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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

Expert verified
\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

01

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, \(K_p = \frac{P_{NH_{3}}^2}{P_{NO_2}^2 \cdot P_{H_{2}}^7}\).
02

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, \(K_p = \frac{P_{SO_2}^2}{P_{O_2}^3}\).
03

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 \(K_p = P_{CO}^2/P_{CO_{2}}\).
04

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 \(K_c = [C_{6}H_{5}COO^-] \cdot [H+]/[C_{6}H_{5}COOH]\)

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

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.

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Most popular questions from this chapter

Consider the dissociation of iodine: $$ \mathrm{I}_{2}(g) \rightleftharpoons 2 \mathrm{I}(g) $$ A \(1.00-\mathrm{g}\) sample of \(\mathrm{I}_{2}\) is heated at \(1200^{\circ} \mathrm{C}\) in a 500 -mL flask. At equilibrium the total pressure is 1.51 atm. Calculate \(K_{P}\) for the reaction. [Hint: Use the result in problem \(15.65(\mathrm{a}) .\) The degree of dissociation \(\alpha\) can be obtained by first calculating the ratio of observed pressure over calculated pressure, assuming no dissociation.

The equilibrium constant \(K_{P}\) for the following reaction is found to be \(4.31 \times 10^{-4}\) at \(375^{\circ} \mathrm{C}\) : $$ \mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \rightleftharpoons 2 \mathrm{NH}_{3}(g) $$ In a certain experiment a student starts with 0.862 atm of \(\mathrm{N}_{2}\) and 0.373 atm of \(\mathrm{H}_{2}\) in a constant-volume vessel at \(375^{\circ} \mathrm{C}\). Calculate the partial pressures of all species when equilibrium is reached.

The equilibrium constant \(K_{\mathrm{c}}\) for the reaction \(2 \mathrm{NH}_{3}(g) \rightleftharpoons \mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g)\) is 0.83 at \(375^{\circ} \mathrm{C} . \mathrm{A}\) 14.6-g sample of ammonia is placed in a 4.00 -L flask and heated to \(375^{\circ} \mathrm{C}\). Calculate the concentrations of all the gases when equilibrium is reached.

Consider the potential energy diagrams for two types of reactions \(\mathrm{A} \rightleftharpoons \mathrm{B}\). In each case, answer the following questions for the system at equilibrium. (a) How would a catalyst affect the forward and reverse rates of the reaction? (b) How would a catalyst affect the energies of the reactant and product? (c) How would an increase in temperature affect the equilibrium constant? (d) If the only effect of a catalyst is to lower the activation energies for the forward and reverse reactions, show that the equilibrium constant remains unchanged if a catalyst is added to the reacting mixture.

About 75 percent of hydrogen for industrial use is produced by the steam- reforming process. This process is carried out in two stages called primary and secondary reforming. In the primary stage, a mixture of steam and methane at about 30 atm is heated over a nickel catalyst at \(800^{\circ} \mathrm{C}\) to give hydrogen and carbon monoxide: $$ \begin{aligned} \mathrm{CH}_{4}(g)+\mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons \mathrm{CO}(g) &+3 \mathrm{H}_{2}(g) \\ \Delta H^{\circ} &=206 \mathrm{~kJ} / \mathrm{mol} \end{aligned} $$ The secondary stage is carried out at about \(1000^{\circ} \mathrm{C}\) in the presence of air, to convert the remaining methane to hydrogen: \(\mathrm{CH}_{4}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \rightleftharpoons \mathrm{CO}(g)+2 \mathrm{H}_{2}(g)\) $$ \Delta H^{\circ}=35.7 \mathrm{~kJ} / \mathrm{mol} $$ (a) What conditions of temperature and pressure would favor the formation of products in both the primary and secondary stages? (b) The equilibrium constant \(K_{\mathrm{c}}\) for the primary stage is 18 at \(800^{\circ} \mathrm{C}\). (i) Calculate \(K_{P}\) for the reaction. (ii) If the partial pressures of methane and steam were both 15 atm at the start, what are the pressures of all the gases at equilibrium?

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