Question

Suppose a reaction has the equilibrium constant \(K=1.3 \times 10^{8}\). What does the magnitude of this constant tell you about the relative concentrations of products and reactants that will be present once equilibrium is reached? Is this reaction likely to be a good source of the products?

Short answer

The equilibrium constant (K) given is \(1.3 \times 10^{8}\), which is a large value. This indicates that the concentrations of products are much higher than the concentrations of reactants at equilibrium, suggesting that the reaction favors the formation of products. Therefore, the reaction is likely to be a good source of the products.

Step-by-step solution

Recall the equilibrium constant expression

Recall that the equilibrium constant (K) is defined as the ratio of the concentration (or partial pressure) of the products raised to their stoichiometric coefficients to the concentration (or partial pressure) of the reactants raised to their stoichiometric coefficients at equilibrium. The general expression for the equilibrium constant is: \[ K = \frac{[C]^c [D]^d}{[A]^a [B]^b} \] Here, [A], [B], [C], and [D] represent the concentrations of reactants A and B and products C and D, respectively, at equilibrium, and a, b, c, and d are their stoichiometric coefficients in the balanced chemical equation.

Interpret the given equilibrium constant value

The equilibrium constant (K) value provided is \(1.3 \times 10^{8}\). This large value indicates that the concentration of products ([C] and [D]) is much higher compared to the concentration of reactants ([A] and [B]) at equilibrium, as: \[ K = \frac{[C]^c [D]^d}{[A]^a [B]^b} = 1.3 \times 10^{8} \] For K >> 1, the reaction favors the formation of products and will have a very high concentration of products relative to reactants at equilibrium.

Determine if the reaction is a good source of products

Given that the equilibrium constant (K) is very large, indicating that the reaction favors the formation of products, we can conclude that this reaction is likely to be a good source of the products. The large value of K suggests that a significant amount of reactants will be converted into products at equilibrium, resulting in a high concentration of products.

Key concepts

Chemical Equilibrium

Chemical equilibrium is a state of balance in a chemical reaction where the rate of the forward reaction equals the rate of the reverse reaction, meaning that the concentrations of reactants and products remain constant over time.

Imagine a simple reaction where the reactants A and B convert to products C and D. At equilibrium, the process of A and B transforming into C and D occurs at the same rate as C and D reverting back to A and B. Equilibrium does not imply that the quantities of reactants and products are equal, but rather that their ratios remain unchanged.

The point at which this balance occurs is determined by the reaction conditions and the inherent nature of the substances involved. It is essential to understand that the state of equilibrium can be reached from either direction of the reaction, whether you start with reactants or products. The equilibrium constant (K) is a numerical value that provides a way to relate the concentration of reactants and products at this state.

Reaction Quotient

The reaction quotient (Q) plays a crucial role in predicting the direction in which a reaction mixture will proceed to achieve equilibrium. The expression for Q is similar to that of the equilibrium constant (K), involving concentrations (or partial pressures) of the reactants and products at a given point in time, not necessarily at equilibrium.

For a reaction of the type: \[ aA + bB \leftrightarrow cC + dD \], the reaction quotient is expressed as: \[ Q = \frac{[C]^c [D]^d}{[A]^a [B]^b} \]

By comparing the value of Q with the known equilibrium constant K, predictions can be made about the state of the reaction:

• If \( Q < K \), the forward reaction is favored, and more reactants will convert to products to reach equilibrium.
• If \( Q > K \), the reverse reaction is favored, and the system will shift to form more reactants.
• If \( Q = K \), the system is already at equilibrium, and no net change will occur.

Utilizing Q is particularly useful for adjusting experimental conditions or when a reaction hasn't yet reached equilibrium and you're trying to determine in which direction it will proceed.

Le Chatelier's Principle

Le Chatelier's principle offers a predictive quality regarding the shifts that take place in a system in response to external changes. It states that if a dynamic equilibrium is disturbed by changing the conditions, such as concentration, temperature, or pressure, the position of equilibrium will shift to counteract the change and restore a new equilibrium.

Let's consider our reaction \( aA + bB \leftrightarrow cC + dD \). If the concentration of one of the reactants is increased, the system will respond by favoring the forward reaction, producing more products, to reduce the effect of the change. Alternatively, if one of the products is removed from the system, the equilibrium will also shift to the right, increasing the production of that product to replace it.

Moreover, changes in temperature can cause the equilibrium position to shift in endothermic or exothermic directions, depending on whether heat is absorbed or released by the reaction. In pressure-sensitive systems, typically those involving gases, an increase in pressure will shift the equilibrium toward the side with fewer gas molecules. Le Chatelier's principle is a powerful tool in chemistry, allowing us to manipulate the yield of products in industrial processes, amongst other applications.