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Chapter 15: Problem 16

Write the expressions for \(K_{c}\) for the following reactions. In each case indicate whether the reaction is homogeneous or heterogeneous. (a) \(\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{O}(g)\) (b) \(\mathrm{Si}(s)+2 \mathrm{Cl}_{2}(g) \rightleftharpoons \mathrm{SiCl}_{4}(g)\) (c) \(\mathrm{H}_{2}(g)+\mathrm{Cl}_{2}(g) \rightleftharpoons 2 \mathrm{HCl}(g)\) (d) \(\mathrm{O}_{2}(g)+2 \mathrm{CO}(g) \rightleftharpoons 2 \mathrm{CO}_{2}(g)\) (e) \(\mathrm{HCO}_{3}^{-}(a q) \rightleftharpoons \mathrm{CO}_{3}^{2-}(a q)+\mathrm{H}^{+}(a q)\) (f) \(\mathrm{Fe}^{2+}(a q)+\mathrm{Ce}^{4+}(a q) \rightleftharpoons \mathrm{Fe}^{3+}(a q)+\mathrm{Ce}^{3+}(a q)\) (g) \(\mathrm{CaCO}_{3}(s) \rightleftharpoons \mathrm{CaO}(s)+\mathrm{CO}_{2}(g)\)

Short Answer

Expert verified
(a) Homogeneous: \\[K_{c} = \frac{[O]^2}{[O_2]}\\] (b) Heterogeneous: \\[K_{c} = \frac{[SiCl_4]}{[Cl_2]^2}\\] (c) Homogeneous: \\[K_{c} = \frac{[HCl]^2}{[H_2][Cl_2]}\\] (d) Homogeneous: \\[K_{c} = \frac{[CO_2]^2}{[O_2][CO]^2}\\] (e) Homogeneous: \\[K_{c} = \frac{[CO_3^{2-} ] [H^+ ] }{[HCO_3^- ]}\\] (f) Homogeneous: \\[K_{c} = \frac{[Fe^{3+}][Ce^{3+}]}{[Fe^{2+}][Ce^{4+}]}\\] (g) Heterogeneous: \\[K_{c} = [CO_2]\\]

Step by step solution

01

Understanding Homogeneous and Heterogeneous Reactions

A homogeneous reaction is one in which all the reactants and products are in the same phase. A heterogeneous reaction involves reactants and products in different phases.
02

Write Expression for Reaction (a)

The reaction is \(\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{O}(g)\). All reactants and products are in the gas phase, so this is a homogeneous reaction. The equilibrium constant is given by \[K_{c} = \frac{[O]^2}{[O_2]}\]
03

Write Expression for Reaction (b)

The reaction is \(\mathrm{Si}(s)+2 \mathrm{Cl}_{2}(g) \rightleftharpoons \mathrm{SiCl}_{4}(g)\). This is a heterogeneous reaction because Si is a solid and the others are gases. Solids do not appear in the expression for \(K_c\), so \[K_{c} = \frac{[SiCl_4]}{[Cl_2]^2}\]
04

Write Expression for Reaction (c)

The reaction is \(\mathrm{H}_{2}(g)+\mathrm{Cl}_{2}(g) \rightleftharpoons 2 \mathrm{HCl}(g)\). This is a homogeneous reaction as all components are gases. The equilibrium expression is \[K_{c} = \frac{[HCl]^2}{[H_2][Cl_2]}\]
05

Write Expression for Reaction (d)

The reaction is \(\mathrm{O}_{2}(g)+2 \mathrm{CO}(g) \rightleftharpoons 2 \mathrm{CO}_{2}(g)\). This is a homogeneous gas-phase reaction. The equilibrium constant is \[K_{c} = \frac{[CO_2]^2}{[O_2][CO]^2}\]
06

Write Expression for Reaction (e)

The reaction is \(\mathrm{HCO}_{3}^{-}(a q) \rightleftharpoons \mathrm{CO}_{3}^{2-}(a q)+\mathrm{H}^{+}(a q)\). This is a homogeneous reaction as all components are in aqueous phase. The equilibrium expression is \[K_{c} = \frac{[CO_3^{2-}][H^+]}{[HCO_3^-]}\]
07

Write Expression for Reaction (f)

The reaction is \(\mathrm{Fe}^{2+}(a q)+\mathrm{Ce}^{4+}(a q) \rightleftharpoons \mathrm{Fe}^{3+}(a q)+\mathrm{Ce}^{3+}(a q)\). This is a homogeneous aqueous reaction. The equilibrium constant expression is \[K_{c} = \frac{[Fe^{3+}][Ce^{3+}]}{[Fe^{2+}][Ce^{4+}]}\]
08

Write Expression for Reaction (g)

The reaction is \(\mathrm{CaCO}_{3}(s) \rightleftharpoons \mathrm{CaO}(s)+\mathrm{CO}_{2}(g)\). This is a heterogeneous reaction involving solids and a gas. The equilibrium expression only includes the gas phase, therefore \[K_{c} = [CO_2]\]

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Key Concepts

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

Homogeneous Reactions
In homogeneous reactions, all reactants and products are in the same phase, usually gas or liquid. This means that every substance involved is either entirely in the gaseous state or completely dissolved in a solution. Homogeneous reactions are straightforward when it comes to writing chemical equilibrium expressions because you consider all reactants and products directly.
For example, in the reaction \( \mathrm{H}_{2}(g)+ \mathrm{Cl}_{2}(g) \rightleftharpoons 2 \mathrm{HCl}(g) \), all reactants and products are gases. The equilibrium expression for this is:
  • \( K_{c} = \frac{[HCl]^2}{[H_2][Cl_2]} \)
This expression illustrates that homogeneous reactions are efficiently handled by including the concentrations of all gaseous species involved. It highlights how concentration changes might influence the direction of the equilibrium.
Heterogeneous Reactions
Heterogeneous reactions involve reactants and products that are in different phases, such as solids, liquids, and gases. In these reactions, while solids and pure liquids participate in the reaction, they do not appear in the equilibrium constant expression. This is because their activity is considered constant.
For instance, consider \( \mathrm{Si}(s)+2 \mathrm{Cl}_{2}(g) \rightleftharpoons \mathrm{SiCl}_{4}(g) \). Si is a solid whereas others are gases. Here, the equilibrium constant expression is:
  • \( K_{c} = \frac{[SiCl_4]}{[Cl_2]^2} \)
Notice that only the gas-phase species' concentrations are included in the equilibrium expression. This simplification helps when calculating the reactions involving substances of different phases.
Chemical Equilibrium Expressions
At equilibrium, the rate of the forward reaction equals the rate of the reverse reaction. The expression for the equilibrium constant, \( K_c \), provides a ratio of the concentrations of products to reactants at equilibrium. When writing these expressions, it's essential to remember:
  • The concentrations of gases and aqueous solutions only should be considered.
  • Solids and liquids are omitted from the \( K_c \) expression.
  • Exponents in the expression correspond to the coefficients of substances in the balanced equation.
For example, in the reaction \( \mathrm{O}_{2}(g)+2 \mathrm{CO}(g) \rightleftharpoons 2 \mathrm{CO}_{2}(g) \), the equilibrium expression is:
  • \( K_{c} = \frac{[CO_2]^2}{[O_2][CO]^2} \)
This highlights the balanced nature of reactions at equilibrium, as well as the importance of considering only reactive phases when constructing equilibrium expressions.

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Most popular questions from this chapter

Consider the hypothetical reaction $$ \mathrm{A}(g) \rightleftharpoons \mathrm{B}(g)+2 \mathrm{C}(g) $$ A flask is charged with \(100 \mathrm{kPa}\) of pure \(\mathrm{A}\), after which it is allowed to reach equilibrium at \(25^{\circ} \mathrm{C}\). At equilibrium, the partial pressure of \(\mathrm{B}\) is \(25 \mathrm{kPa} .(\mathbf{a})\) What is the total pressure in the flask at equilibrium? (b) What is the value of \(K_{p} ?\) (c) What could we do to maximize the yield of \(\mathrm{B}\) ?

At \(80^{\circ} \mathrm{C}, K_{c}=1.87 \times 10^{-3}\) for the reaction $$ \mathrm{PH}_{3} \mathrm{BCl}_{3}(s) \rightleftharpoons \mathrm{PH}_{3}(g)+\mathrm{BCl}_{3}(g) $$ (a) Calculate the equilibrium concentrations of \(\mathrm{PH}_{3}\) and \(\mathrm{BCl}_{3}\) if a solid sample of \(\mathrm{PH}_{3} \mathrm{BCl}_{3}\) is placed in a closed vessel at \(80^{\circ} \mathrm{C}\) and decomposes until equilibrium is reached. (b) If the flask has a volume of \(0.250 \mathrm{~L}\), what is the minimum mass of \(\mathrm{PH}_{3} \mathrm{BCl}_{3}(s)\) that must be added to the flask to achieve equilibrium?

Nitric oxide (NO) reacts readily with chlorine gas as follows: $$ 2 \mathrm{NO}(g)+\mathrm{Cl}_{2}(g) \rightleftharpoons 2 \mathrm{NOCl}(g) $$ At \(700 \mathrm{~K}\), the equilibrium constant \(K_{p}\) for this reaction is \(2.6 \times 10^{-3}\). Predict the behavior of each of the following mixtures at this temperature and indicate whether or not the mixtures are at equilibrium. If not, state whether the mixture will need to produce more products or reactants to reach equilibrium. (a) \(P_{\mathrm{NO}}=20.3 \mathrm{kPa}, P_{\mathrm{Cl}_{2}}=20.3 \mathrm{kPa}, P_{\mathrm{NOCl}}=20.3 \mathrm{kPa}\) (b) \(P_{\mathrm{NO}}=25.33 \mathrm{kPa}, P_{\mathrm{Cl}_{2}}=15.2 \mathrm{kPa}, P_{\mathrm{NOCl}}=2.03 \mathrm{kPa}\) (c) \(P_{\mathrm{NO}}=15.2 \mathrm{kPa}, P_{\mathrm{Cl}_{2}}=42.6 \mathrm{kPa}, P_{\mathrm{NOCl}}=5.07 \mathrm{kPa}\)

Phosphorus trichloride gas and chlorine gas react to form phosphorus pentachloride gas: \(\mathrm{PCl}_{3}(g)+\mathrm{Cl}_{2}(g) \rightleftharpoons\) \(\mathrm{PCl}_{5}(g)\). A 7.5-L gas vessel is charged with a mixture of \(\mathrm{PCl}_{3}(g)\) and \(\mathrm{Cl}_{2}(g)\), which is allowed to equilibrate at 450 K. At equilibrium the partial pressures of the three gases are \(P_{\mathrm{PCl}_{3}}=12.56 \mathrm{kPa}, P_{\mathrm{Cl}_{2}}=15.91 \mathrm{kPa},\) and \(P_{\mathrm{PCl}_{5}}=131.7 \mathrm{kPa}\) (a) What is the value of \(K_{p}\) at this temperature? (b) Does the equilibrium favor reactants or products? (c) Calculate \(K_{c}\) for this reaction at \(450 \mathrm{~K}\).

Gaseous hydrogen iodide is placed in a closed container at \(450^{\circ} \mathrm{C}\), where it partially decomposes to hydrogen and iodine: \(2 \mathrm{HI}(g) \rightleftharpoons \mathrm{H}_{2}(g)+\mathrm{I}_{2}(g)\). At equilibrium it is found that \([\mathrm{HI}]=4.50 \times 10^{-3} \mathrm{M},\left[\mathrm{H}_{2}\right]=5.75 \times 10^{-4} \mathrm{M}\) and \(\left[\mathrm{I}_{2}\right]=5.75 \times 10^{-4} \mathrm{M}\). What is the value of \(K_{c}\) at this temperature?
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