Problem 21 - Chemistry An Atoms First Approach

Question

Write the equilibrium expression \((K)\) for each of the following gas-phase reactions. a. \(\mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{NO}(g)\). b. \(\mathrm{N}_{2} \mathrm{O}_{4}(g) \rightleftharpoons 2 \mathrm{NO}_{2}(g)\). c. \(\operatorname{SiH}_{4}(g)+2 \mathrm{Cl}_{2}(g) \rightleftharpoons \mathrm{SiCl}_{4}(g)+2 \mathrm{H}_{2}(g)\). d. \(2 \mathrm{PBr}_{3}(g)+3 \mathrm{Cl}_{2}(g) \rightleftharpoons 2 \mathrm{PCl}_{3}(g)+3 \mathrm{Br}_{2}(g)\).

Step-by-Step Solution

Answer

The equilibrium expressions for the given gas-phase reactions are as follows: a. \(K = \frac{[NO]^2}{[N2] \times [O2]}\) b. \(K = \frac{[NO2]^2}{[N2O4]}\) c. \(K = \frac{[SiCl4] \times [H2]^2}{[SiH4] \times [Cl2]^2}\) d. \(K = \frac{[PCl3]^2 \times [Br2]^3}{[PBr3]^2 \times [Cl2]^3}\)

Step 1: Identify the reactants and products

In this reaction, the reactants are Nitrogen gas (N2) and Oxygen gas (O2), while the product is Nitrogen Monoxide gas (NO).

Step 2: Write the equilibrium expression

Now, we will use the formula for the equilibrium expression to write the expression for this reaction: \(K = \frac{[NO]^2}{[N2] \times [O2]}\) #a. Reaction 2: N2O4(g) ⇌ 2 NO2(g)#

Step 1: Identify the reactants and products

In this reaction, the reactant is Dinitrogen Tetroxide (N2O4) and the product is Nitrogen Dioxide gas (NO2).

Step 2: Write the equilibrium expression

Now, we will use the formula for the equilibrium expression to write the expression for this reaction: \(K = \frac{[NO2]^2}{[N2O4]}\) #c. Reaction 3: SiH4(g) + 2 Cl2(g) ⇌ SiCl4(g) + 2 H2(g)#

Step 1: Identify the reactants and products

In this reaction, the reactants are Silicon Tetrahydride (SiH4) and Chlorine gas (Cl2), while the products are Silicon Tetrachloride (SiCl4) and Hydrogen gas (H2).

Step 2: Write the equilibrium expression

Now, we will use the formula for the equilibrium expression to write the expression for this reaction: \(K = \frac{[SiCl4] \times [H2]^2}{[SiH4] \times [Cl2]^2}\) #d. Reaction 4: 2 PBr3(g) + 3 Cl2(g) ⇌ 2 PCl3(g) + 3 Br2(g)#

Step 1: Identify the reactants and products

In this reaction, the reactants are Phosphorus Tribromide (PBr3) and Chlorine gas (Cl2), while the products are Phosphorus Trichloride (PCl3) and Bromine gas (Br2).

Step 2: Write the equilibrium expression

Now, we will use the formula for the equilibrium expression to write the expression for this reaction: \(K = \frac{[PCl3]^2 \times [Br2]^3}{[PBr3]^2 \times [Cl2]^3}\)

Key Concepts

Equilibrium Constant

The equilibrium constant, denoted as \(K\), is a fundamental concept in chemical equilibrium. It provides a measure of the ratio of the concentrations of products to reactants for a reaction at equilibrium. This constant is unique to each reaction and only varies with temperature. In the expressions for \(K\), the concentration of each species is raised to the power of its coefficient in the balanced chemical equation. This makes the equilibrium constant a reflection of the stoichiometry of the reaction.

For example, in the reaction \(N_{2}(g) + O_{2}(g) \rightleftharpoons 2NO(g)\), the equilibrium constant expression is written as:

• \(K = \frac{[NO]^2}{[N_2][O_2]}\)

Here, \(2\), the coefficient of \(NO\), becomes an exponent in the expression, underscoring its importance in the equilibrium state. Understanding \(K\) helps predict the position of equilibrium and the concentrations of chemicals involved in a reaction.

Reaction Stoichiometry

Reaction stoichiometry involves the quantitative relationships between the amounts of reactants and products in a chemical reaction. In a balanced chemical equation, the coefficients provide these quantitative relationships, ensuring mass and atom conservation. This stoichiometry is crucial for writing correct equilibrium constant expressions.

The equation \(2PBr_3(g) + 3Cl_2(g) \rightleftharpoons 2PCl_3(g) + 3Br_2(g)\) serves as a perfect illustration. Stoichiometry here dictates the equilibrium expression:

• \(K = \frac{[PCl_3]^2[Br_2]^3}{[PBr_3]^2[Cl_2]^3}\)

Understanding stoichiometry enables accurate predictions of how a reaction will proceed and its equilibrium state. The coefficients in these balanced equations not only help in formulating equilibrium expressions but also play a role in deducing reaction kinetics and mechanisms.

Gas-phase Reactions

Gas-phase reactions occur when the reactants and products are gases. These reactions often proceed under a set of conditions where gases are prevalent, such as high temperature or specific pressure. One key aspect is that the concentrations of gases, typically expressed in molarity \( ext{M}\), can also be related to partial pressures which can affect the equilibrium condition.

Take the example of \(SiH_4(g) + 2Cl_2(g) \rightleftharpoons SiCl_4(g) + 2H_2(g)\). Here, the reaction involves only gaseous substances. The behavior and equilibrium of such a reaction can be dynamically influenced by changes in volume, temperature, and pressure due to the gas phase nature. The equilibrium expression for this reaction is:

• \(K = \frac{[SiCl_4][H_2]^2}{[SiH_4][Cl_2]^2}\)

For gas-phase reactions, Le Chatelier’s Principle can predict how changes in conditions will shift the equilibrium position. This is crucial for industries that rely on controlling reaction conditions to maximize product yield.