Pyrolysis of Dimethyl Ether

An analysis of the published data on the pyrolysis of dimethyl ether shows that the reaction can be interpreted as a chain decomposition initiated by ${\mathrm{CH}}_3{\mathrm{OCH}}_3\to {\mathrm{CH}}_3+{\mathrm{OCH}}_3$ , terminated by CH₃ radical recombination and accelerated by the chain transfer reaction CH₃+H₂→CH₄+H. A simplified Rice‐Herzfeld mechanism then gives for the over‐all rate of reaction the expression $$\frac{\mathrm{-d(}{\mathrm{Me}}_2\mathrm{O})}{\mathrm{dt}}{\mathrm{=k}}_0({\mathrm{Me}}_2\mathrm{O}{)}^{\frac{1}{2}}\left[\text{1+β}\frac{({\mathrm{CH}}_2\mathrm{O})}{({\mathrm{Me}}_2\mathrm{O})}+\frac{\mathrm{\alpha (}{\mathrm{H}}_2)}{({\mathrm{Me}}_2\mathrm{O})}\right]$$ where k₀=k₂(k₁/k₁₀)^½; k₂ representing H abstraction by CH₃ from Me₂O and k₁₀, CH₃ recombination. The data yield a value of k₀=4.31×10^—3 (liter/mole)^½ sec^—1 at 777°K. Using published data on k₂ and k₁₀, an estimated activation energy E₁=81.1 kcal and an estimated value of ΔS₁⁰=38 cal/mole‐°K one finds A₁=6.1×10¹⁶ sec^—1 and for the reverse reaction to 1, A_—1=7.0×10⁹ liter/mole sec. The data do not permit evaluation of β while α is in the range 0.3 to 0.4 for both H₂ and D₂. Independent calculations of α yield the values 0.8 for H₂ and 0.6 for D₂, both calculations having a probable error of a factor of 2. For the over‐all activation energy of the $\frac{3}{2}$ ; order chain, E₀=50.0 kcal. It is proposed that the observed exchange of Me₂O with D₂ is a heterogeneous reaction.