I do not understand how equation(3) occurs.(taken from the book Internal Combustion Engines by John B.Heywood)(adsbygoogle = window.adsbygoogle || []).push({});

$$ $$

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??):

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

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# Chemical equilibrium reaction for burned gases in engine

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