Question

Write the equilibrium constant expression for each of the following reversible reactions: (a) \(\mathrm{H}_{2}(g)+\mathrm{F}_{2}(g) \rightleftarrows 2 \mathrm{HF}(g)\) (b) \(4 \mathrm{NH}_{3}(g)+7 \mathrm{O}_{2}(g) \rightleftarrows 4 \mathrm{NO}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(g)\) (c) \(\mathrm{ZnCO}_{3}(s) \rightleftarrows \mathrm{ZnO}(s)+\mathrm{CO}_{2}(g)\)

Short answer

(a) \( K_c = \frac{[\mathrm{HF}]^2}{[\mathrm{H}_2][\mathrm{F}_2]} \); (b) \( K_c = \frac{[\mathrm{NO}_2]^4 [\mathrm{H}_2\mathrm{O}]^6}{[\mathrm{NH}_3]^4 [\mathrm{O}_2]^7} \); (c) \( K_c = [\mathrm{CO}_2] \).

Step-by-step solution

Understanding Equilibrium Constant Expression

The equilibrium constant expression, \( K_c \), is derived from the balanced chemical equation of a reversible reaction. It is expressed in terms of the concentration of the products over the concentration of the reactants, each raised to the power of their stoichiometric coefficients.

Write Expression for Reaction (a)

For reaction (a) \( \mathrm{H}_2(g) + \mathrm{F}_2(g) \rightleftarrows 2 \mathrm{HF}(g) \), the equilibrium constant expression is: \[ K_c = \frac{[\mathrm{HF}]^2}{[\mathrm{H}_2][\mathrm{F}_2]} \]

Write Expression for Reaction (b)

For reaction (b) \( 4 \mathrm{NH}_3(g) + 7 \mathrm{O}_2(g) \rightleftarrows 4 \mathrm{NO}_2(g) + 6 \mathrm{H}_2\mathrm{O}(g) \), the equilibrium constant expression is: \[ K_c = \frac{[\mathrm{NO}_2]^4 [\mathrm{H}_2\mathrm{O}]^6}{[\mathrm{NH}_3]^4 [\mathrm{O}_2]^7} \]

Write Expression for Reaction (c) and Note

For reaction (c) \( \mathrm{ZnCO}_3(s) \rightleftarrows \mathrm{ZnO}(s) + \mathrm{CO}_2(g) \), the equilibrium constant expression only includes gaseous or aqueous species, so solids are excluded: \[ K_c = [\mathrm{CO}_2] \]

Key concepts

Reversible Reactions

In chemistry, a reversible reaction is a process where the reactants can convert to products, and those products can simultaneously revert back to the original reactants. This dance between reactants and products continues until the system reaches a state of equilibrium. One classic example is the water evaporation and condensation cycle. In this context, the terminology "reversible reaction" highlights the capability of a chemical system to reach a balanced state where neither reactants nor products are fully consumed.

There are a few key characteristics of reversible reactions to understand:

• They contain a bidirectional arrow in their chemical equations, signaling that the reaction can proceed in both forward and backward directions.
• Balance is achieved when the rate of the forward reaction equals the rate of the backward reaction
• No net change in the concentrations of reactants and products at equilibrium.

This balance between directions is crucial for the establishment of chemical equilibrium, which we will explore next.

Chemical Equilibrium

Chemical equilibrium occurs when a reversible reaction reaches a point where the concentrations of reactants and products remain constant over time, though they are not necessarily equal. At this juncture, the rates of the forward and reverse reactions are equal, establishing a dynamic balance. This equilibrium state is described using the equilibrium constant expression, denoted as \( K_c \).

Here's how to perceive chemical equilibrium:

• It is a state of balance in a closed system where macroscopic properties (like concentration) remain unchanged.
• The equilibrium constant, \( K_c \), is a ratio of the concentrations of products to reactants, each raised to the power of their coefficients from the balanced equation.
• A large \( K_c \) (>1) indicates products are favored at equilibrium, whereas a small \( K_c \) (<1) suggests reactants are more prevalent.

Chemical equilibrium is at the core of understanding how and why certain reactions proceed or halt under given conditions.

Stoichiometry

Stoichiometry is an essential part of chemistry that deals with the quantitative relationships between reactants and products in a chemical reaction. When setting up an equilibrium constant expression, understanding stoichiometry helps determine how the concentrations of substances relate to one another based on the balanced chemical equation.

Key aspects of stoichiometry include:

• Stoichiometric coefficients, which are the numbers in front of molecules in a balanced equation, indicating the ratio in which substances react or form.
• They are crucial for accurately writing equilibrium constant expressions, as these coefficients become exponents in the expression.
• For instance, in the reaction \( 4\, \mathrm{NH}_3(g) + 7\, \mathrm{O}_2(g) \rightleftarrows 4\, \mathrm{NO}_2(g) + 6\, \mathrm{H}_2\mathrm{O}(g) \), the stoichiometric coefficients allow you to construct \( K_c = \frac{[\mathrm{NO}_2]^4 [\mathrm{H}_2\mathrm{O}]^6}{[\mathrm{NH}_3]^4 [\mathrm{O}_2]^7} \).

By mastering stoichiometry, students can confidently engage with equilibrium expressions and predict the outcomes of chemical reactions with precision.