Kinetics and mechanism of uncatalyzed and ruthenium(III)-catalyzed oxidation of formamidine derivative by hexacyanoferrate(III) in aqueous alkaline medium

Abstract

The catalytic effect of ruthenium(III) on the oxidation of N, N-dimethyl- N ^′-(4H-1,2,4-triazol- 3-yl) formamidine (ATF) by hexacyanoferrate(III) (HCF) was studied spectrophotometrically in aqueous alkaline medium. Both uncatalyzed and catalyzed reactions showed first order kinetics with respect to [HCF], whereas the reaction orders with respect to [ATF] and [OH ⁻] were apparently less than unity over the concentration range studied. A first order dependence with respect to [Ru^III] was obtained. Increasing ionic strength increased the rate of uncatalyzed reaction and decreased the rate of the catalyzed one Plausible mechanistic schemes of oxidation reactions have been proposed. In both cases, the final oxidation products are identified as aminotriazole, dimethyl amine and carbon dioxide. The rate laws associated with the reaction mechanisms are derived. The reaction constants involved in the different steps of the mechanisms were calculated. The activation and thermodynamic parameters have been computed and discussed.

Appendix A. Derivation of the rate-law expression for the uncatalyzed oxidation reaction.

According to the suggested mechanistic scheme 2,

$$ \text{Rate} = \frac{-d[\text{HCF]}}{dt}\, = k_{1}[\text{C}_{1}] $$

(A1)

$$ \text{K} = \frac{[\text{ATF}^{-}]}{[\text{ATF}][\text{OH}^{-}]}\, , [\text{ATF}^{\mathrm{-}}]= K[\text{ATF}][\text{OH}^{\mathrm{-}}] $$

(A2)

$$\begin{array}{@{}rcl@{}} K_{1} &=& \frac{\text{[C}_{\text{1}} \text{] } }{[\text{ATF}^{-}][\text{HCF}]}\,, [\text{C}_{1}] = K_{1}[\text{ATF}^{\mathrm{-}}][HCF] \\ &=& KK_{1}[\text{ATF}][\text{HCF}][\text{OH}^{\mathrm{-}}] \end{array} $$

(A3)

Substituting Eq. (A3) into Eq. (A1) leads to,

$$ \text{Rate} = k_{1}KK_{1}[\text{ATF}][\text{HCF}][\text{OH}^{\mathrm{-}}] $$

(A4)

The total concentration of ATF is given by,

$$ [\text{ATF}]_{\mathrm{T}} = [\text{ATF}]_{\mathrm{F}} + [\text{ATF}^{\mathrm{-}}] + [\text{C}_{1}] $$

(A5)

$$ [\text{ATF}]_{\mathrm{F}}\,=\,\frac{[\text{ATF}]_{\mathrm{T}}} {1+K[\text{OH}^{-}]+ KK_{1} [\text{HCF}][\text{OH}^{-}]} $$

(A6)

In view of low [HCF], the third denominator term KK ₁[HCF][OH] in the above equation can be neglected. Therefore, Eq. (A6) can be simplified to the following equation,

$$ [\text{ATF}]_{\mathrm{F}}\,=\,\frac{[\text{ATF}]_{\mathrm{T}}} {1+ K[\text{OH}^{-}]} $$

(A7)

$$ [\text{HCF}]_{\mathrm{T}} = [\text{HCF}]_{\mathrm{F}} + [\text{C}_{1}] $$

(A8)

$$ [\text{HCF}]_{\mathrm{F}}\,=\,\frac{[\text{HCF}]_{\mathrm{T}}} {1+ KK_{1} [\text{ATF}][\text{OH}^{-}]} $$

(A9)

Substituting Eqs. (A7) and (A9) into Eq. (A4) (and omitting ‘T’ and ‘F’ subscripts) leads to,

$$ \text{Rate} \,=\,\frac{k_{1} KK_{1} [\text{ATF}][\text{HCF}][\text{OH}^{-}]}{(1 + K[\text{OH}^{-}])(1+KK_{1} [\text{ATF}][\text{OH}^{-}])} $$

(A10)

Under pseudo-first order condition, the rate-law can be expressed by Eq. (A11),

$$ \text{Rate} = \frac{-d[\text{HCF}]}{dt}\,= k_{\mathrm{U}}[\text{HCF}] $$

(A11)

Comparing Eqs. (A10) and (A11), the following relationship is obtained.

$$ k_{\mathrm{U}}{}={}\frac{k_{1} KK_{1} [\text{ATF}][\text{OH}^{-}]}{1 {}+{} K{}[{}\text{O{}H}^{-}{}]{}+{}K{}K_{{}1}{} [{}\text{ATF}]{}[{}\text{O{}H}^{-}{}]{}+{}K^{2}{}K_{{}1}{} [{}\text{ATF}][\text{OH}^{-}]^{2}} $$

(A12)

The term K ² K ₁[ATF][OH ⁻] ² in the denominator of Eq. (A12) is negligibly small compared to unity in view of the low concentration of ATF used. Therefore, this term can be deleted and with rearrangement, the following equations are obtained.

$$ \frac{1}{k_{\mathrm{U}}} \,=\,\left( {\frac{\text{1}}{k_{\text{1}} KK_{\text{1}} [\text{OH}^{-}]}+\frac{\text{1}}{k_{\text{1}} K_{\text{1}}} } \right)\frac{1}{[\text{ATF}]}+\frac{\text{1}}{k_{1}} $$

(A13)

$$ \frac{1}{k_{\mathrm{U}}} \,=\,\left( {\frac{\text{1}}{k_{\text{1}} KK_{\text{1}} [\text{ATF}]}} \right)\frac{1}{[\text{OH}^{-}]}+\frac{1}{k_{\text{1}} K_{\text{1}} [\text{ATF}]}+\frac{\text{1}}{k_{1}} $$

(A14)