Consider the following reaction at 250^∘ C : A(s)+2 B(g) ⇌C(s)+2 D(g) (a) Write an equilibrium

step 1 So for this reaction, we want to first write the equilibrium constant expression. Remember that

Consider the following reaction at 250^∘ C : A(s)+2 B(g)...

Consider the following reaction at $250^{\circ} \mathrm{C}$ : $$ \mathrm{A}(s)+2 \mathrm{~B}(g) \rightleftharpoons \mathrm{C}(s)+2 \mathrm{D}(g) $$ (a) Write an equilibrium constant expression for the reaction. Call the equilibrium constant $K_{1}$. (b) Write an equilibrium constant expression for the formation of one mole of $\mathrm{B}(g)$ and call the equilibrium constant $K_{2}$. (c) Relate $K_{1}$ and $K_{2}$.

Consider the following reaction at $250^{\circ} \mathrm{C}$ :
$$
\mathrm{A}(s)+2 \mathrm{~B}(g) \rightleftharpoons \mathrm{C}(s)+2 \mathrm{D}(g)
$$
(a) Write an equilibrium constant expression for the reaction. Call the equilibrium constant $K_{1}$.
(b) Write an equilibrium constant expression for the formation of one mole of $\mathrm{B}(g)$ and call the equilibrium constant $K_{2}$.
(c) Relate $K_{1}$ and $K_{2}$.

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Key Concepts

Activity of Pure Solids and Liquids

In equilibrium constant expressions, the activities of pure solids and liquids are taken as unity. This assumption simplifies the equilibrium constant expressions by eliminating terms for these phases, so only gases and aqueous species are included in the calculation using their activities or concentrations.

Equilibrium Constant Expression

In chemical reactions, the equilibrium constant expression relates the activities (or partial pressures/concentrations) of the products and reactants, each raised to the power of their stoichiometric coefficients, at equilibrium. This expression quantitatively defines the ratio of the product activities to the reactant activities, reflecting the position of equilibrium under given conditions.

Scaling Relationships and Reaction Manipulation

The relationship between different equilibrium constants for reactions that are algebraically related is governed by principles of reaction manipulation. When a chemical equation is multiplied by a coefficient, the equilibrium constant for the new reaction becomes the original equilibrium constant raised to the power of that coefficient, and similar relations hold when reactions are reversed or when combined. This concept is crucial in connecting equilibrium constants for different formulations of a given reaction.

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