Determination of the Rate Constants of the Reactions Cr + O2 + M → CrO2 + M and Cr + O2 → CrO + O

Abstract

The rate constants of the interactions of chromium atoms with molecular oxygen through recombination Cr + O2 + M → CrO2 + M (I) and exchange Cr + O2 → CrO + O (II) were determined by a new method for treatment of experimental data. The results, together with the available literature data, led to the following equations for the rate constants of recombination in the low-pressure limit and of the exchange reaction: \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{k}_{{1,0}}}(300 < T < 2000\\,\\,{\\text{K}}) = {\\text{ }}3.7{\\text{ }} \\times {\\text{ }}{{10}^{{18}}}{{\\left( {{T \\mathord{\\left/ {\\vphantom {T {1000}}} \\right. \\kern-0em} {1000}}} \\right)}^{{ - 1.49}}},$$\\end{document} cm6 mol–2 s–1, \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{k}_{2}}(700 < T < 4000\\,{\\text{K}}) = $$\\end{document}\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$4.0 \\times {{10}^{{14}}}{{\\left( {{T \\mathord{\\left/ {\\vphantom {T {1000}}} \\right. \\kern-0em} {1000}}} \\right)}^{{ - 0.32}}}exp\\left( { - {{4480{\\kern 1pt} \\,{\\text{K}}} \\mathord{\\left/ {\\vphantom {{4480{\\kern 1pt} \\,{\\text{K}}} T}} \\right. \\kern-0em} T}} \\right)$$\\end{document}, cm3 mol‒1 s‒1. An expression for the rate constant of the reverse reaction was obtained from k2(T) and the equilibrium constant for reaction (II): \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{k}_{{ - 2}}}(700 < T < 4000\\,{\\text{K}}) = 3.6 \\times {{10}^{{13}}}{{\\left( {{T \\mathord{\\left/ {\\vphantom {T {1000}}} \\right. \\kern-0em} {1000}}} \\right)}^{{ - 0.64}}}$$\\end{document} cm3 mol‒1 s‒1. Modeling within the framework of the RRKM theory shows that calculation of the rate constant k1,0(T) requires inclusion of not only the ground electronic state of the CrO2 molecule, but also the low-lying excited electronic states up to the dissociation threshold. A comparison of the experimental and calculated temperature dependences shows that the best agreement between them is achieved at an average portion of energy transferred in deactivating collisions of the excited CrO2 molecule with diluent gas molecules of ΔE = 2.8 kJ/mol.