13.4 Equilibrium Calculations

A reaction is represented by this equation: $\text{A} \left(a q\right) + 2 \text{B} \left(a q\right) \rightleftharpoons 2 \text{C} \left(a q\right) K_{c} = 1 \times 10^{3}$

(a) Write the mathematical expression for the equilibrium constant.

(b) Using concentrations ≤1 M, identify two sets of concentrations that describe a mixture of A, B, and C at equilibrium.

What is the value of the equilibrium constant at 500 °C for the formation of NH₃ according to the following equation?

$\text{N}_{2} \left(g\right) + 3 \text{H}_{2} \left(g\right) \rightleftharpoons 2 \text{NH}_{3} \left(g\right)$

An equilibrium mixture of NH₃(g), H₂(g), and N₂(g) at 500 °C was found to contain 1.35 M H₂, 1.15 M N₂, and 4.12 $\times$ 10⁻¹ M NH₃.

A 0.72-mol sample of PCl₅ is put into a 1.00-L vessel and heated. At equilibrium, the vessel contains 0.40 mol of PCl₃(g) and 0.40 mol of Cl₂(g). Calculate the value of the equilibrium constant for the decomposition of PCl₅ to PCl₃ and Cl₂ at this temperature.

Calculate the value of the equilibrium constant K_P for the reaction $2 \text{NO} \left(g\right) + \text{Cl}_{2} \left(g\right) \rightleftharpoons 2 \text{NOCl} \left(g\right)$ from these equilibrium pressures: NO, 0.050 atm; Cl₂, 0.30 atm; NOCl, 1.2 atm.

A sample of ammonium chloride was heated in a closed container.

$\text{NH}_{4} \text{Cl} \left(s\right) \rightleftharpoons \text{NH}_{3} \left(g\right) + \text{HCl} \left(g\right)$

At equilibrium, the pressure of NH₃(g) was found to be 1.75 atm. What is the value of the equilibrium constant K_P for the decomposition at this temperature?

Complete the following partial ICE tables.

(a)

$\begin{matrix} & 2 \text{SO}_{3} \left(g\right) & \rightleftharpoons & 2 \text{SO}_{2} \left(g\right) + & \text{O}_{2} \left(g\right) \\ \text{change} & ___ & & ___ & + x\end{matrix}$

(b)

$\begin{matrix} & 4 \text{NH}_{3} \left(g\right) & + 3 \text{O}_{2} \left(g\right) & \rightleftharpoons & 2 \text{N}_{2} \left(g\right) + & 6 \text{H}_{2} \text{O} \left(g\right) \\ \text{change} & ___ & + x & & ___ & ___\end{matrix}$

(c)

$\begin{matrix} & 2 \text{CH}_{4} \left(g\right) & \rightleftharpoons & \text{C}_{2} \text{H}_{2} \left(g\right) + & 3 \text{H}_{2} \left(g\right) \\ \text{change} & ___ & & + x & ___\end{matrix}$

(d)

$\begin{matrix} & \text{CH}_{4} \left(g\right) + & \text{H}_{2} \text{O} \left(g\right) & \rightleftharpoons & \text{CO} \left(g\right) + & 3 \text{H}_{2} \left(g\right) \\ \text{change} & ___ & + x & & ___ & ___\end{matrix}$

(e)

$\begin{matrix}\text{NH}_{4} \text{Cl} \left(s\right) & \rightleftharpoons & \text{NH}_{3} \left(g\right) + & \text{HCl} \left(g\right) \\ \text{change} & & + x & ___\end{matrix}$

(f)

$\begin{matrix}\text{Ni} \left(s\right) + & 4 \text{CO} \left(g\right) & \rightleftharpoons & \text{Ni} \left(\text{CO}\right)_{4} \left(g\right) \\ \text{change} & + x & & ___\end{matrix}$

Why are there no changes specified for Ni in the exercise, part (f)? What property of Ni does change?

Analysis of the gases in a sealed reaction vessel containing NH₃, N₂, and H₂ at equilibrium at 400 °C established the concentration of N₂ to be 1.2 M and the concentration of H₂ to be 0.24 M.

$\text{N}_{2} \left(g\right) + 3 \text{H}_{2} \left(g\right) \rightleftharpoons 2 \text{NH}_{3} \left(g\right) K_{c} = 0.50 \text{at} 400 ° \text{C}$

Calculate the equilibrium molar concentration of NH₃.

What is the pressure of BrCl in an equilibrium mixture of Cl₂, Br₂, and BrCl if the pressure of Cl₂ in the mixture is 0.115 atm and the pressure of Br₂ in the mixture is 0.450 atm?

$\text{Cl}_{2} \left(g\right) + \text{Br}_{2} \left(g\right) \rightleftharpoons 2 \text{BrCl} \left(g\right) K_{P} = 4.7 \times 10^{−2}$

Cobalt metal can be prepared by reducing cobalt(II) oxide with carbon monoxide.

$\text{CoO} \left(s\right) + \text{CO} \left(g\right) \rightleftharpoons \text{Co} \left(s\right) + \text{CO}_{2} \left(g\right) K_{c} = 4.90 \times 10^{2} \text{at} 550 °\text{C}$

What concentration of CO remains in an equilibrium mixture with [CO₂] = 0.100 M?

Sodium sulfate 10−hydrate, Na₂SO₄·10H₂O, dehydrates according to the equation

$\text{Na}_{2} \text{SO}_{4} \cdot 10 \text{H}_{2} \text{O} \left(s\right) \rightleftharpoons \text{Na}_{2} \text{SO}_{4} \left(s\right) + 10 \text{H}_{2} \text{O} \left(g\right) K_{P} = 4.08 \times 10^{−25} \text{at} 25 °\text{C}$

What is the pressure of water vapor at equilibrium with a mixture of Na₂SO₄·10H₂O and NaSO₄?

A student solved the following problem and found the equilibrium concentrations to be [SO₂] = 0.590 M, [O₂] = 0.0450 M, and [SO₃] = 0.260 M. How could this student check the work without reworking the problem? The problem was: For the following reaction at 600 °C:

$2 \text{SO}_{2} \left(g\right) + \text{O}_{2} \left(g\right) \rightleftharpoons 2 \text{SO}_{3} \left(g\right) K_{c} = 4.32$

Assume that the change in concentration of N₂O₄ is small enough to be neglected in the following problem.

(a) Calculate the equilibrium concentration of both species in 1.00 L of a solution prepared from 0.129 mol of N₂O₄ with chloroform as the solvent.

$\text{N}_{2} \text{O}_{4} \left(g\right) \rightleftharpoons 2 \text{NO}_{2} \left(g\right) K_{c} = 1.07 \times 10^{−5}$ in chloroform

(b) Confirm that the change is small enough to be neglected.

Assume that the change in pressure of H₂S is small enough to be neglected in the following problem.

(a) Calculate the equilibrium pressures of all species in an equilibrium mixture that results from the decomposition of H₂S with an initial pressure of 0.824 atm.

$2 \text{H}_{2} \text{S} \left(g\right) \rightleftharpoons 2 \text{H}_{2} \left(g\right) + \text{S}_{2} \left(g\right) K_{P} = 2.2 \times 10^{−6}$

(b) Confirm that the change is small enough to be neglected.

What are the concentrations of PCl₅, PCl₃, and Cl₂ in an equilibrium mixture produced by the decomposition of a sample of pure PCl₅ with [PCl₅] = 2.00 M?

$\text{PCl}_{5} \left(g\right) \rightleftharpoons \text{PCl}_{3} \left(g\right) + \text{Cl}_{2} \left(g\right) K_{c} = 0.0211$

Calculate the number of grams of HI that are at equilibrium with 1.25 mol of H₂ and 63.5 g of iodine at 448 °C.

$\text{H}_{2} + \text{I}_{2} \rightleftharpoons 2 \text{HI} K_{c} = 50.2 \text{at} 448 °\text{C}$

What is the minimum mass of CaCO₃ required to establish equilibrium at a certain temperature in a 6.50-L container if the equilibrium constant (K_c) is 0.50 for the decomposition reaction of CaCO₃ at that temperature?

$\text{CaCO}_{3} \left(s\right) \rightleftharpoons \text{CaO} \left(s\right) + \text{CO}_{2} \left(g\right)$

The equilibrium constant (K_c) for this reaction is 5.0 at a given temperature.

$\text{CO} \left(g\right) + \text{H}_{2} \text{O} \left(g\right) \rightleftharpoons \text{CO}_{2} \left(g\right) + \text{H}_{2} \left(g\right)$

(a) On analysis, an equilibrium mixture of the substances present at the given temperature was found to contain 0.20 mol of CO, 0.30 mol of water vapor, and 0.90 mol of H₂ in a liter. How many moles of CO₂ were there in the equilibrium mixture?

(b) Maintaining the same temperature, additional H₂ was added to the syste…

Consider the equilibrium

$4 \text{NO}_{2} \left(g\right) + 6 \text{H}_{2} \text{O} \left(g\right) \rightleftharpoons 4 \text{NH}_{3} \left(g\right) + 7 \text{O}_{2} \left(g\right)$

(a) What is the expression for the equilibrium constant (K_c) of the reaction?

(b) How must the concentration of NH₃ change to reach equilibrium if the reaction quotient is less than the equilibrium constant?

(c) If the reaction were at equilibrium, how would an increase in the volume of the reaction vessel affect the pressure of NO₂?

(d) If the change in the pressure of…

Liquid N₂O₃ is dark blue at low temperatures, but the color fades and becomes greenish at higher temperatures as the compound decomposes to NO and NO₂. At 25 °C, a value of K_P = 1.91 has been established for this decomposition. If 0.236 moles of N₂O₃ are placed in a 1.52-L vessel at 25 °C, calculate the equilibrium partial pressures of N₂O₃(g), NO₂(g), and NO(g).