## Related questions with answers

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.

Solutions

VerifiedThe 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,

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

Balanced equation for complete combustion of propane gas$(C_{3}H_{8})$ with theoretical amount of air

$\begin{align*} C_{3}H_{8} + 5 (O_{2} +3.76N_{2}) \rightarrow 3 CO_{2} + 4 H_{2}O + 18.8 N_{2} \\ \end{align*}$

Balanced equation for complete combustion of propane gas$(C_{3}H_{8})$ with$20 \%$ excess air

$94 \%$ of carbon changed to $CO_{2}$ and rest to $CO$

$\begin{align*} C_{3}H_{8} + 6 (O_{2} +3.76N_{2}) \rightarrow 2.8 CO_{2} + 0.18CO +4 H_{2}O + 22.56 N_{2} + 1.09O_{2} \\ \end{align*}$

Reduced energy rate balanced equation is

$\begin{align*} \dfrac{Q_{CV}}{N_{C_{3}H_{8}}}&= 2.282\overline{h}_{CO_{2}} +1.O9\overline{h}_{O_{2}} + 4 \overline{h}_{H_{2}O} +22.56\overline{h}_{N_{2}} + 0.18 \overline{h}_{CO} - \overline{h}_{C_{3}H_{8}} - 6\overline{h}_{O_{2}} -22.56 \overline{h}_{N_{2}} ................(1) \\ \end{align*}$

Q= heat transfer

$\overline{h}_{CO_{2}}=$ the enthalpy of $CO_{2}$

$\overline{h}_{O_{2}}=$the enthalpy of $O_{2}$

$\overline{h}_{H_{2}O}=$ the enthalpy of $H_{2}O$

$\overline{h}_{N_{2}}=$the enthalpy of $N_{2}$

$\overline{h}_{C_{3}H_{8}}=$ the enthalpy of $C_{3}H_{8}$

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