A gas consisting only of CO and N2 is made by passing a mixture of flue gas and air through a be

step 1 Okay, so first we need to find the moles of CO and O2 produced in this reaction. Since both the

A gas consisting only of CO and N2 is made by passing a...

A gas consisting only of $\mathrm{CO}$ and $\mathrm{N}_2$ is made by passing a mixture of flue gas and air through a bed of incandescent coke (assume pure carbon). The two reactions that occur both go to completion: $$ \mathrm{CO}_2+\mathrm{C} \rightarrow 2 \mathrm{C} 0 \quad \text { and } \quad 2 \mathrm{C}+\mathrm{O}_2 \rightarrow 2 \mathrm{C} 0 $$ They yield a flue gas of composition: $12.8 \mathrm{~mol}-\% \mathrm{CO}, 3.7 \mathrm{~mol}-\% \mathrm{CO}_2, 5.4 \mathrm{~mol}-\% \mathrm{O}_2$, and $78.1 \mathrm{~mol}-\% \mathrm{~N}_2$. The flue gas/air mixture is so proportioned that the heats of the two reactions cancel, and the temperature of the coke bed is therefore constant. If this temperature is $1148.15 \mathrm{~K}\left(875^{\circ} \mathrm{C}\right)$, if the feed stream is preheated to $1148.15 \mathrm{~K}\left(875^{\circ} \mathrm{C}\right)$, and if the process is adiabatic, what ratio of moles of flue gas to moles of air is required, and what is the composition of the gas produced?

A gas consisting only of $\mathrm{CO}$ and $\mathrm{N}_2$ is made by passing a mixture of flue gas and air through a bed of incandescent coke (assume pure carbon). The two reactions that occur both go to completion:
$$
\mathrm{CO}_2+\mathrm{C} \rightarrow 2 \mathrm{C} 0 \quad \text { and } \quad 2 \mathrm{C}+\mathrm{O}_2 \rightarrow 2 \mathrm{C} 0
$$
They yield a flue gas of composition: $12.8 \mathrm{~mol}-\% \mathrm{CO}, 3.7 \mathrm{~mol}-\% \mathrm{CO}_2, 5.4 \mathrm{~mol}-\% \mathrm{O}_2$, and $78.1 \mathrm{~mol}-\% \mathrm{~N}_2$. The flue gas/air mixture is so proportioned that the heats of the two reactions cancel, and the temperature of the coke bed is therefore constant. If this temperature is $1148.15 \mathrm{~K}\left(875^{\circ} \mathrm{C}\right)$, if the feed stream is preheated to $1148.15 \mathrm{~K}\left(875^{\circ} \mathrm{C}\right)$, and if the process is adiabatic, what ratio of moles of flue gas to moles of air is required, and what is the composition of the gas produced?

Key Concepts

Adiabatic Process

An adiabatic process is one in which no heat is exchanged with the surroundings. This concept is crucial in chemical engineering and thermodynamics, especially when analyzing reaction systems where the only heat changes come from the chemical reactions themselves. In the context of the problem, since the process is adiabatic, the energy balance must consider only the reaction heats, ensuring that the energy produced by exothermic reactions exactly cancels the energy consumed by endothermic reactions, thereby maintaining a constant temperature.

Reaction Stoichiometry

Reaction stoichiometry involves the quantitative relationships between reactants and products in a chemical reaction. It determines the proportions in which chemicals react and the amounts of products formed. In this problem, stoichiometry is essential for understanding how the flue gas reacts with carbon to yield carbon monoxide and to calculate the necessary ratios of the reactants and products, as well as to resolve the overall composition of the exiting gas stream.

Heat Balancing in Chemical Reactions

Heat balancing in chemical reactions refers to the management of the heat released or absorbed during the course of a reaction. In scenarios where multiple reactions occur simultaneously, it is important to design the system such that their heats of reaction cancel or balance each other, ensuring a desired thermal condition. Here, the composition of the flue gas and air is deliberately adjusted so that the exothermic and endothermic reaction heats offset each other, maintaining a constant temperature without external heat exchange.

Gas Mixture Composition and Mole Fractions

Understanding gas mixture composition and mole fractions is key to analyzing and designing processes involving multiple gaseous species. Mole fraction gives the ratio of moles of a particular component to the total number of moles in the mixture and is used to describe the composition of gas streams. In this problem, the mole percentages of CO, CO2, O2, and N2 in the flue gas are used to determine the appropriate mixing ratio with air, and ultimately, to predict the composition of the produced gas under the given process conditions.

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