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reaction_rate_equation [2015/08/15 20:33]
nikolaj
reaction_rate_equation [2015/08/15 20:34] (current)
nikolaj
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 | @#55EE55: postulate ​  | @#55EE55: $ \frac{\partial}{\partial t}[A]_j=\sum_{r=1}^R k_r\cdot(\nu_{rj}^+-\nu_{rj}^-)\cdot\prod_{i=1}^J [A]_i^{\nu_{ri}^-} $ | | @#55EE55: postulate ​  | @#55EE55: $ \frac{\partial}{\partial t}[A]_j=\sum_{r=1}^R k_r\cdot(\nu_{rj}^+-\nu_{rj}^-)\cdot\prod_{i=1}^J [A]_i^{\nu_{ri}^-} $ |
  
-==== Discussion ====+-----
 The quantities $R$ and $J$ denote the number of reactions and the number of different species. The quantities $R$ and $J$ denote the number of reactions and the number of different species.
 Then $\nu_{rj}^-$ and $\nu_{rj}^+$ are stochastic coefficients of the reactants and products and $k_r$ is the reaction rate coefficient of the $r$'s reaction. ​ Then $\nu_{rj}^-$ and $\nu_{rj}^+$ are stochastic coefficients of the reactants and products and $k_r$ is the reaction rate coefficient of the $r$'s reaction. ​
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 Non-time resolved, this reads for all $r$ Non-time resolved, this reads for all $r$
  
-$\sum_{j=1}^J \nu_{rj}^{(e)} A_j \overset{k_r}{\longrightarrow} \sum_{j=1}^J \nu_{rj}^{(p)} A_j$ +$\sum_{j=1}^J \nu_{rj}^{(e)} A_j \overset{k_r}{\longrightarrow} \sum_{j=1}^J \nu_{rj}^{(p)} A_j.$
- +
-e.g. the simplest carbon combustion process+
  
 +For example, the simplest carbon combustion process:
 $\mathrm{C}\mathrm{H}_4 + 2\ \mathrm{O}_2 \longrightarrow \mathrm{C}\mathrm{O}_2 + 2\ \mathrm{H}_2\mathrm{O}.$ $\mathrm{C}\mathrm{H}_4 + 2\ \mathrm{O}_2 \longrightarrow \mathrm{C}\mathrm{O}_2 + 2\ \mathrm{H}_2\mathrm{O}.$
  
-(Or more explicitly  ​+(Or more explicitly 
 $1\ \mathrm{C}\mathrm{H}_4 + 2\ \mathrm{O}_2 + 0\ \mathrm{C}\mathrm{O}_2 + 0\ \mathrm{H}_2\mathrm{O} \longrightarrow 0\ \mathrm{C}\mathrm{H}_4 + 0\ \mathrm{O}_2 + 1\ \mathrm{C}\mathrm{O}_2 + 2\ \mathrm{H}_2\mathrm{O}$.) $1\ \mathrm{C}\mathrm{H}_4 + 2\ \mathrm{O}_2 + 0\ \mathrm{C}\mathrm{O}_2 + 0\ \mathrm{H}_2\mathrm{O} \longrightarrow 0\ \mathrm{C}\mathrm{H}_4 + 0\ \mathrm{O}_2 + 1\ \mathrm{C}\mathrm{O}_2 + 2\ \mathrm{H}_2\mathrm{O}$.)
  
 In practice, $k$ depends on the temperature,​ which, through the equation of state, can again be a nonlinear function of the concentrations. In practice, $k$ depends on the temperature,​ which, through the equation of state, can again be a nonlinear function of the concentrations.
 +
 === Reference === === Reference ===
 Wikipedia: [[https://​en.wikipedia.org/​wiki/​Rate_equation|Rate equation]] Wikipedia: [[https://​en.wikipedia.org/​wiki/​Rate_equation|Rate equation]]
  
-==== Parents ====+-----
 === Subset of === === Subset of ===
 [[ODE system]] [[ODE system]]
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