Catalytic Activity of Ruthenium(III) and Thermodynamic Study of Oxidative Degradation of Chloramphenicol by Cerium(IV) in Sulfuric Acid Medium

Abstract

The micro amounts of ruthenium(III) catalyzed oxidation of chloramphenicol by cerium(IV) in an aqueous sulphuric acid medium has been studied spectrophotometrically at 25 °C and at I = 1.60 mol·dm⁻³. The order with respect to [Ce(IV)] and [Ru(III)] was found to be unity. Increasing [H⁺] accelerates the rate with less than unit order in [H⁺]. The reaction rate decreases with increasing ionic strength and increases with decreasing dielectric constant of the medium. The experimental results suggest that the active species of cerium(IV) and ruthenium(III) were CeSO₄ ²⁺ and [Ru(H₂O)₆]³⁺, respectively. Based on the experimental results a suitable mechanism was proposed and the rate law was derived. The activation parameters were calculated with respect to the slow step of the proposed mechanism and thermodynamic quantities were also determined. The reaction constants involved in the mechanism have been computed. There is a good agreement between the experimental and calculated rate constants under different experimental conditions.

Appendix: Derivation of Rate Law

According to Scheme 2:

$$ {\text{Rate = }}\frac{{ - {\text{d}}\left[ {{\text{Ce}}\left[ {\text{IV}} \right]} \right]}}{\text{dt}}{ = }k\left[ {\text{complex}} \right]\left[ {{\text{Ce}}\left( {\text{IV}} \right) \cdot {\text{H}}^{ + } } \right] $$

(13)

From second step of Scheme 2 we have,

$$ K_{6} = \frac{{\left[ {\text{complex}} \right]}}{{\left[ {\text{CHP}} \right]\left[ {{\text{Ru}}\left( {\text{III}} \right)} \right]}} $$

$$ \left[ {\text{complex}} \right]{ = }K_{6} \left[ {\text{CHP}} \right]\left[ {{\text{Ru}}\left( {\text{III}} \right)} \right] $$

(14)

Therefore,

From the first step of Scheme 2 we have,

$$ K_{5} = \frac{{\left[ {{\text{Ce}}\left( {\text{IV}} \right)} \cdot {\text{H}}^{ + }\right] }}{{\left[ {{\text{Ce}}\left({\text{IV}} \right)} \right][{\text{H}}^{ + } ]}} $$

$$ \left[ {{\text{Ce}}\left( {\text{IV}} \right) \cdot {\text{H}}^{ + } } \right] = K_{5} \left[ {{\text{Ce}}\left( {\text{IV}} \right)} \right]\left[ {{\text{H}}^{ + } } \right] $$

(15)

Substituting Eqs. 14 and 15 in Eq. 13 we get

$$ {\text{Rate }} = \frac{{ - {\text{d}}\left[ {{\text{Ce}}\left[ {\text{IV}} \right]} \right]}}{\text{dt}} = kK_{5} K_{6} \left[ {\text{CHP}} \right]\left[ {{\text{Ce}}\left( {\text{IV}} \right)\left[ {{\text{H}}^{ + } } \right]} \right]\left[ {{\text{Ru}}\left( {\text{III}} \right)} \right] $$

(16)

The total concentration of chloramphenicol, [CHP]_t is given by,

$$ \left[ {\text{CHP}} \right]_{\text{t}} = \left[ {\text{CHP}} \right]_{\text{f}} { + }\left[ {\text{complex}} \right] $$

$$ \left[ {\text{CHP}} \right]_{\text{t}} = \left[ {\text{CHP}} \right]_{\text{f}} { + }K_{6} \left[ {\text{CHP}} \right]_{\text{f}} \left[ {{\text{Ru}}\left( {\text{III}} \right)} \right] $$

$$ \left[ {\text{CHP}} \right]_{\text{f}} = \frac{{\left[ {\text{CHP}} \right]_{\text{t}} }}{{\left\{ { 1 { + }K_{6} \left[ {{\text{Ru}}\left( {\text{III}} \right)} \right]} \right\}}} $$

(17)

But in the experiment a very low concentration of ruthenium(III) is used, hence the term K ₆[Ru(III)] may be neglected in comparison with unity in Eq. 17. So,

$$ \left[ {\text{CHP}} \right] = \left[ {\text{CHP}} \right]_{\text{f}} $$

(18)

Similarly,

$$ \left[ {{\text{Ru}}\left( {\text{III}} \right)} \right]_{\text{t}} = \left[ {{\text{Ru}}\left( {\text{III}} \right)} \right]_{\text{f}} { + }\left[ {\text{complex}} \right] $$

$$ \left[ {{\text{Ru}}\left( {\text{III}} \right)} \right]_{\text{t}} = \left[ {{\text{Ru}}\left( {\text{III}} \right)} \right]_{\text{f}} { + }K_{6} \left[ {\text{CHP}} \right]\left[ {{\text{Ru}}\left( {\text{III}} \right)} \right]_{\text{f}} $$

$$ \left[ {{\text{Ru}}\left( {\text{III}} \right)} \right]_{\text{f}} { = }\frac{{\left[ {{\text{Ru}}\left( {\text{III}} \right)} \right]_{\text{t}} }}{{\left\{ { 1 { + }K_{6} \left[ {\text{CHP}} \right]} \right\}}} $$

(19)

and,

$$ \begin{gathered} \left[ {{\text{Ce}}\left( {\text{IV}} \right)} \right]_{\text{t}} = \left[ {{\text{Ce}}\left( {\text{IV}} \right)} \right]_{\text{f}} + \left[ {\text{Ce}\left( {\text{IV}} \right)} \cdot {\rm H}^{+}\right] \end{gathered} $$

$$ \left[ {{\text{Ce}}\left( {\text{IV}} \right)} \right]_{\text{t}} = \left[ {{\text{Ce}}\left( {\text{IV}} \right)} \right]_{\text{f}} { + }K_{5} \left[ {{\text{Ce}}\left( {\text{IV}} \right)} \right]_{\text{f}} \left[ {\rm H}^{+} \right] $$

$$ \left[ {{\text{Ce}}\left( {\text{IV}} \right)} \right]_{\text{f}} = \frac{{\left[ {{\text{Ce}}\left( {\text{IV}} \right)} \right]_{\text{t}} }}{{\left\{ { 1 { + }K_{5} \left[ {{\text{H}}^{ + } } \right]} \right\}}} $$

(20)

Substituting from Eqs. 18, 19 and 20 in Eq. 16 and omitting the subscripts we have,

$$ {\text{Rate = }}\frac{{ - {\text{d}}\left[ {{\text{Ce}}\left[ {\text{IV}} \right]} \right]}}{\text{dt}}{ = }\frac{{kK_{5} K_{6} \left[ {\text{CHP}} \right]\left[ {{\text{Ce}}\left( {\text{IV}} \right){\text{H}}^{ + } } \right]\left[ {{\text{Ru}}\left( {\text{III}} \right)} \right]}}{{1 + K_{6} \left[ {\text{CHP}} \right] + K_{5} \left[ {{\text{H}}^{ + } } \right] + K_{5} K_{6} \left[ {\text{CHP}} \right]\left[ {{\text{H}}^{ + } } \right]}} $$

(21)