Chemical equilibrium reaction for burned gases in engine

[marellasunny]

I do not understand how equation(3) occurs.(taken from the book Internal Combustion Engines by John B.Heywood)
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Consider a reactive mixture of ideal gases. The reactant species $M_a,M_b$ etc.and the product species $M_l,M_m$ 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 $\upsilon _i$ are the stoichiometric coefficients and by convention are positive for the product species and negative for the reactant species.

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

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

1.*Does $\delta n$ 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??):

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

 

[Navin A S]

1.*Does \delta n here signify 'extent of reaction'?*Yes, \delta n here signifies the 'extent of reaction', which is the amount of reactants or products that has reacted. 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?*Equation 3 states that the amounts of the reactants and products are proportional to their respective stoichiometric coefficients (\upsilon _i). For example, if we have the reaction A + B -> C + D, with stoichiometric coefficients \upsilon _A = -1, \upsilon _B = -1, \upsilon _C = 1, and \upsilon _D = 1. This means that for every molecule of A, one molecule of B must be consumed, and for every molecule of B, one molecule of A must be consumed. Additionally, for every molecule of A and B consumed, one molecule of C and D will be produced. So, if we have \delta n of A and B reacted, then we will have \delta n of C and D produced.