Question

How can an equilibrium system contain small and unchanging amounts of products yet have large amounts of reactants? What can you say about the relative size of \(K\) eq for such an equilibrium?

Short answer

In an equilibrium system with small and unchanging amounts of products and large amounts of reactants, the equilibrium constant (Keq) will be small (less than 1). This is because the denominator in the Keq equation, which represents the concentration of reactants, is much larger than the numerator representing the concentration of products. A small Keq indicates that the reaction does not favor the formation of products and primarily consists of reactants at equilibrium.

Step-by-step solution

1. Chemical Equilibrium

Chemical equilibrium is a state in a reversible chemical reaction where the rate of the forward reaction equals the rate of the reverse reaction. In this state, the concentrations of reactants and products remain constant over time. It is important to note that even though the reaction is in equilibrium, reactant and product molecules are continually converting to each other at equal rates. The equilibrium constant, Keq, helps us quantify this balance and predict the composition of the equilibrium mixture.

2. Equilibrium Constant (Keq)

The equilibrium constant (Keq) is a dimensionless value that relates the concentrations of reactants and products at equilibrium. It is calculated using the following formula: \( Keq = \frac{[Products]^n}{[Reactants]^m} \) Here, [Products] and [Reactants] represent the molar concentrations of the products and reactants, respectively, and n and m are their respective stoichiometric coefficients. The larger the value of Keq, the more the reaction favors the formation of products. Conversely, if Keq is small, the reaction favors the formation of reactants.

3. Analyzing the Given Scenario

In the given exercise, it is mentioned that the equilibrium system contains small and unchanging amounts of products and large amounts of reactants. This suggests that the system is predominantly composed of reactants, and the reaction does not favor the formation of products.

4. Determining the Relative Size of Keq

Since the system contains a higher concentration of reactants compared to products, the denominator in the Keq equation is much larger than the numerator. As a result, the overall value of Keq will be smaller than 1. In conclusion, for an equilibrium system with small and unchanging amounts of products and large amounts of reactants, the relative size of the equilibrium constant (Keq) will be small (less than 1). This indicates that the reaction does not favor the formation of products and primarily consists of reactants at equilibrium.

Key concepts

Equilibrium Constant (Keq)

Understanding the equilibrium constant, abbreviated as Keq, is crucial when analyzing chemical reactions at equilibrium. Imagine we have a simple reversible reaction where A transforms into B. The Keq for this reaction is calculated by dividing the concentration of product B by the concentration of reactant A once the reaction has reached a stable state.

The equation for equilibrium constant is given by:
\[ Keq = \frac{{[B]^n}}{{[A]^m}} \]
where [A] and [B] are the molar concentrations of the reactant and product, respectively, and 'n' and 'm' are the coefficients from the balanced chemical equation. If Keq is greater than 1, the reaction favors the products; the larger the value, the more products are present at equilibrium. A Keq less than 1 indicates a preference for reactants, with smaller values signifying a larger proportion of reactants. When Keq is around 1, it suggests a fairly balanced amount of reactants and products.

For reactions involving small amounts of products and large amounts of reactants, Keq would be a small number. This means we have a reaction that does not greatly favor product formation and remains heavily reactant-biased, even when it achieves equilibrium.

Rate of Reaction

The rate of a chemical reaction tells us how quickly reactants are converted into products. It is influenced by various factors like temperature, concentration, surface area, and the presence of catalysts. At the beginning of a reaction, the rate is generally faster because the concentration of reactants is high and they collide more frequently. As the reaction progresses, the rate typically slows down as reactants are consumed and their concentrations decrease.

During a reversible reaction, as we approach equilibrium, the rate of the forward reaction — which produces products — decreases, while the rate of the reverse reaction — turning products back into reactants — increases. At equilibrium, these rates are equal, meaning the amounts of reactants and products stay constant. However, this does not mean that the reactions have stopped, but rather that the rate of product formation is exactly balanced by the rate of reactant formation, keeping the overall concentrations unaltered.

For a system at equilibrium with a small Keq, the initial rate of the forward reaction might be low or the rate of the reverse reaction might be adequately high to ensure that only small amounts of products are formed. The equilibrium is reached quickly and maintained as long as the external conditions such as temperature and pressure remain constant.

Reaction Quotient

The reaction quotient, denoted as Q, is similar to the equilibrium constant, but is used to determine the direction in which a reaction is likely to proceed at any given point before it reaches equilibrium. Like Keq, Q is calculated in the same way, using the current concentrations of the products and reactants.\[ Q = \frac{{[Products]^n}}{{[Reactants]^m}} \]When you compute Q for a reaction mixture, you can predict how the reaction will shift to reach equilibrium. If Q < Keq, the reaction will proceed forward, producing more products. If Q > Keq, the reaction will go in reverse, creating more reactants. If Q = Keq, the system is already at equilibrium and no net change will occur. By comparing Q to Keq, you can tell not only which way the reaction will go, but also how far from equilibrium the system is at the moment.

Factoring in the concept of small Keq and large reactant concentrations, Q would initially be greater than Keq, pushing the reaction to favor the reverse process to achieve equilibrium. This aligns with having small, unchanging amounts of products as described in our exercise, indicating the system's tendency to revert to reactants.