7.3 Equilibrium calculations  (Page 11/11)

Antimony pentachloride decomposes according to this equation:

${\text{SbCl}}_5(g)\rightleftharpoons {\text{SbCl}}_3(g)+{\text{Cl}}_2(g)$

An equilibrium mixture in a 5.00-L flask at 448 °C contains 3.85 g of SbCl ₅ , 9.14 g of SbCl ₃ , and 2.84 g of Cl ₂ . How many grams of each will be found if the mixture is transferred into a 2.00-L flask at the same temperature?

Consider the reaction between H ₂ and O ₂ at 1000 K
${\text{2H}}_2(g)+{\text{O}}_2(g)\rightleftharpoons {\text{2H}}_2\text{O}(g)K_P=\frac{{(P_{{\text{H}}_2\text{O}})}^{\text{2}}}{(P_{{\text{O}}_2}){(P_{{\text{H}}_2})}^{\text{3}}}=1.33\times {10}^{20}$

If 0.500 atm of H ₂ and 0.500 atm of O ₂ are allowed to come to equilibrium at this temperature, what are the partial pressures of the components?

An equilibrium is established according to the following equation

${\text{Hg}}_2{}^{\mathrm{2+}}(aq)+{\text{NO}}_3{}^{\text{−}}(aq)+3{\text{H}}^{\text{+}}(aq)\rightleftharpoons 2{\text{Hg}}^{\mathrm{2+}}(aq)+{\text{HNO}}_2(aq)+{\text{H}}_2\text{O}(l)K_c=4.6$

What will happen in a solution that is 0.20 M each in ${\text{Hg}}_2{}^{\mathrm{2+}},$ ${\text{NO}}_3{}^{\text{−}},$ H ⁺ , Hg ²⁺ , and HNO ₂ ?

(a) ${\text{Hg}}_2{}^{\mathrm{2+}}$ will be oxidized and ${\text{NO}}_3{}^{\text{−}}$ reduced.

(b) ${\text{Hg}}_2{}^{\mathrm{2+}}$ will be reduced and ${\text{NO}}_3{}^{\text{−}}$ oxidized.

(c) Hg ²⁺ will be oxidized and HNO ₂ reduced.

(d) Hg ²⁺ will be reduced and HNO ₂ oxidized.

(e) There will be no change because all reactants and products have an activity of 1.

Consider the equilibrium

$4{\text{NO}}_2(g)+6{\text{H}}_2\text{O}(g)\rightleftharpoons 4{\text{NH}}_3(g)+7{\text{O}}_2(g)$

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

(b) How must the concentration of NH ₃ change to reach equilibrium if the reaction quotient is less than the equilibrium constant?

(c) If the reaction were at equilibrium, how would a decrease in pressure (from an increase in the volume of the reaction vessel) affect the pressure of NO ₂ ?

(d) If the change in the pressure of NO ₂ is 28 torr as a mixture of the four gases reaches equilibrium, how much will the pressure of O ₂ change?

The binding of oxygen by hemoglobin (Hb), giving oxyhemoglobin (HbO ₂ ), is partially regulated by the concentration of H ₃ O ⁺ and dissolved CO ₂ in the blood. Although the equilibrium is complicated, it can be summarized as

${\text{HbO}}_2(aq)+{\text{H}}_3{\text{O}}^{\text{+}}(aq)+{\text{CO}}_2(g)\rightleftharpoons {\text{CO}}_2\text{−}\text{Hb}\text{−}{\text{H}}^{\text{+}}+{\text{O}}_2(g)+{\text{H}}_2\text{O}(l)$

(a) Write the equilibrium constant expression for this reaction.

(b) Explain why the production of lactic acid and CO ₂ in a muscle during exertion stimulates release of O ₂ from the oxyhemoglobin in the blood passing through the muscle.

The hydrolysis of the sugar sucrose to the sugars glucose and fructose follows a first-order rate equation for the disappearance of sucrose.

${\text{C}}_{12}{\text{H}}_{22}{\text{O}}_{11}(aq)+{\text{H}}_2\text{O}(l)⟶{\text{C}}_6{\text{H}}_{12}{\text{O}}_6(aq)+{\text{C}}_6{\text{H}}_{12}{\text{O}}_6(aq)$

Rate = k [C ₁₂ H ₂₂ O ₁₁ ]

In neutral solution, k = 2.1 $\times$ 10 ⁻¹¹ /s at 27 °C. (As indicated by the rate constant, this is a very slow reaction. In the human body, the rate of this reaction is sped up by a type of catalyst called an enzyme.) (Note: That is not a mistake in the equation—the products of the reaction, glucose and fructose, have the same molecular formulas, C ₆ H ₁₂ O ₆ , but differ in the arrangement of the atoms in their molecules). The equilibrium constant for the reaction is 1.36 $\times$ 10 ⁵ at 27 °C. What are the concentrations of glucose, fructose, and sucrose after a 0.150 M aqueous solution of sucrose has reached equilibrium? Remember that the activity of a solvent (the effective concentration) is 1.

The density of trifluoroacetic acid vapor was determined at 118.1 °C and 468.5 torr, and found to be 2.784 g/L. Calculate K _c for the association of the acid.

Liquid N ₂ O ₃ is dark blue at low temperatures, but the color fades and becomes greenish at higher temperatures as the compound decomposes to NO and NO ₂ . At 25 °C, a value of K _P = 1.91 has been established for this decomposition. If 0.236 moles of N ₂ O ₃ are placed in a 1.52-L vessel at 25 °C, calculate the equilibrium partial pressures of N ₂ O ₃ ( g ), NO ₂ ( g ), and NO( g ).

A 1.00-L vessel at 400 °C contains the following equilibrium concentrations: N ₂ , 1.00 M ; H ₂ , 0.50 M ; and NH ₃ , 0.25 M . How many moles of hydrogen must be removed from the vessel to increase the concentration of nitrogen to 1.1 M ?

A 0.010 M solution of the weak acid HA has an osmotic pressure (see chapter on solutions and colloids) of 0.293 atm at 25 °C. A 0.010 M solution of the weak acid HB has an osmotic pressure of 0.345 atm under the same conditions.

(a) Which acid has the larger equilibrium constant for ionization

HA $[\text{HA}(aq)\rightleftharpoons {\text{A}}^{\text{−}}(aq)+{\text{H}}^{\text{+}}(aq)]$ or HB $[\text{HB}(aq)\rightleftharpoons {\text{H}}^{\text{+}}(aq)+{\text{B}}^{\text{−}}(aq)]$ ?

(b) What are the equilibrium constants for the ionization of these acids?

(Hint: Remember that each solution contains three dissolved species: the weak acid (HA or HB), the conjugate base (A ⁻ or B ⁻ ), and the hydrogen ion (H ⁺ ). Remember that osmotic pressure (like all colligative properties) is related to the total number of solute particles. Specifically for osmotic pressure, those concentrations are described by molarities.)