An equimolar mixture of nitrogen and acetylene enters a...

An equimolar mixture of nitrogen and acetylene enters a steady-flow reactor at $298.15 \mathrm{~K}$ $\left(25^{\circ} \mathrm{C}\right)$ and atmospheric pressure. The only reaction occurring is: $$ \mathrm{N}_2(g)+\mathrm{C}_2 \mathrm{H}_2 \rightarrow 2 \mathrm{HCN}(g) $$ The product gases leave the reactor at $873.15 \mathrm{~K}\left(600^{\circ} \mathrm{C}\right)$ and contain $24.2 \mathrm{~mole}-\% \mathrm{HCN}$. How much heat is supplied to the reactor per mole of product gas?

An equimolar mixture of nitrogen and acetylene enters a steady-flow reactor at $298.15 \mathrm{~K}$ $\left(25^{\circ} \mathrm{C}\right)$ and atmospheric pressure. The only reaction occurring is:
$$
\mathrm{N}_2(g)+\mathrm{C}_2 \mathrm{H}_2 \rightarrow 2 \mathrm{HCN}(g)
$$

The product gases leave the reactor at $873.15 \mathrm{~K}\left(600^{\circ} \mathrm{C}\right)$ and contain $24.2 \mathrm{~mole}-\% \mathrm{HCN}$. How much heat is supplied to the reactor per mole of product gas?

Key Concepts

Steady-Flow Reactor Analysis

This concept involves understanding how reactors operate under constant flow conditions where the system properties remain constant with time. The steady-flow assumption simplifies mass and energy balances, making it possible to relate the input and output streams via conservation laws without accumulation terms. It is fundamental for evaluating chemical processes under continuous operation.

Reaction Stoichiometry

Stoichiometry is the quantitative relationship between reactants and products in a chemical reaction. It allows the determination of how much of each reactant is needed or how much product is formed, based on the balanced chemical equation. This concept is crucial to link the conversion of reactants to product yields and calculate parameters like heat released or absorbed.

Energy Balance and Enthalpy Change

Applying the first law of thermodynamics to chemical reactors allows the calculation of the heat effects involved in a reaction. The energy balance accounts for changes in enthalpy between the inlet and outlet streams and the heat added or removed from the system. This concept helps in determining how much heat must be supplied (or removed) to maintain reactor conditions during an exothermic or endothermic reaction.

Mole Fraction and Conversion Calculations

Mole fraction is a way of representing the composition of a mixture by accounting for the ratio of moles of a component to the total number of moles. In reactor analysis, knowing the mole fractions at the outlet aids in determining the extent of reaction and conversion of reactants into products. This concept bridges the gap between measured composition data and reaction parameters.

Standard Enthalpy of Reaction

This concept refers to the change in enthalpy, or heat content, that occurs during a reaction under standard conditions. By using standard enthalpies of formation for reactants and products, one can compute the overall enthalpic change of the reaction. This is critical for understanding the heat effects and calculating the required energy input in chemical process design.

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