Problem 19 - Chemistry The Molecular Science

Question

Write the equilibrium constant expression for each reaction. (a) The oxidation of ammonia with \(\mathrm{ClF}_{3}\) in a rocket motor $$ \mathrm{NH}_{3}(\mathrm{~g})+\mathrm{ClF}_{3}(\mathrm{~g}) \rightleftharpoons 3 \mathrm{HF}(\mathrm{g})+\frac{1}{2} \mathrm{~N}_{2}(\mathrm{~g})+\frac{1}{2} \mathrm{Cl}_{2}(\mathrm{~g}) $$ (b) The simultaneous oxidation and reduction of a chlorite ion $$ \begin{aligned} 3 \mathrm{ClO}_{2}^{-}(\mathrm{aq}) \rightleftharpoons 2 \mathrm{ClO}_{3}^{-}(\mathrm{aq})+\mathrm{Cl}^{-}(\mathrm{aq}) \\ \text { (c) } \mathrm{IO}_{3}^{-}(\mathrm{aq})+6 \mathrm{OH}^{-}(\mathrm{aq})+\mathrm{Cl}_{2}(\mathrm{aq}) \rightleftharpoons & \\\ & \mathrm{IO}_{6}^{5-}(\mathrm{aq})+2 \mathrm{Cl}^{-}(\mathrm{aq})+3 \mathrm{H}_{2} \mathrm{O}(\ell) \end{aligned} $$

Step-by-Step Solution

Answer

(a) \( K_c = \frac{[\text{HF}]^3 [\text{N}_2]^{1/2} [\text{Cl}_2]^{1/2}}{[\text{NH}_3] [\text{ClF}_3]} \); (b) \( K_c = \frac{[\text{ClO}_3^-]^2 [\text{Cl}^-]}{[\text{ClO}_2^-]^3} \); (c) \( K_c = \frac{[\text{IO}_6^{5-}] [\text{Cl}^-]^2}{[\text{IO}_3^-] [\text{OH}^-]^6 [\text{Cl}_2]} \).

Step 1: Identify Reactants and Products (Part a)

For the reaction \( \text{NH}_3(g) + \text{ClF}_3(g) \rightleftharpoons 3 \text{HF}(g) + \frac{1}{2} \text{N}_2(g) + \frac{1}{2} \text{Cl}_2(g) \), identify the gaseous products and reactants. These include \( \text{NH}_3(g) \), \( \text{ClF}_3(g) \) (reactants) and \( \text{HF}(g) \), \( \text{N}_2(g) \), and \( \text{Cl}_2(g) \) (products).

Step 2: Write the Equilibrium Expression (Part a)

The equilibrium constant \( K_c \) for gaseous reactions is represented by concentrations of gases raised to the power of their stoichiometric coefficients. For this reaction, the expression is: \[ K_c = \frac{[\text{HF}]^3 [\text{N}_2]^{1/2} [\text{Cl}_2]^{1/2}}{[\text{NH}_3] [\text{ClF}_3]} \]

Step 3: Identify Reactants and Products (Part b)

For the reaction \( 3 \text{ClO}_2^-(\text{aq}) \rightleftharpoons 2 \text{ClO}_3^-(\text{aq}) + \text{Cl}^-(\text{aq}) \), identify the aqueous reactants and products: \( \text{ClO}_2^- \) (reactant), and \( \text{ClO}_3^- \), \( \text{Cl}^- \) (products).

Step 4: Write the Equilibrium Expression (Part b)

For reactions involving aqueous species, the equilibrium constant \( K_c \) is similarly determined by concentrations raised to their coefficients. For this reaction: \[ K_c = \frac{[\text{ClO}_3^-]^2 [\text{Cl}^-]}{[\text{ClO}_2^-]^3} \]

Step 5: Identify Reactants and Products (Part c)

For the reaction \( \text{IO}_3^-(\text{aq}) + 6 \text{OH}^-(\text{aq}) + \text{Cl}_2(\text{aq}) \rightleftharpoons \text{IO}_6^{5-}(\text{aq}) + 2 \text{Cl}^-(\text{aq}) + 3 \text{H}_2\text{O}(\ell) \), identify the reactants as \( \text{IO}_3^- \), \( \text{OH}^- \), and \( \text{Cl}_2 \), and the products as \( \text{IO}_6^{5-} \), and \( \text{Cl}^- \). Water, being a liquid, is omitted from the expression.

Step 6: Write the Equilibrium Expression (Part c)

Write the equilibrium constant \( K_c \) for the aqueous reaction, omitting the liquid water: \[ K_c = \frac{[\text{IO}_6^{5-}] [\text{Cl}^-]^2}{[\text{IO}_3^-] [\text{OH}^-]^6 [\text{Cl}_2]} \]

Key Concepts

Chemical Reactions

Chemical reactions are processes in which substances known as reactants are transformed into different substances known as products. This transformation involves the breaking and forming of chemical bonds, resulting in a change in the chemical structure of the involved substances.
For example, in the reaction between ammonia \(\text{NH}_3\) and chlorine trifluoride \(\text{ClF}_3\), reactants (\(\text{NH}_3\) and \(\text{ClF}_3\)) are transformed into products like hydrogen fluoride \(\text{HF}\), nitrogen \(\text{N}_2\), and chlorine \(\text{Cl}_2\).
The chemical reaction involves changes in the physical and chemical properties. The arrangement of atoms changes leading to new substances that have unique characteristics than the initial reactants.

• A balanced chemical equation describes the changes by showing equal numbers of atoms for each element on both the reactant and product sides.
• Chemical reactions are governed by conservation laws, like the conservation of mass and charge.

Understanding these changes through equations helps chemists predict the substances produced and their quantities in various reactions.

Oxidation-Reduction Reactions

Oxidation-reduction reactions, also known as redox reactions, are a type of chemical reaction that involves a transfer of electrons between substances. In such reactions, one substance loses electrons (oxidation), and another gains electrons (reduction).
In the reaction involving chlorite ions \(\text{ClO}_2^-\), this process is evident. When chlorite ions transform into \(\text{ClO}_3^-\) and \(\text{Cl}^-\), electrons are transferred between species.
To better understand redox reactions, consider these key points:

• Assign oxidation states to atoms before and after the reaction to identify which are oxidized and reduced.
• Use the mnemonic "OIL RIG" which stands for "Oxidation Is Loss, Reduction Is Gain" of electrons.
• An oxidizing agent is a substance that gains electrons whereas a reducing agent is one that loses electrons.

These reactions are pervasive in many processes including energy generation in batteries and metabolic reactions in living organisms.

Equilibrium Expressions

Equilibrium expressions are mathematical representations of a chemical reaction at equilibrium. At this state, the forward and reverse reaction rates are equal. Hence, the concentrations of the reactants and products remain constant.
The equilibrium constant \(K_c\) value can be expressed in terms of the concentrations of the gaseous or aqueous reactants and products, each raised to the power of their coefficients in the balanced equation.
For example, the equilibrium expression for the reaction involving \(\text{NH}_3(g)\) and \(\text{ClF}_3(g)\) is written as:\[ K_c = \frac{[\text{HF}]^3 [\text{N}_2]^{1/2} [\text{Cl}_2]^{1/2}}{[\text{NH}_3][\text{ClF}_3]} \] Understanding equilibrium expressions involves:

• Recognizing that only gases and aqueous species are included in the expressions. Solids and liquids are excluded.
• Using balanced chemical equations to determine the stoichiometric coefficients as powers in the \(K_c\) expression.
• Valuing \(K_c\) offers insight into the position of equilibrium: a large value suggests products dominate, while a small value indicates reactants are predominant.

Grasping these concepts is crucial for predicting how changes in conditions will affect the system's equilibrium, an essential aspect of chemical kinetics and thermodynamics.