Question

Write equilibrium-constant equations for each reversible process. a. \(\mathrm{NH}_{3}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \leftrightharpoons \mathrm{NH}_{4}^{+}(a q)+\mathrm{OH}^{2-}(a q)\) b. \(\mathrm{Na}_{2} \mathrm{SO}_{4}(s) \leftrightharpoons 2 \mathrm{Na}^{+}(a q)+\mathrm{SO}_{4}^{2-}(a q)\) c. \(\mathrm{C}_{2} \mathrm{H}_{4}(g)+\mathrm{H}_{2}(g) \leftrightharpoons \mathrm{C}_{2} \mathrm{H}_{6}(g)\)

Short answer

a) \( K_c = \frac{[\mathrm{NH}_{4}^{+}][\mathrm{OH}^{-}]}{[\mathrm{NH}_{3}]} \) ; b) \( K_c = [\mathrm{Na}^{+}]^2[\mathrm{SO}_{4}^{2-}] \) ; c) \( K_c = \frac{[\mathrm{C}_{2} \mathrm{H}_{6}]}{[\mathrm{C}_{2} \mathrm{H}_{4}][\mathrm{H}_2]} \)

Step-by-step solution

Understand the Reaction

For each chemical equation, identify the reactants and products in order to determine the equilibrium expression. Remember that solids and pure liquids do not appear in equilibrium constant expressions.

Reaction a - Write Equilibrium Expression

The expression for the equilibrium constant (K_c) is written as follows: For \( \mathrm{NH}_{3}(aq)+\mathrm{H}_{2} \mathrm{O}(l) \leftrightharpoons \mathrm{NH}_{4}^{+}(aq)+\mathrm{OH}^{-}(aq) \), exclude water because it's a liquid: \[ K_c = \frac{[\mathrm{NH}_{4}^{+}][\mathrm{OH}^{-}]}{[\mathrm{NH}_{3}]} \]

Reaction b - Write Equilibrium Expression

For \( \mathrm{Na}_{2} \mathrm{SO}_{4}(s) \leftrightharpoons 2 \mathrm{Na}^{+}(aq)+\mathrm{SO}_{4}^{2-}(aq) \), exclude the solid sodium sulfate from K_c: \[ K_c = [\mathrm{Na}^{+}]^2[\mathrm{SO}_{4}^{2-}] \]

Reaction c - Write Equilibrium Expression

For \( \mathrm{C}_{2} \mathrm{H}_{4}(g)+\mathrm{H}_{2}(g) \leftrightharpoons \mathrm{C}_{2} \mathrm{H}_{6}(g) \), all are gases, so the equilibrium expression includes all terms: \[ K_c = \frac{[\mathrm{C}_{2} \mathrm{H}_{6}]}{[\mathrm{C}_{2} \mathrm{H}_{4}][\mathrm{H}_2]} \]

Key concepts

Equilibrium Constant

In a chemical reaction, the equilibrium constant, denoted as \( K_c \) for concentrations or \( K_p \) for pressures, is a numerical value that indicates the ratio of product concentrations to reactant concentrations at equilibrium. This powerful tool helps chemists predict the extent of a reaction and to what degree a reaction proceeds before reaching equilibrium. At equilibrium, the forward and reverse reactions occur at the same rate, and the concentrations of reactants and products remain constant.

• If \( K_c \) is greater than 1, the equilibrium favors the formation of products.
• If \( K_c \) is less than 1, the equilibrium favors the reactants.
• A larger \( K_c \) suggests that nearly all reactants are converted to products.

Calculating \( K_c \) involves using the concentrations (or pressures) of the products and reactants raised to their respective stoichiometric coefficients. Understanding \( K_c \) allows chemists to control and manipulate chemical reactions for desired outcomes.

Reversible Reactions

Reversible reactions are those that can proceed in both the forward and reverse directions under the right conditions. This means that both the conversion of reactants to products and the conversion of products back to reactants are possible. These reactions reach a state of equilibrium where the rate of the forward reaction equals the rate of the backward reaction.
Reversible reactions are represented by the double arrow symbol (\( \leftrightharpoons \)), highlighting their dynamic nature. These reactions are influenced by changes in concentration, temperature, and pressure.

• Increasing temperature can shift the equilibrium position, favoring either the endothermic or exothermic direction.
• Changing concentrations of reactants or products can also shift the equilibrium position, following Le Chatelier’s principle.

Understanding reversible reactions is crucial, as many biological and industrial processes rely on reactions that must reach equilibrium efficiently.

Equilibrium Expression

An equilibrium expression is a mathematical equation that relates the concentrations of reactants and products in a reversible reaction at equilibrium. It is used to calculate the equilibrium constant \( K_c \). For a generic reaction \( aA + bB \leftrightharpoons cC + dD \), the equilibrium expression is:
\[K_c = \frac{[C]^c[D]^d}{[A]^a[B]^b}\]
This expression indicates the ratio of the concentrations of the products to those of the reactants, each raised to the power of their respective coefficients from the balanced equation.

• The equilibrium expression excludes pure solids and liquids since their concentrations are constant.
• It includes only species in the gaseous or aqueous phases.

By applying these expressions, chemical equilibrium can be quantitatively assessed, leading to better understanding and predictability of chemical behaviors.

Chemical Reactions

Chemical reactions involve the transformation of substances, known as reactants, into new substances called products. These reactions can be classified as reversible or irreversible, depending on whether the products can reconvert into reactants under certain conditions. Chemical reactions are fundamental in creating the materials and energy sources essential to daily life.
Chemical reactions occur due to rearrangements of atoms, often involving energy changes. Reactions are influenced by factors such as temperature, pressure, concentration, and catalysts, all of which can alter the rate and extent of a reaction.

• In a reversible reaction, achieving and maintaining equilibrium is key to optimizing the desired product yield.
• Understanding chemical kinetics and mechanisms provides insights into how and why reactions occur as they do.

Knowledge of chemical reactions not only aids in academic pursuits, but also drives innovation and efficiency in industry, such as in pharmaceuticals, agriculture, and manufacturing.