Problem 1 - Chemistry and Chemical Reactivity

Question

Write equilibrium constant expressions for the following reactions. For gases, use either pressures or concentrations. (a) \(2 \mathrm{H}_{2} \mathrm{O}_{2}(\mathrm{g}) \rightleftarrows 2 \mathrm{H}_{2} \mathrm{O}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g})\) (b) \(\mathrm{CO}(\mathrm{g})+1 / 2 \mathrm{O}_{2}(\mathrm{g}) \rightleftarrows \mathrm{CO}_{2}(\mathrm{g})\) (c) \(\mathbf{C}(\mathrm{s})+\mathbf{C O}_{2}(\mathrm{g}) \rightleftharpoons 2 \mathbf{C O}(\mathrm{g})\) (d) \(\mathrm{NiO}(\mathrm{s})+\mathrm{CO}(\mathrm{g}) \rightleftarrows \mathrm{Ni}(\mathrm{s})+\mathrm{CO}_{2}(\mathrm{g})\)

Step-by-Step Solution

Answer

(a) \(K_p = \frac{(p_{H_2O})^2 \cdot p_{O_2}}{(p_{H_2O_2})^2}\); (b) \(K_p = \frac{p_{CO_2}}{p_{CO} \cdot (p_{O_2})^{1/2}}\); (c) \(K_p = \frac{(p_{CO})^2}{p_{CO_2}}\); (d) \(K_p = \frac{p_{CO_2}}{p_{CO}}\).

Step 1: Understand the equilibrium constant expression

The equilibrium constant expression for a given reaction quantifies the ratio of the concentrations or pressures of products to reactants at equilibrium. For gases, pressures ( 𝑝 ) or concentrations ( 𝐶 ) can be used. Solids and liquids are not included in the expressions, as they are considered to have constant activity.

Step 2: Write the expression for reaction (a)

For the reaction \(2 \mathrm{H}_2\mathrm{O}_2(\mathrm{g}) \rightleftarrows 2 \mathrm{H}_2\mathrm{O}(\mathrm{g})+\mathrm{O}_2(\mathrm{g})\), the equilibrium constant expression using pressures is given by \[K_p = \frac{(p_{H_2O})^2 \cdot p_{O_2}}{(p_{H_2O_2})^2}\].

Step 3: Write the expression for reaction (b)

For the reaction \(\mathrm{CO}(\mathrm{g})+\frac{1}{2}\mathrm{O}_2(\mathrm{g}) \rightleftarrows \mathrm{CO}_2(\mathrm{g})\), the equilibrium constant expression is \[K_p = \frac{p_{CO_2}}{p_{CO} \cdot (p_{O_2})^{1/2}}\].

Step 4: Write the expression for reaction (c)

For the reaction \(\mathrm{C}(\mathrm{s})+\mathrm{CO}_2(\mathrm{g}) \rightleftharpoons 2 \mathrm{CO}(\mathrm{g})\), carbon is a solid and is not included in the expression. Thus, the equilibrium constant expression is \[K_p = \frac{(p_{CO})^2}{p_{CO_2}}\].

Step 5: Write the expression for reaction (d)

For the reaction \(\mathrm{NiO}(\mathrm{s})+\mathrm{CO}(\mathrm{g}) \rightleftarrows \mathrm{Ni}(\mathrm{s})+\mathrm{CO}_2(\mathrm{g})\), both \(\mathrm{NiO}\) and \(\mathrm{Ni}\) are solids and are not part of the expression. Hence the equilibrium constant expression is \[K_p = \frac{p_{CO_2}}{p_{CO}}\].

Key Concepts

Chemical Reactions

Chemical reactions involve the transformation of reactants into products. In chemical equations, each substance is represented with symbols and formulas. The arrow in the equation, such as \( \rightleftarrows \), indicates the direction of the reaction.
In reversible reactions, as shown in the given exercises, both the forward and reverse reactions occur. These reach a state of balance, which is why they are called equilibrium reactions.

• Reactants are substances that start a chemical reaction.
• Products are substances formed as a result of a chemical reaction.
• Reversible reactions can move forward (towards products) or backward (towards reactants).

Understanding chemical reactions and their directionality is vital in predicting the yields and the stability of the systems involved.

Gas Equilibrium

Gas equilibrium refers to the state at which the ratio of the concentrations (or pressures) of gases in a reaction mixture remains constant over time. It occurs when the rates of the forward and reverse reactions are equal.
This equilibrium is dynamic, meaning that the reactions continue to happen, but there is no net change in the concentrations or pressures of the gases.

• The concept of dynamic equilibrium is key: reactions never stop but balance each other out.
• Equilibrium can be disturbed by changes in conditions, such as temperature or pressure.
• Once disturbed, the system will adjust to re-establish equilibrium.

Consider the first exercise reaction: \(2 \mathrm{H}_2\mathrm{O}_2(\mathrm{g}) \rightleftarrows 2 \mathrm{H}_2 \mathrm{O}(\mathrm{g})+\mathrm{O}_2(\mathrm{g})\). It achieves gas equilibrium when the production and consumption rates of each gas become consistent.

Pressure Equilibrium

In a gaseous system at equilibrium, pressure equilibrium comes into play. It involves the balance of pressures of gases in a sealed system. The equilibrium constant expressed in terms of pressure is denoted as \(K_p\). To write these expressions, use the formula:
\[ K_p = \frac{ \text{pressure of products} }{ \text{pressure of reactants} } \]
When calculating \(K_p\), only include gases whose pressures can change; solids and liquids are typically excluded.

• The pressures of reactants and products are used to find \(K_p\).
• Partial pressures refer to the pressure each gas component would exert if it were the only gas present.
• Only gases in the equation affect pressure equilibrium.

For instance, in the second exercise equation, \[K_p = \frac{p_{CO_2}}{p_{CO} \cdot (p_{O_2})^{1/2}}\], we assess the influence of each gaseous component on the overall pressure equilibrium.

Concentration Equilibrium

Concentration equilibrium, analogously to pressure equilibrium, deals with the concentration of substances in a reaction at equilibrium. Equilibrium constant using concentrations is denoted as \(K_c\). This is typically used for reactions where substances are in a dissolved or mixed state rather than gaseous.To establish \(K_c\), use the expression:
\[ K_c = \frac{ \text{concentration of products} }{ \text{concentration of reactants} } \]
Similar to pressure equilibrium, only active substances in solution typically count.

• Concentrations are measured in molarity (moles per liter).
• Solids and liquids are usually excluded from \(K_c\) calculations.
• Both \(K_c\) and \(K_p\) provide insight into the equilibrium position but may give different values depending on the reaction conditions.

These concepts are fundamental to understanding chemical balance, particularly in fields like chemistry and biochemistry.