Question

Write the equilibrium constant expression for each of the following reactions: (a) \(2 \mathrm{~N}_{2} \mathrm{O}_{5}(g) \rightleftharpoons 4 \mathrm{NO}_{2}(g)+\mathrm{O}_{2}(g)\) (b) \(\mathrm{Br}_{2}(g)+2 \mathrm{HI}(g) \rightleftharpoons \mathrm{I}_{2}(g)+2 \mathrm{HBr}(g)\) (c) \(4 \mathrm{NH}_{3}(g)+3 \mathrm{O}_{2}(g) \Longrightarrow 2 \mathrm{~N}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(g)\)

Short answer

The equilibrium constant expressions for the reactions are as follows: (a) \( Kc = [NO_{2}]^{4} [O_{2}]/[N_{2}O_{5}]^{2} \) (b) \( Kc = [I_{2}] [HBr]^{2}/([Br_{2}][HI]^{2}) \) (c) \( Kc = [N_{2}]^{2} [H_{2}O]^{6}/([NH_{3}]^{4}[O_{2}]^{3}) \)

Step-by-step solution

- Writing first equation's equilibrium constant expression

The reaction is: \(2 N_{2}O_{5}(g) \rightleftharpoons 4 NO_{2}(g) + O_{2}(g)\) The equilibrium constant expression is denoted by Kc. It is given by the concentration of the products to the power of their stoichiometric coefficients divided by the concentration of the reactants to the power of their stoichiometric coefficients.Thus, for this reaction, Kc = \([NO_{2}]^{4} [O_{2}]^{1}/[N_{2}O_{5}]^{2}\)

- Writing second equation's equilibrium constant expression

The reaction is: \(Br_{2}(g)+ 2 HI(g) \rightleftharpoons I_{2}(g)+ 2 HBr(g)\) The equilibrium constant expression is denoted by Kc. Kc = \([I_{2}]^{1} [HBr]^{2}/([Br_{2}]^{1}[HI]^{2})\)

- Writing third equation's equilibrium constant expression

The reaction is: \(4 NH_{3}(g)+ 3 O_{2}(g) \rightleftharpoons 2 N_{2}(g) + 6 H_{2}O(g)\) The equilibrium constant expression Kc = \([N_{2}]^{2} [H_{2}O]^{6}/([NH_{3}]^{4} [O_{2}]^{3})\)

Key concepts

Chemical Reactions

In a chemical reaction, substances, known as reactants, transform into new substances called products. Chemical reactions happen when molecules interact, leading to changes in molecular structure. This process can be represented through chemical equations, which balance the number of atoms of each element involved. For example, the reaction \(2 \mathrm{~N}_{2} \mathrm{O}_{5}(g) \rightleftharpoons 4 \mathrm{NO}_{2}(g)+\mathrm{O}_{2}(g)\) describes how dinitrogen pentoxide converts to nitrogen dioxide and oxygen.

• Reactants come before the arrow.
• Products are listed after the arrow.
• The arrow indicates the direction of the chemical process.

The state of the substances, like (g) for gases, is shown beside their chemical formulas. Understanding chemical reactions is essential, as they serve as the groundwork for many chemical processes.

Stoichiometry

Stoichiometry is the study of the quantitative relationships between reactants and products in a chemical reaction. It involves using balanced chemical equations to calculate amounts of substances involved. For example, in the equation \(Br_{2}(g) + 2 HI(g) \rightleftharpoons I_{2}(g) + 2 HBr(g)\), stoichiometry ensures that the same number of each type of atom is present on both sides of the equation.

• Coefficients in the equation show the proportion of moles of each substance.
• This ensures the law of conservation of mass is followed.
• Calculations can involve finding the amount of product formed or reactant used.

Using stoichiometry, one can determine the equilibrium constant expression \( K_c\) by applying the stoichiometric coefficients to the concentrations. This approach highlights the interactions within the chemical system.

Gaseous Reactions

Gaseous reactions are processes where the reactants, products, or both, are in the gaseous state. These reactions can be influenced by variables such as pressure, temperature, and volume. The reaction \(4 NH_{3}(g)+ 3 O_{2}(g) \rightleftharpoons 2 N_{2}(g) + 6 H_{2}O(g)\) exemplifies a gaseous reaction.

• Gas laws, such as the ideal gas law, are often used to relate these variables.
• Equilibrium concepts help predict how changing conditions affect the system.
• Balancing gaseous reactions often involves ensuring the volume of gases is conserved.

Given the gaseous nature of the substances, it is important to understand how conditions like pressure can shift the equilibrium in these reactions. Analyzing these aspects assists in understanding how gaseous reactions contribute to various industrial and laboratory processes.