A coal gasifier produces a mixture of 1 CO and 2 H2 that is fed to a catalytic converter to prod

step 1 So we have a coal gasifier that produces a mix of carbon dioxide and hydrogen that is fed to a c

A coal gasifier produces a mixture of 1 CO and 2 H2 that is...

A coal gasifier produces a mixture of $1 \mathrm{CO}$ and $2 \mathrm{H}_{2}$ that is fed to a catalytic converter to produce methane. The reaction is $\mathrm{CO}+3 \mathrm{H}_{2} \Leftrightarrow \mathrm{CH}_{4}+$ $\mathrm{H}_{2} \mathrm{O} .$ The equilibrium constant at $600 \mathrm{K}$ is $K=$ $1.83 \times 10^{6} .$ What is the composition of the exit flow assuming a pressure of $600 \mathrm{kPa} ?$

A coal gasifier produces a mixture of $1 \mathrm{CO}$ and $2 \mathrm{H}_{2}$ that is fed to a catalytic converter to produce methane. The reaction is $\mathrm{CO}+3 \mathrm{H}_{2} \Leftrightarrow \mathrm{CH}_{4}+$
$\mathrm{H}_{2} \mathrm{O} .$ The equilibrium constant at $600 \mathrm{K}$ is $K=$ $1.83 \times 10^{6} .$ What is the composition of the exit flow assuming a pressure of $600 \mathrm{kPa} ?$

Key Concepts

Partial Pressure and Mole Fraction Analysis

In gas-phase reactions, the concept of partial pressure is important because the overall behavior of the system is determined by the pressure exerted by each gas individually. The mole fraction relates the amount of each component to the total amount of gas, allowing for the calculation of partial pressures using the total system pressure. This analysis is critical for applying the equilibrium constant expression in terms of partial pressures.

Reaction Stoichiometry

Reaction stoichiometry involves the quantitative relationships between reactants and products as defined by the balanced chemical equation. It is essential for tracking the changes in amounts of substances as the reaction proceeds, enabling the setup of material balances that relate initial conditions to equilibrium conditions.

Chemical Equilibrium

Chemical equilibrium refers to the state in which the forward and reverse reactions occur at the same rate, resulting in constant concentrations of the reactants and products. In heterogeneous systems such as gas-phase reactions, equilibrium is determined by the interplay between reaction kinetics and thermodynamics, making it crucial for understanding and predicting the final composition of reaction mixtures.

Equilibrium Constant (K)

The equilibrium constant (K) is a dimensionless number that expresses the ratio of the concentrations or partial pressures of products to reactants at equilibrium, each raised to the power of its stoichiometric coefficient. It serves as an indicator of the position of equilibrium and is highly dependent on temperature, providing insight into whether products or reactants are favored in a given reaction.

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