The equilibrium constant Kc for the reaction I2(g) ⇄2 I(g)...

The equilibrium constant $K_{\mathrm{c}}$ for the reaction $$\mathrm{I}_{2}(g) \rightleftarrows 2 \mathrm{I}(g)$$ is $3.8 \times 10^{-5}$ at $727^{\circ} \mathrm{C}$. Calculate $K_{\mathrm{c}}$ and $K_{P}$ for the equilibrium $$2 \mathrm{I}(g) \rightleftarrows \mathrm{I}_{2}(g)$$ at the same temperature.

The equilibrium constant $K_{\mathrm{c}}$ for the reaction
$$\mathrm{I}_{2}(g) \rightleftarrows 2 \mathrm{I}(g)$$
is $3.8 \times 10^{-5}$ at $727^{\circ} \mathrm{C}$. Calculate $K_{\mathrm{c}}$ and $K_{P}$ for the equilibrium
$$2 \mathrm{I}(g) \rightleftarrows \mathrm{I}_{2}(g)$$
at the same temperature.

Key Concepts

Equilibrium Constant Reversal

When the direction of a chemical reaction is reversed, the equilibrium constant for the new reaction is the reciprocal of the equilibrium constant for the forward reaction. This principle allows one to easily determine the equilibrium constant of the reverse reaction by inverting the value of the given equilibrium constant.

Relationship Between Kc and Kp

For gaseous reactions, there is a relationship between the equilibrium constant in terms of concentration (Kc) and in terms of pressure (Kp), given by the equation Kp = Kc(RT)^??, where R is the gas constant, T is the temperature in Kelvin, and ?? is the change in moles of gas (moles of gaseous products minus moles of gaseous reactants). This relationship is essential when converting between concentration and pressure-based equilibrium data.

Reaction Stoichiometry and ??

The stoichiometry of a reaction determines the ?? term in the conversion between Kc and Kp. ?? is calculated as the difference in the number of moles of gaseous products and reactants. A change in the number of gas molecules directly affects the pressure equilibrium constant, emphasizing the importance of correctly accounting for stoichiometric coefficients in equilibrium calculations.

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