Equilibrium Constant: 2A(g) + 2B(s) ⇌ D(g) + 2F(s)

Understanding chemical equilibrium and how to express it mathematically is super important in chemistry, guys. Let's break down how to determine the equilibrium constant for the given reaction: 2A(g) + 2B(s) ⇌ D(g) + 2F(s).

Understanding the Equilibrium Constant

The equilibrium constant (K) is a value that represents the ratio of products to reactants at equilibrium. Only gaseous and aqueous species are included in the equilibrium constant expression because the concentrations of solids and pure liquids remain constant during the reaction. Remember that the equilibrium constant provides valuable insight into the extent to which a reaction will proceed to completion. A large K indicates that the reaction favors the formation of products, while a small K indicates that the reaction favors the reactants. It's a fundamental concept for anyone studying chemical kinetics and thermodynamics. Keep in mind that the equilibrium constant is temperature-dependent, so changes in temperature will affect its value. When writing the equilibrium constant expression, you should only include the concentrations (or partial pressures for gases) of species that actually change during the reaction. Solid and liquid phases are excluded because their activities are considered to be 1, meaning their "effective concentrations" don't change significantly. For instance, think of adding more solid salt to a saturated solution; the concentration of the salt in the solution doesn't increase because the excess salt simply remains undissolved. This is why we only focus on the species whose concentrations are variable and can influence the equilibrium position. In our particular case, we need to carefully assess which components are in the gaseous phase and which are in the solid phase, as this will directly affect how we construct the equilibrium expression. The equilibrium constant is an indispensable tool for predicting the behavior of chemical reactions under different conditions. So, let's dive into how to correctly determine it for the reaction at hand!

Applying the Concept to the Reaction

For the reaction 2A(g) + 2B(s) ⇌ D(g) + 2F(s), we need to consider the phases of each component. Here, A and D are gases (g), while B and F are solids (s). As mentioned earlier, we only include gases and aqueous solutions in the equilibrium constant expression. Solids are excluded because their concentrations do not change during the reaction. With that in mind, the equilibrium constant expression will only involve the concentrations of A and D. The general form of the equilibrium constant expression is:

K = $\frac{[Products]}{[Reactants]}$

Considering the stoichiometry of the reaction, the equilibrium constant expression will be:

K = $\frac{[D]}{[A]^2}$

Notice that the concentration of A is squared because its stoichiometric coefficient is 2. It’s crucial to remember that the coefficients in the balanced chemical equation become exponents in the equilibrium constant expression. This reflects how the rate of the forward and reverse reactions depends on the concentrations of the reactants and products. The solids B and F are not included because their activities are considered to be 1 and do not affect the equilibrium. To illustrate, if we were to double the amount of solid B, it would not shift the equilibrium position because the concentration of B in its solid phase remains constant. Understanding these principles helps in accurately predicting how changes in concentration of gaseous or aqueous species will influence the reaction’s equilibrium.

Evaluating the Given Options

Now, let's evaluate the options provided in the question, keeping in mind that the correct equilibrium constant expression should be K = $\frac{[D]}{[A]^2}$.

a) $\frac{c(D) cdot c(F)}{c(A)}$: This option includes the concentration of F, which is a solid, making it incorrect.

b) $\frac{c(F)}{c(A) cdot c(B)}$: This option includes both F and B, which are solids, making it incorrect.

c) $\frac{c(D)}{c(A)}$: This option is close but doesn't account for the stoichiometric coefficient of A.

d) $\frac{c(D) cdot c(F)}{c(A) cdot c(B)}$: This option includes F and B, which are solids, making it incorrect.

e) $\frac{c(D)}{c(B)}$: This option includes B, which is a solid, making it incorrect, and also omits A entirely.

However, upon closer inspection, it seems there was a slight oversight in the options provided. The correct equilibrium constant expression, based on our understanding, should be:

K = $\frac{c(D)}{c(A)^2}$

None of the provided options perfectly match the correct expression. The closest one is option (c), but it's missing the exponent for the concentration of A. In a real test scenario, you might need to choose the best possible answer among the given options, or there might have been a typo in the question. Understanding how to derive the correct expression is more important than simply memorizing formulas. Ensure you grasp the underlying principles of chemical equilibrium and how to apply them to different reactions.

Conclusion

In summary, the key to determining the equilibrium constant is to correctly identify which species are included in the expression (gases and aqueous solutions only) and to account for the stoichiometric coefficients. While none of the provided options perfectly matched the correct equilibrium constant expression K = $\frac{c(D)}{c(A)^2}$, understanding the process helps you identify the closest possible answer and recognize potential errors in the question. Always remember to focus on the fundamentals of chemical equilibrium, and you'll be well-prepared to tackle these types of problems! Understanding equilibrium constants is crucial for predicting the behavior of chemical reactions. Make sure you nail this concept, guys!