Question

When this reaction comes to equilibrium, will the concentrations reactants or products be greater? Does the answer to this question pend on the initial concentrations of the reactants and products? \begin{equation}\mathrm{A}(g)+\mathrm{B}(g) \rightleftharpoons 2 \mathrm{C}(g) \quad K_{\mathrm{c}}=1.4 \times 10^{-5}\end{equation}

Short answer

At equilibrium, the concentrations of reactants (A and B) will be greater than the concentration of the product (C) due to the small Kc value. The initial concentrations do affect exact concentrations at equilibrium but do not change the Kc value.

Step-by-step solution

Interpret the Equilibrium Constant (Kc)

The value of the equilibrium constant, Kc, indicates the extent of the reaction. If Kc is much less than 1, it suggests that the reaction favors the reactants at equilibrium. If Kc is much greater than 1, the reaction favors the products. Here, Kc is 1.4 × 10^-5, which is much less than 1, indicating that at equilibrium, the concentrations of the reactants, A and B, will likely be greater than the concentration of the product, C.

Understand the Dependence on Initial Concentrations

Although the value of Kc gives us an idea of the reaction's favorability, the actual concentrations of reactants and products at equilibrium depend on their initial concentrations. The path to equilibrium can vary, but the value of Kc remains constant. Thus, different sets of equilibrium concentrations may exist for varying initial conditions, as long as they satisfy the equilibrium expression.

Conclude the Predominant Species at Equilibrium

From the given Kc, we can conclude that upon reaching equilibrium, the reactants (A and B) will likely have greater concentrations than the products (C), assuming that the initial concentrations are not extremely low for reactants or extremely high for products, which could shift the equilibrium position.

Key concepts

Equilibrium Constant

Understanding the concept of equilibrium constant (Kc) is crucial for grasping how chemical reactions behave at equilibrium. For a given reversible reaction like \[\text{A}(g) + \text{B}(g) \rightleftharpoons 2\text{C}(g)\], the equilibrium constant is a way of expressing the ratio of the concentration of the products to the reactants raised to the power of their stoichiometric coefficients when the system is at equilibrium.

In simple terms, if we have a small Kc value, much smaller than 1, such as the mentioned \(1.4 \times 10^{-5}\), it infers that the equilibrium position lies far to the left, meaning that the reactants are favored, and their concentrations are higher compared to the products when equilibrium is reached. Conversely, a large Kc indicates a greater concentration of products. This gives us a general prediction about the dominant species at equilibrium.

However, while Kc offers valuable information, it's not the sole factor to consider. It does not tell us the exact concentrations but instead provides a guideline on the direction the reaction equilibrium favors.

Reactant and Product Concentration

Reactant and product concentrations at equilibrium are tied intimately to the equilibrium constant, but are distinct because they represent the actual amounts of substances present when the reaction ceases to change over time.

For instance, once the reversible reaction between A, B, and C has reached equilibrium, we'll have certain concentrations of each that don't alter. While Kc gives us an indication of which will be in excess, these concentrations are determined by the balanced equation and the starting amounts of reactants and products. Ultimately, to get the equilibrium concentrations, we apply the equilibrium constant formula:\[ K_c = \frac{[\text{C}]^2}{[\text{A}][\text{B}]} \],where square brackets denote the molarity (M) or concentration of a substance.

Even when the calculations may initially seem daunting, it's essential to grasp how these concentrations are calculated from the initial amounts and the reaction stoichiometry – these are the components that ultimately establish 'where' the equilibrium lies, and hence, the concentrations of reactants and products.

Dependence on Initial Concentrations

The initial concentrations of reactants and products have a profound impact on the position of equilibrium. This is despite the fact that Kc itself is a constant value and does not change with different initial conditions. Through a process known as the 'reaction quotient,' Q, we can evaluate the direction in which a reaction will proceed to reach equilibrium based on the starting concentrations.

When a reaction is initiated, if Q is less than Kc, the forward reaction is favored to form more products. If Q is greater than Kc, the reaction moves in the reverse direction to produce more reactants.

Ultimately, any set of equilibrium concentrations must uphold the condition \[ Q = K_c \]. Therefore, if we start with high amounts of reactants and low products, the system will move toward producing more C until equilibrium is established at the value of Kc.

Keep in mind that while Kc is invariant, the path to reach an equilibrium state, varying in terms of product and reactant concentrations, is heavily reliant on their initial amounts. This interplay confirms that although Kc predicts the leanings of the reaction, the initial concentrations are the driving forces that settle the actual mixture we find at equilibrium.