Question

Write the equilibrium constant expressions for \(K_{\mathrm{c}}\) and \(K_{P}\), if applicable, for these reactions: (a) \(2 \mathrm{NO}_{2}(g)+7 \mathrm{H}_{2}(g) \rightleftharpoons 2 \mathrm{NH}_{3}(g)+4 \mathrm{H}_{2} \mathrm{O}(l)\) (b) \(2 \mathrm{ZnS}(s)+3 \mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{ZnO}(s)+2 \mathrm{SO}_{2}(g)\) (c) \(\mathrm{C}(s)+\mathrm{CO}_{2}(g) \rightleftharpoons 2 \mathrm{CO}(g)\) (d) \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COOH}(a q) \rightleftharpoons \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COO}^{-}(a q)+\mathrm{H}^{+}(a q)\)

Short answer

\n(a) \(K_c = \frac{[NH_{3}]^2 \cdot [H_{2}O]^4}{[NO_{2}]^2 \cdot [H_{2}]^7}\) and \(K_p = \frac{P_{NH_{3}}^2}{P_{NO_2}^2 \cdot P_{H_{2}}^7}\).\n(b) \(K_c = \frac{[SO_{2}]^2}{[O_{2}]^3}\) and \(K_p = \frac{P_{SO_2}^2}{P_{O_2}^3}\).\n(c) \(K_c = [CO]^2/[CO_2]\) and \(K_p = P_{CO}^2/P_{CO_{2}}\). \n(d) \(K_c = [C_{6}H_{5}COO^-] \cdot [H+]/[C_{6}H_{5}COOH]\)

Step-by-step solution

Determine the \(K_c\) and \(K_p\) for reaction (a)

Reaction (a) involves both gases and liquids. \(K_c\) expression involves concentrations of both reactants and products regardless of their states. Therefore, \(K_c = \frac{[NH_{3}]^2 \cdot [H_{2}O]^4}{[NO_{2}]^2 \cdot [H_{2}]^7}\). For \(K_p\) expression, we only consider gas species. Thus, \(K_p = \frac{P_{NH_{3}}^2}{P_{NO_2}^2 \cdot P_{H_{2}}^7}\).

Determine the \(K_c\) and \(K_p\) for reaction (b)

Reaction (b) involves both gases and solids. \(K_c\) expression involves concentrations of both reactants and products. Therefore, \(K_c = \frac{[SO_{2}]^2}{[O_{2}]^3}\) as ZnS and ZnO are omitted due to thier solid states. For \(K_p\) expression, we only consider gas species. Thus, \(K_p = \frac{P_{SO_2}^2}{P_{O_2}^3}\).

Determine the \(K_c\) and \(K_p\) for reaction (c)

In reaction (c), as Carbon is a solid, it is omitted from both \(K_c\) and \(K_p\) expressions. Hence, \(K_c = [CO]^2/[CO_2]\) and \(K_p = P_{CO}^2/P_{CO_{2}}\).

Determine the \(K_c\) for reaction (d)

Reaction (d) only involves aqueous species and no gas species. Thus, a \(K_p\) expression won't be applicable. For \(K_c\), it would be \(K_c = [C_{6}H_{5}COO^-] \cdot [H+]/[C_{6}H_{5}COOH]\)

Key concepts

Chemical Equilibrium

Chemical equilibrium is a key concept in chemistry that describes a state where the concentrations of reactants and products remain constant over time. This occurs when the forward and reverse reactions happen at the same rate. At equilibrium, no net change in concentrations is observed, though microscopic transformations continue. Chemical equilibrium does not mean the reactants and products are present in equal quantities. Instead, it's a balance that's specific to each reaction based on reaction conditions.

In equilibrium constant expressions, denoted as \(K_c\) for concentrations and \(K_p\) for partial pressures, you quantify this balance.

• For gases and solutions, equilibrium constants provide a means to predict the extent of a reaction.
• The constant remains unchanged unless the temperature changes, emphasizing the reaction's dependence on temperature.
• For instance, the equilibrium expression for the gaseous reaction \(2NO_2(g) + 7H_2(g)\rightleftharpoons 2NH_3(g) + 4H_2O(l)\) will only include the species with concentrations in the \(K_c\) expression and only gases in the \(K_p\) expression.

Le Chatelier's Principle

Le Chatelier's principle is a valuable tool in understanding how systems at equilibrium respond to external changes. According to this principle, if a system at equilibrium is subjected to a change in concentration, pressure, or temperature, the system will adjust itself to counteract the effect of the change and establish a new equilibrium.

This principle helps predict the direction of a reaction shift:

• Increasing the concentration of reactants drives the equilibrium to produce more products.
• Conversely, increasing the concentration of products shifts the equilibrium to favor the formation of reactants.
• Changing pressure affects gaseous equilibria; increasing pressure favors a shift towards the side with fewer gas molecules.
• Temperature changes cause equilibrium shifts depending on the exothermic or endothermic nature of the reaction.

For example, in a reaction involving gases, such as \(2ZnS(s) + 3O_2(g)\rightleftharpoons 2ZnO(s) + 2SO_2(g)\), increasing the pressure would favor the formation of fewer gas molecules.

Reaction Quotient

The reaction quotient, denoted as \(Q\), is a measure that predicts the direction a reaction will proceed to reach equilibrium. Like the equilibrium constant \(K\), the reaction quotient is calculated using the concentrations or pressures of the involved species, but it is used at non-equilibrium conditions. Here's how \(Q\) helps in determining the reaction's progression:

• If \(Q = K\), the system is at equilibrium, so no shift is needed.
• If \(Q < K\), the reaction shifts towards the products to reach equilibrium.
• Conversely, if \(Q > K\), the reaction shifts towards the reactants to restore equilibrium.

Consider the reaction \(C(s) + CO_2(g)\rightleftharpoons 2CO(g)\). The reaction quotient can instantly reveal if the reaction is currently balanced, or if it needs to adjust to reach equilibrium. By comparing \(Q\) with \(K\), chemists can ascertain whether the ongoing changes in concentration are leading the system towards equilibrium or away from it.