Question

Write the equilibrium expression for each of the following reactions. a. \(\mathrm{H}_{2}(g)+\mathrm{Br}_{2}(g) \rightleftharpoons 2 \mathrm{HBr}(g)\) b. \(2 \mathrm{H}_{2}(g)+\mathrm{S}_{2}(g) \rightleftharpoons 2 \mathrm{H}_{2} \mathrm{~S}(g)\) c. \(\mathrm{H}_{2}(g)+\mathrm{C}_{2} \mathrm{~N}_{2}(g) \rightleftharpoons 2 \mathrm{HCN}(g)\)

Short answer

The short answers for the equilibrium expressions are: a. \(K_c = \frac{[\mathrm{HBr}]^2}{[\mathrm{H}_2][\mathrm{Br}_2]}\) b. \(K_c = \frac{[\mathrm{H}_{2}\mathrm{S}]^2}{[\mathrm{H}_2]^2[\mathrm{S}_2]}\) c. \(K_c = \frac{[\mathrm{HCN}]^2}{[\mathrm{H}_2][\mathrm{C}_2\mathrm{N}_2]}\)

Step-by-step solution

Identify the reactants and products

In the reaction \(\mathrm{H}_{2}(g)+\mathrm{Br}_{2}(g) \rightleftharpoons 2 \mathrm{HBr}(g)\), the reactants are \(\mathrm{H}_{2}\) and \(\mathrm{Br}_{2}\), and the product is \(\mathrm{HBr}\).

Write the equilibrium expression

For the given reaction, the equilibrium expression is given by: \[K_c = \frac{[\mathrm{HBr}]^2}{[\mathrm{H}_2][\mathrm{Br}_2]}\] #b. Writing the equilibrium expression for reaction b#

Identify the reactants and products

In the reaction \(2 \mathrm{H}_{2}(g)+\mathrm{S}_{2}(g) \rightleftharpoons 2 \mathrm{H}_{2}\mathrm{S}(g)\), the reactants are \(\mathrm{H}_{2}\) and \(\mathrm{S}_{2}\), and the product is \(\mathrm{H}_{2}\mathrm{S}\).

Write the equilibrium expression

For the given reaction, the equilibrium expression is given by: \[K_c = \frac{[\mathrm{H}_{2}\mathrm{S}]^2}{[\mathrm{H}_2]^2[\mathrm{S}_2]}\] #c. Writing the equilibrium expression for reaction c#

Identify the reactants and products

In the reaction \(\mathrm{H}_{2}(g)+\mathrm{C}_{2}\mathrm{N}_{2}(g) \rightleftharpoons 2 \mathrm{HCN}(g)\), the reactants are \(\mathrm{H}_{2}\) and \(\mathrm{C}_{2}\mathrm{N}_{2}\), and the product is \(\mathrm{HCN}\).

Write the equilibrium expression

For the given reaction, the equilibrium expression is given by: \[K_c = \frac{[\mathrm{HCN}]^2}{[\mathrm{H}_2][\mathrm{C}_2\mathrm{N}_2]}\]

Key concepts

Equilibrium Expression

In chemical equilibrium, the equilibrium expression is a mathematical formula that represents the state at which the concentrations of reactants and products are constant. It is crucial to understanding how reactions behave under different conditions. Let's look deeper into how this works.

The equilibrium constant, commonly denoted as \(K_c\), relates the concentrations of products and reactants in a reversible chemical reaction at equilibrium. The general form of an equilibrium expression for a reaction \(aA + bB \rightleftharpoons cC +dD\) is given by:

• \(K_c = \frac{[C]^c[D]^d}{[A]^a[B]^b}\)

Here, \([C]\) and \([D]\) are the concentrations of the products, \(A\) and \(B\) are the reactants, and \(a\), \(b\), \(c\), and \(d\) are their respective coefficients from the balanced chemical equation.

Understanding how to construct and interpret these expressions can help predict how changes in conditions might shift the balance of a reaction. This insight is vital for fields like chemical engineering and environmental science.

Reactants and Products

In any chemical reaction, identifying reactants and products is an essential first step. Reactants are substances that start a reaction, while products are the new substances formed as a result of the reaction.

For example, consider the following reaction: \(\mathrm{H}_{2}(g)+\mathrm{Br}_{2}(g) \rightleftharpoons 2 \mathrm{HBr}(g)\). Here, \(\mathrm{H}_{2}\) and \(\mathrm{Br}_{2}\) are reactants, and \(\mathrm{HBr}\) is the product. These molecules undergo a transformation, forming new chemical bonds to create the product.

• Reactants have their bonds broken, which requires energy.
• Products are formed by creating new bonds, often releasing energy.

This simple concept of breaking and forming bonds lies at the heart of understanding chemical reactions and dictates the resulting equilibrium state, playing a significant role in what you'll see in an equilibrium expression.

Chemical Reactions

Chemical reactions are processes in which substances undergo conversion to form new substances. An essential aspect of these reactions is determining their direction and extent, aspects inherently connected to the concept of equilibrium.

Each chemical reaction can reach a state of equilibrium where the rates of the forward and reverse reactions are equal, meaning that the concentrations of reactants and products remain constant over time. Recognizing this balance is crucial for applications such as drug interactions in medicine or nutrient cycles in ecology.

Reactions can be manipulated or driven to completion by changing:

• Temperature
• Pressure
• Concentration of reactants and products

By influencing these factors, one can steer the equilibrium position. For instance, adding more reactants typically shifts equilibrium toward the products, according to Le Chatelier's Principle. Understanding and predicting these shifts is fundamental for optimizing reactions in both laboratory and industrial settings.