A gas mixture of methane and steam at atmospheric pressure...

A gas mixture of methane and steam at atmospheric pressure and $773.15 \mathrm{~K}\left(500^{\circ} \mathrm{C}\right)$ is fed to a reactor, where the following reactions occur: $$ \mathrm{CH}_4+\mathrm{H}_2 \mathrm{O} \rightarrow \mathrm{CO}+3 \mathrm{H}_2 \text { and } \mathrm{CO}+\mathrm{H}_2 \mathrm{O} \rightarrow \mathrm{CO}_2+\mathrm{H}_2 $$ The product stream leaves the reactor at $1123.15 \mathrm{~K}\left(850^{\circ} \mathrm{C}\right)$. Its composition (mole fractions) is: $$ y_{\mathrm{CO}_2}=0.0275 \quad y_{\mathrm{CO}}=0.1725 \quad y_{\mathrm{H}_2 \mathrm{O}}=0.1725 \quad y_{\mathrm{H}_2}=0.6275 $$ Determine the quantity of heat added to the reactor per mole of product gas.

A gas mixture of methane and steam at atmospheric pressure and $773.15 \mathrm{~K}\left(500^{\circ} \mathrm{C}\right)$ is fed to a reactor, where the following reactions occur:
$$
\mathrm{CH}_4+\mathrm{H}_2 \mathrm{O} \rightarrow \mathrm{CO}+3 \mathrm{H}_2 \text { and } \mathrm{CO}+\mathrm{H}_2 \mathrm{O} \rightarrow \mathrm{CO}_2+\mathrm{H}_2
$$

The product stream leaves the reactor at $1123.15 \mathrm{~K}\left(850^{\circ} \mathrm{C}\right)$. Its composition (mole fractions) is:
$$
y_{\mathrm{CO}_2}=0.0275 \quad y_{\mathrm{CO}}=0.1725 \quad y_{\mathrm{H}_2 \mathrm{O}}=0.1725 \quad y_{\mathrm{H}_2}=0.6275
$$

Determine the quantity of heat added to the reactor per mole of product gas.

Key Concepts

Gas Mixture Composition Analysis

Gas mixture composition analysis involves using mole fractions to describe the relative amounts of various species present in a gas phase. This quantitative description is important for determining the overall properties of the mixture, such as enthalpy, and for calculating reaction yields and energy balances in processes involving gaseous reactants and products.

Energy Balance in Reactors

This concept pertains to accounting for all the energy entering and leaving a reactor system, including the heat added, the enthalpy of the reactants, and the products. An energy balance is critical in reactor design and operation, ensuring that the energy input matches the energy changes due to chemical reactions and in maintaining desired reactor conditions.

Temperature Effects on Reaction Energetics

Temperature effects on reaction energetics examine how reaction enthalpy and equilibrium shift as a function of temperature. Changes in temperature can alter the reaction pathway, affect catalyst behavior, and influence the amount of heat required or released in a chemical process, making it a key consideration in reactor design and thermal management.

Chemical Reaction Stoichiometry

This concept involves understanding how reactants combine in fixed proportions to form products in a chemical reaction, ensuring mass balance and proper mole ratios. It is crucial in determining how the quantity of each species changes during the reaction, which is fundamental when converting between reactants and products and in calculating the overall energy change in the system.

Reaction Thermochemistry

Reaction thermochemistry is the study of the energy changes, particularly the enthalpy changes, that accompany chemical reactions. It involves computing the heat released or absorbed during reactions, which is essential when assessing how much heat must be added or removed to maintain a reactor's temperature.

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