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Chemical equilibrium reaction for burned gases in engine

  1. May 31, 2013 #1
    I do not understand how equation(3) occurs.(taken from the book Internal Combustion Engines by John B.Heywood)
    $$ $$
    Consider a reactive mixture of ideal gases. The reactant species [itex] M_a,M_b [/itex] etc.and the product species [itex]M_l,M_m[/itex] etc. are related by the general reaction whose stoichiometry is given by:
    $$\upsilon _aM_a+\upsilon _bM_b+...=\upsilon _lM_l+\upsilon _mM_m+...$$

    This can be otherwise written as:
    $$ \sum_{i}\upsilon _iM_i=0$$
    where the [itex]\upsilon _i[/itex] are the stoichiometric coefficients and by convention are positive for the product species and negative for the reactant species.

    Let [itex]\delta n_a[/itex] of [itex]M_a[/itex] react with [itex]\delta n_b[/itex] of [itex]M_b[/itex],etc. and produce [itex]\delta n_l[/itex] of [itex]M_l[/itex],[itex]\delta n_m[/itex] of [itex]M_m[/itex],etc.. These amounts are in proportion,given by the equation (3):

    (3) $$\delta n_i=\upsilon _i\delta n$$

    1.*Does [itex]\delta n[/itex] here signify 'extent of reaction'?*

    2.*I would eventually like to use the number of moles of each species in expressing the chemical potential,with the gibbs free energy already known. But,the part I don't understant is equation 3. What does the author mean by proportional? Could you give a example?*

    Gibbs free energy is given as:
    $$(\Delta G)_(pressure,temper_)=\sum_{i}\mu _i\delta n_i$$

    which by equation(3) can be re-written as(WHY??):

    $$(\Delta G)_(pressure,temper_)=\sum_{i}\mu _i\nu _i\delta n$$
  2. jcsd
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