Problem 41 - Chemistry Matter and Change

Question

What happens to \(K_{\mathrm{eq}}\) for an equilibrium system if the equation for the reaction is rewritten in the reverse?

Step-by-Step Solution

Answer

The equilibrium constant becomes the reciprocal of the original.

Step 1: Understanding the Equilibrium Constant

The equilibrium constant (\(K_{\mathrm{eq}}\)) represents the ratio of the concentrations of products to reactants, each raised to the power of their respective stoichiometric coefficients, at equilibrium for a given chemical reaction.

Step 2: Original Reaction vs. Reverse Reaction

Let's assume the original reaction is:\(aA + bB \rightleftharpoons cC + dD\). For this reaction, the equilibrium constant is given by:\(K_{\mathrm{eq}} = \frac{[C]^c[D]^d}{[A]^a[B]^b}\).

Step 3: Writing the Reverse Reaction

The reverse reaction is written as:\(cC + dD \rightleftharpoons aA + bB\). In this case, the products and reactants swap places compared to the original reaction.

Step 4: Reversed Equilibrium Expression

For the reverse reaction, the new equilibrium constant (\(K_{\mathrm{eq, rev}}\)) is given by the expression:\(K_{\mathrm{eq, rev}} = \frac{[A]^a[B]^b}{[C]^c[D]^d}\).

Step 5: Comparing the Original and Reverse Equilibrium Constants

By comparing the expressions:\[K_{\mathrm{eq}} = \frac{[C]^c[D]^d}{[A]^a[B]^b}\]\[K_{\mathrm{eq, rev}} = \frac{[A]^a[B]^b}{[C]^c[D]^d}\] we see that the reverse equilibrium constant is the reciprocal of the original equilibrium constant:\(K_{\mathrm{eq, rev}} = \frac{1}{K_{\mathrm{eq}}}\).

Key Concepts

Chemical Equilibrium

Chemical equilibrium is a fascinating state in which the concentrations of reactants and products remain constant over time, indicating a balance in a chemical reaction. This occurs when the forward reaction, where reactants turn into products, happens at the same rate as the reverse reaction, where products revert back into reactants.

In a chemical equilibrium,

• The rate of the forward reaction equals the rate of the reverse reaction.
• There is no net change in the concentration of reactants and products.
• The system appears static on a macroscopic level but remains dynamic microscopically.

It’s important to understand that equilibrium does not mean the reactants and products are present in equal amounts, but rather that their concentrations have stabilized at specific values.

Reversible Reactions

Reversible reactions are those in which the conversion of reactants to products and the conversion of products back to reactants occur simultaneously. Unlike irreversible reactions that proceed to completion and result in having all reactants converted into products, reversible reactions can establish a dynamic balance under suitable conditions.

Characteristics of reversible reactions:

• They are indicated by the double arrow (⇌) in the chemical equation.
• Can proceed in both forward and backward directions.
• Reach a state of equilibrium where both forward and reverse reactions occur at equal rates.

Reversibility is influenced by factors such as temperature, pressure, and concentration. Changing these can shift the equilibrium position, favoring either the forward or reverse reaction.

Reaction Stoichiometry

Reaction stoichiometry is the quantitative relationship between reactants and products in a chemical reaction. It is expressed in terms of stoichiometric coefficients, which are the numbers in front of the chemical formulas in a balanced equation. These coefficients indicate the proportions in which substances react and are produced.

To understand reaction stoichiometry, keep in mind:

• Stoichiometric coefficients are essential for writing equilibrium expressions.
• They help determine the amount of reactants needed for a complete reaction or the amount of product formed.
• In equilibrium expressions, each concentration term is raised to the power of its stoichiometric coefficient.

By utilizing stoichiometry, you can predict how changes in the quantities of reactants and products affect the equilibrium of the reaction. This understanding is crucial in calculating the equilibrium constant, which describes the extent of a reaction under certain conditions.