At 1500^∘ C, Kc=5.67 for the reaction CH4(g)+H2 O(g) ⇌CO(g)+3 H2(g) Calculate the value of ΔG177

step 1 This question is pretty straightforward. We are given an equilibrium constant at 1 ,500 degrees

At 1500^∘ C, Kc=5.67 for the reaction CH4(g)+H2 O(g)...

At $1500^{\circ} \mathrm{C}, K_{\mathrm{c}}=5.67$ for the reaction
$$
\mathrm{CH}_{4}(g)+\mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons \mathrm{CO}(g)+3 \mathrm{H}_{2}(g)
$$
Calculate the value of $\Delta G_{1773}^{\circ}$ for the reaction at this temperature.

Key Concepts

Equilibrium Constant

The equilibrium constant (K) is a dimensionless number that indicates the extent to which a chemical reaction proceeds under equilibrium conditions. It is defined by the ratio of the activities (or concentrations, or partial pressures) of the products to those of the reactants, each raised to the power of their stoichiometric coefficients. In the context of thermodynamics, K provides insights into the position of equilibrium and the favorability of the reaction under a specific set of conditions.

Gibbs Free Energy and its Standard State

Gibbs free energy (?G) is a thermodynamic potential that measures the maximum reversible work obtainable from a system at constant temperature and pressure. The standard Gibbs free energy change (?G°) pertains to the change in free energy when reactants in their standard states are converted to products in their standard states. A negative ?G° indicates that the reaction is spontaneous under standard conditions, while a positive ?G° suggests non-spontaneity.

Relationship Between ?G° and the Equilibrium Constant

The connection between the standard Gibbs free energy change and the equilibrium constant is given by the equation ?G° = -RT ln(K), where R is the universal gas constant and T is the absolute temperature in Kelvin. This relationship allows for the calculation of ?G° when the equilibrium constant is known, reflecting how a large equilibrium constant (favoring products) corresponds to a more negative ?G°.

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