mathrm{dm}^{3}\,\mathrm{s}^{-1})-0.490=-2.461
k_{0}=3.5\times10^{-3}\,\mathrm{mol}^{-1}\,\mathrm{d}\mathrm{m}^{3}\,\mathrm{s}^{-1}
- \mathrm{Ptdien}X^{+}(\mathrm{aq})+Y^{-}(\mathrm{aq})\to
z_{\mathrm{A}}z_{\mathrm{B}}=1\times(-1)=-1
\log_{10}k=\log_{10}k_{0}+2\times(-1)\times0.510{\frac{\sqrt{0.100}}{1+{\sqrt{0.100}}}}
\log_{10}k_{0}=\log_{10}(3.6\times10^{-3}\,\mathrm{{mol}}^{-1}\,\mathrm{{dm}}^{3}\,\mathrm{{s}}^{-1})+0.245=-2.199
k_{0}=6.3\times10^{-3}\,\mathrm{mol}^{-1}\,\mathrm{d}\mathrm{m}^{3}\,\mathrm{s}^{-1}.
- When the rate constants at zero ionic strength are compared, the reaction between \mathrm{Ptdien}X^{+}(\mathrm{aq})\;\;\;\mathrm{and}\;\;\;Y^{-}(\mathrm{aq})now has the larger rate constant. If conclusions and inferences were made on the basis of non-ideal rate constants (i.e. non-zero ionic strengths) they would be misleading. This problem shows that the relative order of magnitude for these two reactions changes as the ionic strength increases, and emphasizes the need to use ideal rate constants
whenever possible. This is particularly so when the products of the charges on the reactants are different. However, other less specific salt effects, such as charge separation in the activated complex, may also be important even for reactions of the same charge type.