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# Propane gas $(C_3H_8)$ at $25^\circ C,$ 1 atm enters a reactor operating at steady state and burns with 20% excess au entering at $25^\circ C,$ 1 atm. Of the carbon entering with the fuel, 94% (molar basis) appears in the products as $CO_2$ and the rest as CO. Heat transfer from the reactor occurs at a rate of $1.4 \times 10^6 kJ$ per kmol of propane. Ignoring kinetic and potential energy effects, determine the temperature of the combustion products exiting the reactor, in K.

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The ratio of $\ce{N2}$ to $\ce{O2}$ in air is,

\begin{align*} \dfrac{n_{\ce{N2}}}{n_{\ce{O2}}} &= \dfrac{0.79}{0.21} \\ &= 3.76 \end{align*}

The chemical reaction is,

$\ce{C3H8 + x (O2 + 3.76 N2) -> a CO2 + b H2O + 3.76x N2}$

The mass balance of C is:

\begin{align*} 3 &= a \end{align*}

The mass balance of H is:

\begin{align*} 8 &= 2b \\ 4 &= b \end{align*}

The mass balance of O is:

\begin{align*} 2x &= 2a + b \\ 2x &= 6 + 4 \\ x &= 5 \end{align*}

Substitute in the chemical reaction,

$\ce{C3H8 + 5 (O2 + 3.76 N2) -> 3 CO2 + 4 H2O + 18.8 N2}$

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