Determine the equilibrium constant for the reaction CH4+2 O2 ⇌CO2+2 H2 O when the reaction occur

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Determine the equilibrium constant for the reaction CH4+2 O2...

Determine the equilibrium constant for the reaction $\mathrm{CH}_{4}+2 \mathrm{O}_{2} \rightleftharpoons \mathrm{CO}_{2}+2 \mathrm{H}_{2} \mathrm{O}$ when the reaction occurs at $100 \mathrm{kPa}$ and $2000 \mathrm{K} .$ The natural logarithms of the equilibrium constant for the reaction $\mathrm{C}+2 \mathrm{H}_{2} \rightleftharpoons \mathrm{CH}_{4}$ and $\mathrm{C}+\mathrm{O}_{2} \rightleftharpoons \mathrm{CO}_{2}$ at $2000 \mathrm{K}$ are 7.847 and 23.839, respectively.

Key Concepts

Chemical Equilibrium Constant

The chemical equilibrium constant is a number that relates the activities or concentrations (or partial pressures for gases) of the products and reactants at equilibrium. It is fundamentally linked to the change in Gibbs free energy for the reaction by the relationship ln(K) = –?G/RT, which means that knowing either the free energy change or the value of K gives insight into the favorability of the reaction under given conditions.

Reaction Combination and Hess’s Law for Equilibrium Constants

When dealing with complex reaction systems, the overall equilibrium constant can be determined by mathematically combining the equilibrium constants of several individual reactions that add up to the overall reaction. This process follows a 'Hess’s law’-like approach for equilibrium constants where reversing a reaction inverts its constant (taking the reciprocal) and adding reactions corresponds to multiplying their equilibrium constants. This technique allows one to build the equilibrium constant of a net reaction from known equilibrium data of component reactions.

Standard State Conditions and Pressure Effects

Chemical equilibria are defined with respect to standard states, which for gases is often taken as a specified pressure (for example, 100 kPa). When a reaction is conducted under these standard conditions, the equilibrium constants are directly applicable. Moreover, if there is no net change in the number of moles of gas (?n = 0), there is no need to adjust the equilibrium expression for a change in total pressure. This concept is key when applying provided equilibrium data at a specified pressure.

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