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# Methyl alcohol $(CH_3OH)$ burns with 200% theoretical air, yielding $CO_2, H_2O, O_2,$ and $N_2.$ Determine the a. balanced reaction equation. b. air-fuel ratio on a mass basis. c. molar analysis of the products.

Solution

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(a) The chemical equation

\begin{align*} CH_3OH + (2.0)a(O_2 + 3.76N_2) \rightarrow b CO_2 + cH_2O + aO_2 + dN_2 \end{align*}

To balance the equation we have

\begin{align*} C:& \quad 1 = b \\ H:& \quad 4 = 2c \\ O:& \quad 1 + 4a = 2b + c + 2a \\ N:& \quad 2a(3.76)(2) = 2d \\ \end{align*}

Thus, $b = 1$; $c = 2$, $a = 1.5$, $d = 11.28$

The balanced reaction is

\begin{align*} CH_3OH + (2.0)(1.5)(O_2 + 3.76N_2) \rightarrow CO_2 + 2H_2O + 1.5O_2 + 11.28N_2 \end{align*}

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