Question

Write the equilibrium expression for each of the following reactions. a. \(\mathrm{NO}_{2}(g)+\mathrm{ClNO}(g) \rightleftharpoons \mathrm{ClNO}_{2}(g)+\mathrm{NO}(g)\) b. \(\mathrm{Br}_{2}(g)+5 \mathrm{~F}_{2}(g) \rightleftharpoons 2 \mathrm{BrF}_{5}(g)\) c. \(4 \mathrm{NH}_{3}(g)+6 \mathrm{NO}(g) \rightleftharpoons 5 \mathrm{~N}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(g)\)

Short answer

The equilibrium expressions for the given reactions are as follows: a. \[K_c = \frac{[\mathrm{ClNO}_{2}][\mathrm{NO}]}{[\mathrm{NO}_{2}][\mathrm{ClNO}]}\] b. \[K_c = \frac{[\mathrm{BrF}_{5}]^2}{[\mathrm{Br}_{2}][\mathrm{F}_{2}]^5}\] c. \[K_c = \frac{[\mathrm{N}_{2}]^5 [\mathrm{H}_{2} \mathrm{O}]^6}{[\mathrm{NH}_{3}]^4 [\mathrm{NO}]^6}\]

Step-by-step solution

Identify reactants and products

The reactants are \(\mathrm{NO}_{2}(g)\) and \(\mathrm{ClNO}(g)\) while the products are \(\mathrm{ClNO}_{2}(g)\) and \(\mathrm{NO}(g)\).

Write the equilibrium expression

Based on the stoichiometric coefficients in the balanced equation, the equilibrium expression will be: \[K_c = \frac{[\mathrm{ClNO}_{2}][\mathrm{NO}]}{[\mathrm{NO}_{2}][\mathrm{ClNO}]}\] b. Writing the equilibrium expression for reaction \(\mathrm{Br}_{2}(g)+5 \mathrm{F}_{2}(g) \rightleftharpoons 2 \mathrm{BrF}_{5}(g)\)

Identify reactants and products

The reactants are \(\mathrm{Br}_{2}(g)\) and \(5 \mathrm{F}_{2}(g)\) while the product is \(2 \mathrm{BrF}_{5}(g)\).

Write the equilibrium expression

Based on the stoichiometric coefficients in the balanced equation, the equilibrium expression will be: \[K_c = \frac{[\mathrm{BrF}_{5}]^2}{[\mathrm{Br}_{2}][\mathrm{F}_{2}]^5}\] c. Writing the equilibrium expression for reaction \(4 \mathrm{NH}_{3}(g)+6 \mathrm{NO}(g) \rightleftharpoons 5 \mathrm{N}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(g)\)

Identify reactants and products

The reactants are \(4 \mathrm{NH}_{3}(g)\) and \(6 \mathrm{NO}(g)\) while the products are \(5 \mathrm{N}_{2}(g)\) and \(6 \mathrm{H}_{2}\mathrm{O}(g)\).

Write the equilibrium expression

Based on the stoichiometric coefficients in the balanced equation, the equilibrium expression will be: \[K_c = \frac{[\mathrm{N}_{2}]^5 [\mathrm{H}_{2} \mathrm{O}]^6}{[\mathrm{NH}_{3}]^4 [\mathrm{NO}]^6}\]

Key concepts

Understanding Chemical Reactions

A chemical reaction involves the transformation of substances, called reactants, into different substances, known as products. This process can involve breaking bonds in the reactants and forming new bonds in the products. In our examples, the chemicals are given in a gaseous state.

• Case (a) involves nitrogen dioxide (\(\mathrm{NO}_{2})\), chlorine nitroxyl (\(\mathrm{ClNO}\), and their resultant products.
• Case (b) features bromine (\(\mathrm{Br}_{2}\)) and fluorine (\(\mathrm{F}_{2}\)), transforming to bromine pentafluoride.
• Case (c) includes ammonia (\(\mathrm{NH}_{3}\)) and nitric oxide (\(\mathrm{NO}\)). These rearrange to produce nitrogen gas and water vapor.

The forward and reverse processes can occur simultaneously, creating a dynamic balance. Understanding these reaction components is critical to determining how various factors influence reaction rates and equilibrium.

Stoichiometry: The Recipe of Chemical Reactions

Stoichiometry acts as a "chemical recipe" dictating the ratios and amounts of reactants required to form products. It is derived from the balanced equation of a chemical reaction, showing the precise proportions.
Each reaction mentioned is defined by specific stoichiometric coefficients which indicate:

• How many moles of each reactant are consumed, and how many moles of each product are formed.
• In reaction (a), there's an implied "1" in front of each reactant and product, indicating a one-to-one-to-one-to-one ratio.
• For reaction (b), 1 mole of bromine reacts with 5 moles of fluorine to produce 2 moles of bromine pentafluoride.
• Reaction (c) requires precise proportions: 4 moles of ammonia to 6 moles of nitric oxide produce 5 moles of nitrogen gas and 6 moles of water.

Mastery of stoichiometry helps in predicting the outcomes of reactions, calculating necessary reactant quantities, and analyzing elemental makeup of substances involved.

Balanced Equations and Equilibrium Expressions

A balanced chemical equation reflects the conservation of matter, ensuring the same number of atoms of each element in the reactants and products. It is fundamental in determining the equilibrium expression, \( K_c \), which provides insight into the state of reaction equilibrium.
Equilibrium expressions are determined by:

• Identifying the reactants and products from a balanced equation.
• Using the stoichiometric coefficients to formulate a ratio of the concentration of products to reactants.

For each example:

• Reaction (a): The expression \( K_c = \frac{[\mathrm{ClNO}_{2}][\mathrm{NO}]}{[\mathrm{NO}_{2}][\mathrm{ClNO}]} \) illustrates a balance.
• Reaction (b): \( K_c = \frac{[\mathrm{BrF}_{5}]^2}{[\mathrm{Br}_{2}][\mathrm{F}_{2}]^5} \), demonstrates the varied influence of different reactants' concentrations.
• Reaction (c): \( K_c = \frac{[\mathrm{N}_{2}]^5 [\mathrm{H}_{2} \mathrm{O}]^6}{[\mathrm{NH}_{3}]^4 [\mathrm{NO}]^6} \), underscores a complex equilibrium state.

This concept not only assists in assessing reaction conditions but also predicts shifts in reaction dynamics when conditions change.