Kinetic and Mechanistic Aspects of Oxidation of Aminotriazole Formamidine by Cerium(IV) in Aqueous Perchloric and Sulfuric Acid Solutions: A Comparative Study

Abstract

The kinetics of the oxidation of an aminotriazole formamidine derivative, N,N-dimethyl-N′-(4H-1,2,4-triazol-3-yl) formamidine (ATF) by cerium(IV) has been studied spectrophotometrically in aqueous perchloric and sulfuric acid solutions at constant ionic strength of 1.0 mol·dm⁻³. In both acids, the reaction shows first order kinetics with respect to [Ce(IV)], whereas the orders with respect to [ATF] are less than unity. The reaction exhibits negative fractional order kinetics with respect to [H⁺]. The rates of reaction are not significantly affected by variations of either ionic strength or relative permittivity of the reaction’s media. Addition of cerium(III) product does not affect the rates. Plausible mechanistic schemes for the reactions have been proposed. In both cases, the final oxidation products were identified as aminotriazole, dimethyl amine and carbon dioxide. Under comparable experimental conditions, the oxidation rate in perchloric acid solution is about sixfold higher than that in sulfuric acid solution. The effect of temperature on the rates has also been studied and activation parameters have been evaluated and discussed. The rate laws associated with the reaction mechanisms are derived.

Appendices

Appendix 1

Derivation of rate law in the case of perchloric acid.

According to the suggested mechanism and regarding to reaction (5),

$$ {\text{Rate}} = \frac{{ - {\text{d}}[{\text{Ce}}({\text{IV}})]}}{{{\text{d}}t}} = k_{1} [{\text{C}}_{1} ] $$

(25)

Regarding to reactions (3) and (4),

$$ K_{\text{OH}} = \frac{{[{\text{Ce}}({\text{OH}})^{3 + } ][{\text{H}}^{ + } ]}}{{[{\text{Ce}}^{4 + } ]}},\quad [ {\text{Ce}}({\text{OH}})^{3 + } ] { } = \frac{{K_{\text{OH}} [{\text{Ce}}^{4 + } ]}}{{[{\text{H}}^{ + } ]}} $$

(26)

and

$$ K = \frac{{[{{C}}_{1} ] \, }}{{[{\text{Ce}}({\text{OH}})^{3 + } ][{\text{ATF}}]}},\quad [{{C}}_{1} ] = K[{\text{Ce(OH)}}^{3 + } ][{\text{ATF}}] \, = \frac{{K_{\text{OH}} K[{\text{Ce}}^{4 + } ][{\text{ATF}}]}}{{[{\text{H}}^{ + } ]}} $$

(27)

Substituting Eq. 27 into Eq. 25 leads to,

$$ {\text{Rate}} = \frac{{k_{1}^{{}} K_{\text{OH}} K[{\text{Ce}}^{4 + } ][{\text{ATF}}]}}{{[{\text{H}}^{ + } ]}} $$

(28)

The total concentration of ATF is given by:

$$ [{\text{ATF}}]_{\text{T}}\, =\, \left[ {ATF} \right]_{\text{F}} \,+\, \left[ {{{C}}_{1} } \right] $$

(29)

where ‘T’ and ‘F’ stand for total and free concentrations.

Substituting Eq. 27 into Eq. 29 and rearrangement gives,

$$ \left[ {\text{ATF}} \right]_{\text{T}}\, = \, \left[ {\text{ATF}} \right]_{\text{F}}\, + \,\frac{{K_{\text{OH}} K[{\text{Ce}}^{ 4+ } ] [ {\text{ATF]}}}}{{[{\text{H}}^{ + } ]}} $$

(30)

$$ [{\text{ATF}}]_{\text{T}} = [{\text{ATF}}]_{\text{F}} \left( {1 + \frac{{K_{\text{OH}} K[{\text{Ce}}^{4 + } ]}}{{[{\text{H}}^{ + } ]}}} \right) $$

(31)

Therefore,

$$ \left[ {\text{ATF}} \right]_{\text{F}}\, = \,\frac{{[{\text{ATF}}]}}{{1 + \frac{{K_{\text{OH}} K[{\text{Ce}}^{4 + } ]}}{{[{\text{H}}^{ + } ]}}}}\, $$

(32)

In view of low [Ce⁴⁺], the second denominator term K _OH K[Ce⁴⁺]/[H⁺] in the above equation is neglected. Therefore,

$$ [{\text{ATF}}]_{\text{F}} = [{\text{ATF}}]_{\text{T}} $$

(33)

Also,

$$ [{\text{Ce}}({\text{IV}})]_{\text{T}} = [{\text{Ce}}^{4 + } ]_{\text{F}} + [{\text{Ce}}({\text{OH}})^{3 + } ] \, + [C_{1} ] $$

(34)

Substituting Eqs. 26 and 27 into Eq. 34,

$$ [{\text{Ce}}({\text{IV}})]_{\text{T}} = [{\text{Ce}}^{4 + } ]_{\text{F}} + \frac{{K_{\text{OH}} [{\text{Ce}}^{4 + } ]}}{{[{\text{H}}^{ + } ]}} + \frac{{K_{\text{OH}} K[{\text{Ce}}^{4 + } ][{\text{ATF}}]}}{{[{\text{H}}^{ + } ]}} $$

(35)

$$ [{\text{Ce(IV)}}]_{\text{T}} = [{\text{Ce}}^{4 + } ]_{\text{F}} \left( {1 + \frac{{K_{\text{OH}} }}{{[{\text{H}}^{ + } ]}} + \frac{{K_{\text{OH}} K[{\text{ATF}}]}}{{[{\text{H}}^{ + } ]}}} \right) $$

(36)

$$ [{\text{Ce}}^{4 + } ]_{\text{F}} = \frac{{[{\text{Ce}}({\text{IV}})]_{T} }}{{1 + \frac{{K_{\text{OH}} }}{{[{\text{H}}^{ + } ]}} + \frac{{K_{\text{OH}} K[{\text{ATF}}]}}{{[{\text{H}}^{ + } ]}}}} $$

(37)

Substituting Eqs. 33 and 37 into Eq. 28 (and omitting ‘T’ and ‘F’ subscripts) leads to,

$$ {\text{Rate}} = \frac{{k_{1} K_{\text{OH}} K[{\text{Ce}}({\text{IV}})][{\text{ATF}}]}}{{1 + \frac{{K_{\text{OH}} }}{{[{\text{H}}^{ + } ]}} + \frac{{K_{\text{OH}} K[{\text{ATF}}]}}{{[{\text{H}}^{ + } ]}}}} = \frac{{k_{1} K_{\text{OH}} K[{\text{Ce}}({\text{IV}})][{\text{ATF}}]}}{{[{\text{H}}^{ + } ] + K_{\text{OH}} + K_{\text{OH}} K[{\text{ATF}}]}}\, $$

(38)

Under pseudo-first order condition, the rate-law can be expressed by Eq. 39,

$$ {\text{Rate}} = \frac{{ - {\text{d}}[{\text{Ce}}({\text{IV}})]}}{{{\text{d}}t}} = k_{\text{obs}} [{\text{Ce(IV)}}] $$

(39)

Comparing Eqs. 38 and 39, the following relationship is obtained,

$$ k_{\text{obs}} = \frac{{k_{1} K_{\text{OH}} K[{\text{ATF}}]}}{{[{\text{H}}^{ + } ] + K_{\text{OH}} + K_{\text{OH}} K[{\text{ATF}}]}} $$

(40)

and with rearrangement, the following equations are obtained,

$$ \frac{1}{{k_{\text{obs}} }} = \left( {\frac{{[H^{ + } ] + K_{\text{OH}} }}{{k_{1} K_{\text{OH}} K_{1} }}} \right)\frac{1}{{[{\text{ATF}}]}} + \frac{1}{{k_{1} }} $$

(41)

$$ \frac{1}{{k_{\text{obs}} }} = \left( {\frac{1}{{k_{1} K_{\text{OH}} K_{1} [{\text{ATF}}]}}} \right)[{\text{H}}^{ + } ] + \frac{1}{{k_{1} K_{1} [{\text{ATF}}]}} + \frac{1}{{k_{1} }}. $$

(42)

Appendix 2

Derivation of rate law in case of sulfuric acid.

According to the suggested mechanism and regarding to reaction (16),

$$ {\text{Rate}} = \frac{{ - {\text{d}}[{\text{Ce}}({\text{IV}})]}}{{{\text{d}}t}} = k_{2} [{{C}}_{2} ] $$

(43)

Regarding reactions (14) and (15),

$$ K_{4} = \frac{{[{\text{H}}_{3} {\text{Ce}}({\text{SO}}_{4} )_{4}^{ - } ]}}{{[{\text{HCe}}({\text{SO}}_{4} )_{3}^{ - } ][{\text{HSO}}_{4}^{ - } ][{\text{H}}^{ + } ]}},\quad [{\text{H}}_{3} {\text{Ce}}({\text{SO}}_{4} )_{4}^{ - } ] = K_{4} [{\text{HCe(SO}}_{4} )_{3}^{ - } ][{\text{HSO}}_{4}^{ - } ][{\text{H}}^{ + } ] $$

(44)

$$ K_{5} = \frac{{[{{C}}_{2} ] \, }}{{[{\text{HCe}}({\text{SO}}_{4} )_{3}^{ - } ][{\text{ATF}}]}},\quad [{{C}}_{2} ] = K_{5} [{\text{HCe}}({\text{SO}}_{4} )_{3}^{ - } ][{\text{ATF}}] $$

(45)

Substituting Eq. 45 into Eq. 43 leads to,

$$ {\text{Rate}} = k_{2} K_{5} [{\text{HCe}}({\text{SO}}_{4} )_{3}^{ - } ][{\text{ATF}}] $$

(46)

The total concentration of ATF is given by:

$$ [{\text{ATF}}]_{\text{T}} = [{\text{ATF}}]_{\text{F}} + [{{C}}_{2} ] $$

(47)

Substituting Eq. 45 into Eq. 47 and rearrangement gives,

$$ [{\text{ATF}}]_{\text{T}} = [{\text{ATF}}]_{\text{F}} + K_{5} [{\text{HCe}}({\text{SO}}_{4} )_{3}^{ - } ][{\text{ATF}}] $$

(48)

$$ [{\text{ATF}}]_{{}} = [{\text{ATF}}]_{\text{F}} (1 + K_{5} [{\text{HCe}}({\text{SO}}_{4} )_{3}^{ - } ]) $$

(49)

Therefore,

$$ \left[ {\text{ATF}} \right]_{\text{F}} \,=\, \frac{{[{\text{ATF}}]_{\text{T}} }}{{1 + K_{5} [{\text{HCe}}({\text{SO}}_{4} )_{3}^{ - } ]}} $$

(50)

In view of low [HCe(SO₄) ⁻₃ ], the second numerator term in the above equation is neglected. Therefore,

$$ [{\text{ATF}}]_{\text{F}} = [{\text{ATF}}]_{\text{T}} $$

(51)

Also,

$$ [{\text{Ce}}({\text{IV}})]_{\text{T}} = [{\text{HCe}}({\text{SO}}_{4} )_{3}^{ - } ] + [{\text{H}}_{3} {\text{Ce}}({\text{SO}}_{4} )_{4}^{ - } ] + [{{C}}_{2} ] $$

(52)

Substituting Eqs. 44 and 45 into Eq. 52,

$$ [{\text{Ce}}({\text{IV}})]_{\text{T}} = [{\text{HCe(SO}}_{4} )_{3}^{ - } ] + K_{4} [{\text{HCe(SO}}_{4} )_{3}^{ - } ][{\text{HSO}}_{4}^{ - } ][{\text{H}}^{ + } ] + K_{5} [{\text{HCe(SO}}_{4} )_{3}^{ - } ][{\text{ATF}}] $$

(53)

$$ [{\text{Ce}}({\text{IV}})]_{\text{T}} = [{\text{HCe(SO}}_{4} )_{3}^{ - } ](1 + K_{4} [{\text{HSO}}_{4}^{ - } ][{\text{H}}^{ + } ] + K_{5} [{\text{ATF}}]) $$

(54)

$$ [{\text{HCe}}({\text{SO}}_{4} )_{3}^{ - } ] = \frac{{[{\text{Ce}}({\text{IV}})]_{\text{T}} }}{{1 + K_{4} [{\text{HSO}}_{4}^{ - } ][{\text{H}}^{ + } ] + K_{5} [{\text{ATF}}]}} $$

(55)

Substituting Eqs. 51 and 55 into Eq. 46 leads to,

$$ {\text{Rate}} = \frac{{k_{2} K_{5} [{\text{Ce}}({\text{IV}})][{\text{ATF}}]}}{{1 + K_{4} [{\text{HSO}}_{4}^{ - } ][{\text{H}}^{ + } ] + K_{5} [{\text{ATF}}]}} $$

(56)

Under pseudo-first order condition, the rate-law can be expressed by Eq. 57,

$$ {\text{Rate}} = \frac{{ - {\text{d}}[{\text{Ce}}({\text{IV}})]}}{{{\text{d}}t}} = k_{\text{obs}} [{\text{Ce}}({\text{IV}})] $$

(57)

Comparing Eqs. 56 and 57, the following relationship is obtained,

$$ k_{\text{obs}} = \frac{{k_{2} K_{5} [{\text{ATF}}]}}{{1 + K_{4} [{\text{HSO}}_{4}^{ - } ][{\text{H}}^{ + } ] + K_{5} [{\text{ATF}}]}} $$

(58)

and with rearrangement, the following equations are obtained:

$$ \frac{1}{{k_{\text{obs}} }} = \left( {\frac{{1 + K_{4} [{\text{HSO}}_{4}^{ - } ][{\text{H}}^{ + } ]}}{{k_{2} K_{5} }}} \right)\frac{1}{{[{\text{ATF}}]}} + \frac{1}{{k_{2} }} $$

(59)

$$ \frac{1}{{k_{\text{obs}} }} = \left( {\frac{{K_{4} }}{{k_{2} K_{5} }}} \right)[{\text{HSO}}_{4}^{ - } ][{\text{H}}^{ + } ] + \frac{1}{{k_{2} K_{5} [{\text{ATF}}]}} + \frac{1}{{k_{2} }}. $$

(60)