Problem 36 - Chemistry Class 9

Question

Apply the law of mass action to the following equilibria (a) \(\mathrm{PCl}_{5} \rightleftharpoons \mathrm{PCl}_{3}+\mathrm{Cl}_{2}\) (b) \(2 \mathrm{NO}+\mathrm{O}_{2} \rightleftharpoons 2 \mathrm{NO}_{2}\)

Step-by-Step Solution

Answer

Answer: The factors that can influence the position of the equilibria in both reactions include the concentrations of the reactants and products. An increase in the concentration of the products will drive the equilibrium to the left, favoring the formation of reactants, while an increase in the concentration of the reactants will drive the equilibrium to the right, favoring the formation of products. The value of K determines the extent of the reaction and the ratio of the concentrations of the products to the reactants at equilibrium. If K is much greater than 1, the reaction is product-favored, and if K is much less than 1, the reaction is reactant-favored. If K is close to 1, significant amounts of both reactants and products are present at equilibrium.

Step 1: Identify the reactants and products in each reaction.

For each reaction, the reactants are the compounds on the left-hand side of the equation, and the products are the compounds on the right-hand side. (a) \(\mathrm{PCl}_{5} \rightleftharpoons \mathrm{PCl}_{3}+\mathrm{Cl}_{2}\) Reactants: PCl5 Products: PCl3, Cl2 (b) \(2 \mathrm{NO}+\mathrm{O}_{2} \rightleftharpoons 2 \mathrm{NO}_{2}\) Reactants: NO, O2 Products: NO2

Step 2: Write the expression for the equilibrium constant.

We will now write the expression for the equilibrium constant, K, for each reaction using the law of mass action. The equilibrium constant is equal to the product of the concentrations of the products raised to the power of their stoichiometric coefficients, divided by the product of the concentrations of the reactants raised to the power of their stoichiometric coefficients. (a) For the reaction \(\mathrm{PCl}_{5} \rightleftharpoons \mathrm{PCl}_{3}+\mathrm{Cl}_{2}\), the expression for the equilibrium constant is: K = \(\frac{[\mathrm{PCl}_{3}][\mathrm{Cl}_{2}]}{[\mathrm{PCl}_{5}]}\) (b) For the reaction \(2 \mathrm{NO}+\mathrm{O}_{2} \rightleftharpoons 2 \mathrm{NO}_{2}\), the expression for the equilibrium constant is: K = \(\frac{[\mathrm{NO}_{2}]^{2}}{[\mathrm{NO}]^{2}[\mathrm{O}_{2}]}\)

Step 3: Analyze the equilibrium expressions.

Now that we have expressions for the equilibrium constants (K) for each reaction, we can analyze the equilibria. If K is much greater than 1, the reaction is product-favored, meaning that the products are more abundant than the reactants at equilibrium. If K is much less than 1, the reaction is reactant-favored, meaning that the reactants are more abundant than the products at equilibrium. If K is close to 1, the reaction is close to balance, with significant amounts of both reactants and products present at equilibrium. (a) In the expression K = \(\frac{[\mathrm{PCl}_{3}][\mathrm{Cl}_{2}]}{[\mathrm{PCl}_{5}]}\), we can see that an increase in either the concentration of PCl3 or Cl2 will drive the equilibrium to the right. The value of K will determine the extent of the reaction and the ratio of the concentrations of the products to the reactants at equilibrium. (b) In the expression K = \(\frac{[\mathrm{NO}_{2}]^{2}}{[\mathrm{NO}]^{2}[\mathrm{O}_{2}]}\), we can see that an increase in the concentration of either NO or O2 will drive the equilibrium to the right, favoring the formation of NO2. Conversely, an increase in the concentration of NO2 will drive the equilibrium to the left, favoring the formation of NO and O2. Again, the value of K will determine the extent of the reaction and the ratio of the concentrations of the products to the reactants at equilibrium.

Key Concepts

Equilibrium Constant

In chemical reactions, the equilibrium constant, commonly denoted as \(K\), is a fundamental concept used to describe the balance between reactants and products in a reaction at equilibrium. It provides insight into where the chemical balance lies and which is favored more—reactants or products. For any given reaction, \(K\) is calculated using the concentrations of the chemical species involved, each raised to the power of their respective stoichiometric coefficients.

For instance, consider the reaction of \(\text{PCl}_5\) dissociating into \(\text{PCl}_3\) and \(\text{Cl}_2\). The equilibrium expression for this would be \(K = \frac{[\text{PCl}_3][\text{Cl}_2]}{[\text{PCl}_5]}\). In this case, the concentrations of \(\text{PCl}_3\) and \(\text{Cl}_2\) are multiplied together and divided by the concentration of \(\text{PCl}_5\).

Similarly, for another reaction, like \(2 \text{NO} + \text{O}_2 \rightleftharpoons 2 \text{NO}_2\), the equilibrium constant becomes \(K = \frac{[\text{NO}_2]^2}{[\text{NO}]^2 [\text{O}_2]}\). Here, the products and reactants are raised to the power of their coefficients, reflecting how they proportionally contribute to the system’s equilibrium.

Understanding \(K\) values helps chemists predict the direction of a reaction and the potential yield of products.

Chemical Equilibrium

Chemical equilibrium is a dynamic state in a chemical reaction where the rate of the forward reaction equals the rate of the reverse reaction. This doesn't mean the reactants and products are equal in concentration, but rather their amounts remain constant over time as long as the system is closed.

When a reaction reaches equilibrium, it doesn't "stop" but continues to proceed in both directions at an equal rate. This balance can adjust when external conditions change, such as temperature, pressure, or concentration. For example, in the decomposition of \(\text{PCl}_5\) to \(\text{PCl}_3\) and \(\text{Cl}_2\), if we increase the amount of \(\text{PCl}_5\), the system shifts to create more \(\text{PCl}_3\) and \(\text{Cl}_2\) to reach a new equilibrium.

Key indicators of equilibrium include:

• The concentrations of reactants and products remain constant.
• The forward and backward reactions occur at equal rates.
• The equilibrium position can shift with changes in conditions due to factors like Le Chatelier's principle.

Reaching chemical equilibrium is crucial for processes in industries such as pharmaceuticals and manufacturing, where control over reaction products is necessary.

Reaction Products and Reactants

The fundamental participants in any chemical reaction are the reactants and products. Reactants are the starting materials present at the beginning of a chemical reaction and are generally consumed as the reaction proceeds. Products, on the other hand, are the new substances formed as a result of the chemical reaction.

In the example of \(\text{PCl}_5 \rightleftharpoons \text{PCl}_3 + \text{Cl}_2\), \(\text{PCl}_5\) is the reactant, while \(\text{PCl}_3\) and \(\text{Cl}_2\) are the products. Conversely, in \(2 \text{NO} + \text{O}_2 \rightleftharpoons 2 \text{NO}_2\), \(\text{NO}\) and \(\text{O}_2\) are reactants, and \(\text{NO}_2\) is the product.

The transformation of reactants to products is what defines a chemical reaction. Understanding the specific roles and the stoichiometric relationships between these entities is crucial, as it allows chemists to predict the outcome of reactions, calculate yields, and optimize reaction conditions for maximum efficiency.

Key concepts related to reactants and products include:

• Stoichiometry, which involves the calculation of reactant and product quantities.
• Limiting reactants, which determine the extent of a reaction.
• Reversibility, which allows the interconversion between reactants and products until equilibrium is reached.

By comprehending these basics, students build a foundation for more advanced studies in chemical reactions and processes.