Effect of number of moles of carbon on the Stoichiometric co-efficient in Stoichiometric Combustion for Alkane, Alkene and Alkyne fuels.

In the theory of the Stoichiometric combustion assuming when the fuel and air mix, the products produced are only CO_2, H₂O, and N_2. 

                                                                                     ALKANES 

 The governing equation for the stoichiometric combustion for alkane is :

              C_nH_2n+2 + ar ( O₂ + 3.76N₂ ) = aCO₂ + bH₂O + cN₂

 Where, 

 n = Number of moles of C

ar = Stoichiometric co-efficient

 a = Number of moles of Carbon-di-oxide

 b = Number of moles of water

 c = number of moles of nitrogen

Assuming 100% yeild rate ; we get :

             n = a;

            2n +2 = 2b     or      n + 1 = b;

            2ar = 2a + b     or      2ar = 2(n) + ( n + 1 )        or     ar = `frac(3n +1)(2)`;    and

            3.76 ar = c      or      `frac(3.76 xx (3n +1))(2)` = c = 5.64n + 1.88 ;

In the problem statement, it is given to compare the relationship between the stoichiometric co-efficient ar and the number of moles of carbon i.e. n

From the above equations we have,

                                     ar = `frac(3n +1)(2)` 

In the plot between ar vs. n, we will have a graph with a positive slope of +1.5 and varying linearly.

                                                                                             ALKENES 

The governing equation for the stoichiometric combustion for an alkene is :

              C_nH_2n + ar ( O₂ + 3.76N₂ ) = aCO₂ + bH₂O + cN₂

Where

 n = Number of moles of C

ar = Stoichiometric co-efficient

 a = Number of moles of Carbon-di-oxide

 b = number of moles of water

 c = number of moles of nitrogen

Assuming 100% yeild rate ; we get :

             n = a;

            2n = 2b     or      n = b;

            2ar = 2a + b     or      2ar = 2(n) + (n) = `frac(3n)(2)`;    and

            3.76 ar = c      or      `frac(3.76 xx 3n)(2)` = c = 5.64n  ;

In the problem statement, it is given to compare the relationship between the stoichiometric co-efficient ar and the number of moles of carbon i.e. n

From the above equations we have,

                                        ar = `frac(3n)(2)` 

In the plot between ar vs. n, we will have a graph with a positive slope of +1.5 and varying linearly.

                                                                                         ALKYNES 

The governing equation for the stoichiometric combustion for an alkyne is :

              C_nH_2n-2 + ar ( O₂ + 3.76N₂ ) = aCO₂ + bH₂O + cN₂

Where

 n = Number of moles of C

ar = Stoichiometric co-efficient

 a = Number of moles of Carbon-di-oxide

 b = number of moles of water

 c = number of moles of nitrogen

Assuming 100% yeild rate ; we get :

             n = a;

            2n - 2 = 2b     or      n - 1 = b;

            2ar = 2a + b     or      2ar = 2(n) + (n - 1) = `frac(3n-1)(2)`;    and

            3.76 ar = c      or      `frac(3.76 xx (3n-1))(2)` = c = 5.64n - 1.88  ;

In the problem statement, it is given to compare the relationship between the stoichiometric co-efficient ar and the number of moles of carbon i.e. n

From the above equations we have,

                                     ar = `frac(3n -1)(2)` 

In the plot between ar vs. n, we will have a graph with a positive slope of +1.5 and varying linearly.

Conclusion: The variation of the number of moles of carbon on the stoichiometric coefficient is linear as is confirmed in the MATLAB study.