A reaction that can convert coal to methane (the chief...

A reaction that can convert coal to methane (the chief component of natural gas) is $$ \mathrm{C}(s)+2 \mathrm{H}_{2}(g) \rightleftharpoons \mathrm{CH}_{4}(g) $$ for which $\Delta G^{\circ}=-50.79 \mathrm{~kJ} \mathrm{~mol}^{-1}$. What is the value of $K_{\mathrm{p}}$ for this reaction at $25^{\circ} \mathrm{C}$ ? Does this value of $K_{\mathrm{p}}$ suggest that studying this reaction as a means of methane production is worthwhile pursuing?

A reaction that can convert coal to methane (the chief component of natural gas) is $$
\mathrm{C}(s)+2 \mathrm{H}_{2}(g) \rightleftharpoons \mathrm{CH}_{4}(g)
$$
for which $\Delta G^{\circ}=-50.79 \mathrm{~kJ} \mathrm{~mol}^{-1}$. What is the value of $K_{\mathrm{p}}$ for this reaction at $25^{\circ} \mathrm{C}$ ? Does this value of $K_{\mathrm{p}}$ suggest that studying this reaction as a means of methane production is worthwhile pursuing?

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Gibbs Free Energy and Reaction Equilibrium

This concept explains the relationship between the standard Gibbs free energy change (?G°) and the equilibrium constant (K) through the equation ?G° = -RT lnK. It shows that a negative ?G° indicates a thermodynamically favorable reaction at standard conditions and that the magnitude of K can be determined directly from this energy change.

Equilibrium Constant (Kp) Calculation

Kp represents the equilibrium constant expressed in terms of partial pressures of gaseous components. Calculating Kp from ?G° involves using the equation ?G° = -RT lnK, where R is the gas constant and T is the temperature in Kelvin. This gives insight into the position of equilibrium and the extent to which products are favored over reactants in a chemical reaction.

Process Feasibility Beyond Thermodynamics

While a large Kp or a negative ?G° indicates that the reaction is thermodynamically favorable with products being predominantly formed at equilibrium, practical viability also depends on factors beyond these thermodynamic parameters. Kinetic factors, energy requirements, economic considerations, and technological challenges must also be examined to determine if a reaction is worthwhile for industrial methane production.

Transcript

Please give Ace some feedback