Question

Write the \(K_{\text {eq }}\) expression for each reaction. a) \(\mathrm{H}_{2}+\mathrm{Cl}_{2} \rightleftarrows 2 \mathrm{HCl}\) b) \(\mathrm{NO}+\mathrm{NO}_{2} \rightleftarrows \mathrm{N}_{2} \mathrm{O}_{3}\)

Short answer

a) \(K_{\text{eq}} = \frac{[\mathrm{HCl}]^2}{[\mathrm{H}_2][\mathrm{Cl}_2]}\) b) \(K_{\text{eq}} = \frac{[\mathrm{N}_2O_3]}{[\mathrm{NO}][\mathrm{NO}_2]}\)

Step-by-step solution

Understand the Equilibrium Expression

The equilibrium constant expression, denoted as \( K_{\text{eq}} \), is derived from the balanced chemical equation. It is the ratio of the concentrations of the products to the reactants, each raised to the power of their respective coefficients.

Analyze Reaction a

For the reaction \( \mathrm{H}_2 + \mathrm{Cl}_2 \rightleftarrows 2 \mathrm{HCl} \), identify the products and reactants. The products are \(\mathrm{HCl}\) and the reactants are \( \mathrm{H}_2 \) and \( \mathrm{Cl}_2 \).

Write \( K_{\text{eq}} \) for Reaction a

The equation is \( \mathrm{H}_2 + \mathrm{Cl}_2 \rightleftarrows 2 \mathrm{HCl} \). The \( K_{\text{eq}} \) expression is: \[ K_{\text{eq}} = \frac{[\mathrm{HCl}]^2}{[\mathrm{H}_2][\mathrm{Cl}_2]} \] where \([\mathrm{HCl}]\), \([\mathrm{H}_2]\), and \([\mathrm{Cl}_2]\) are the concentrations at equilibrium.

Analyze Reaction b

For the reaction \( \mathrm{NO} + \mathrm{NO}_2 \rightleftarrows \mathrm{N}_2O_3 \), identify the products and reactants. The product is \(\mathrm{N}_2O_3\) and the reactants are \( \mathrm{NO} \) and \( \mathrm{NO}_2 \).

Write \( K_{\text{eq}} \) for Reaction b

The equation is \( \mathrm{NO} + \mathrm{NO}_2 \rightleftarrows \mathrm{N}_2O_3 \). The \( K_{\text{eq}} \) expression is: \[ K_{\text{eq}} = \frac{[\mathrm{N}_2O_3]}{[\mathrm{NO}][\mathrm{NO}_2]} \] where \([\mathrm{N}_2O_3]\), \([\mathrm{NO}]\), and \([\mathrm{NO}_2]\) are the concentrations at equilibrium.

Key concepts

Chemical Equilibrium

Chemical equilibrium refers to the state in a chemical reaction where the rates of the forward and reverse reactions are equal. At this point, the concentrations of the reactants and products remain constant over time. It doesn't mean the concentrations are the same, but rather that their ratios remain steady. Understanding chemical equilibrium is crucial because:

• It describes a dynamic situation where reactions still take place, but no net change occurs in the concentration of reactants and products.
• It allows prediction of how changes in conditions (like temperature or pressure) can affect the concentrations of substances in a system.

To grasp equilibrium, think of it as a balance or a seesaw where both sides are equal in activity but perhaps not in appearance. The system can be seen as having reached a perfect state of balance where the forward path cancels the reverse path. This concept is fundamental in chemistry and helps us predict and manipulate reaction outcomes.

Law of Mass Action

The Law of Mass Action provides the foundation for understanding chemical equilibrium and the formation of equilibrium expressions. It states that the rate of a chemical reaction is directly proportional to the product of the concentrations of the reactants, each raised to the power of their respective coefficients in the balanced equation. This law helps chemists determine:

• How to write the equilibrium constant expressions for reactions.
• The importance of balancing chemical equations accurately, since coefficients play a critical role in the expression.

Applying this principle involves identifying the reactants and products, and then constructing an expression that shows the relationship between their concentrations at equilibrium. This approach is crucial when studying reactions in closed systems where the proportions and concentrations of substances define the system's status.

Equilibrium Expressions

Equilibrium expressions, often represented as \( K_{\text{eq}} \), are mathematical descriptions of a system at equilibrium. These expressions relate the concentrations of reactants and products in a way that reflects the balanced chemical equation. They are crucial because:

• They allow chemists to calculate the concentration of reactants and products once the reaction has reached equilibrium.
• They help in predicting how the reaction will respond to changes in conditions due to Le Chatelier's Principle.

For example, for the reaction \( \mathrm{H}_2 + \mathrm{Cl}_2 \rightleftarrows 2 \mathrm{HCl} \), the equilibrium expression is: \[ K_{\text{eq}} = \frac{[\mathrm{HCl}]^2}{[\mathrm{H}_2][\mathrm{Cl}_2]} \]This formula involves raising the concentration of products to the power of their coefficients and placing that in the numerator, while the denominator includes the concentrations of the reactants raised to the power of their coefficients. Understanding how to build these expressions is key for students learning to predict the behavior of chemical systems.