Chapter 14

Sketch a graph showing how the concentrations of the reactant \(A\) and product \(P\) of a typical chemical reaction \((A \rightleftharpoons P)\) vary with time during the course of the reaction. Assume that no products are present at the start of the reaction. Indicate on the graph where the system has reached equilibrium.

What meanings do the terms reactants and products have when describing a chemical equilibrium?

How is the term reaction quotient defined? What symbol is it given?

When a chemical equation and its equilibrium constant are given, why is it not necessary to also specify the form of the mass action expression?

Under what conditions does the reaction quotient equal \(K_{c}\)??

State in words how \(K_{\mathrm{p}}\) is written.

State the equation relating \(K_{\mathrm{P}}\) to \(K_{\mathrm{c}}\) and define all terms. Which is the only value of \(R\) that can be properly used in this equation?

Consider the following equilibrium. \(2 \mathrm{NaHCO}_{3}(s) \rightleftharpoons \mathrm{Na}_{2} \mathrm{CO}_{3}(s)+\mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g)\) If you were converting between \(K_{\mathrm{P}}\) and \(K_{\mathrm{c}}\), what value of \(\Delta n_{\mathrm{g}}\) would you use?

Use the ideal gas law to show that the partial pressure of a gas is directly proportional to its molar concentration. What is the proportionality constant?

What is the difference between a heterogeneous equilibrium and a homogeneous equilibrium?

Why do we omit the concentrations of pure liquids and pure solids from the mass action expression of heterogeneous reactions?

Suppose for the reaction \(A \longrightarrow B\) the value of \(Q\) is less than \(K_{\mathrm{c}}\). Which way does the reaction have to proceed to reach equilibrium-in the forward or reverse direction?

Here are some reactions and their equilibrium constants. (a) \(\begin{aligned} 2 \mathrm{CH}_{4}(g) \rightleftharpoons \mathrm{C}_{2} \mathrm{H}_{6}(g)+\mathrm{H}_{2}(g) & \\ K_{\mathrm{c}}=9.5 \times 10^{-13} \end{aligned}\) (b) \(\mathrm{CH}_{3} \mathrm{OH}(g)+\mathrm{H}_{2}(g) \rightleftharpoons \mathrm{CH}_{4}(g)+\mathrm{H}_{2} \mathrm{O}(g)\) \(K_{\mathrm{c}}=3.6 \times 10^{20}\) (c) \(\mathrm{H}_{2}(g)+\mathrm{Br}_{2}(g) \rightleftharpoons 2 \mathrm{HBr}(g) \quad K_{\mathrm{c}}=2.0 \times 10^{9}\) Arrange these reactions in order of their increasing tendency to go to completion.

State Le Châtelier's principle in your own words.

Explain, using its effect on the reaction quotient, why adding a reactant to the following equilibrium shifts the position of equilibrium to the right. $$ \mathrm{PCl}_{3}(g)+\mathrm{Cl}_{2}(g) \rightleftharpoons \mathrm{PCl}_{5}(g) $$

Halving the volume of a gas doubles its pressure. Using the reaction quotient corresponding to \(K_{\mathrm{P}}\), explain why halving the volume shifts the following equilibrium to the left. $$ \mathrm{N}_{2} \mathrm{O}_{4}(g) \rightleftharpoons 2 \mathrm{NO}_{2}(g) $$

How will the value of \(K_{\mathrm{P}}\) for the following reactions be affected by an increase in temperature? (a) \(\mathrm{CO}(g)+2 \mathrm{H}_{2}(g) \rightleftharpoons \mathrm{CH}_{3} \mathrm{OH}(g)\) $$ \Delta H^{\circ}=-18 \mathrm{~kJ} $$ (b) \(\mathrm{N}_{2} \mathrm{O}(g)+\mathrm{NO}_{2}(g) \rightleftharpoons 3 \mathrm{NO}(g)\) $$ \Delta H^{\circ}=+155.7 \mathrm{~kJ} $$ (c) \(2 \mathrm{NO}(g)+\mathrm{Cl}_{2}(g) \rightleftharpoons 2 \mathrm{NOCl}(g)\) \(\Delta H^{\circ}=-77.07 \mathrm{~kJ}\)

Why doesn't a catalyst affect the position of equilibrium in a chemical reaction?

Why doesn't adding an inert gas to increase the pressure, while keeping the volume constant, have any effect on the position of equilibrium?

Write the equilibrium law for each of the following gas phase reactions in terms of molar concentrations: (a) \(2 \mathrm{PCl}_{3}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{POCl}_{3}(g)\) (b) \(2 \mathrm{SO}_{3}(g) \rightleftharpoons 2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g)\) (c) \(\mathrm{N}_{2} \mathrm{H}_{4}(g)+2 \mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{NO}(g)+2 \mathrm{H}_{2} \mathrm{O}(g)\) (d) \(\mathrm{N}_{2} \mathrm{H}_{4}(g)+6 \mathrm{H}_{2} \mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{NO}_{2}(g)+8 \mathrm{H}_{2} \mathrm{O}(g)\) (e) \(\mathrm{SOCl}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons \mathrm{SO}_{2}(g)+2 \mathrm{HCl}(g)\)

Write the equilibrium law for each of the following gas phase reactions in terms of molar concentrations. (a) \(3 \mathrm{Cl}_{2}(g)+\mathrm{NH}_{3}(g) \rightleftharpoons \mathrm{NCl}_{3}(g)+3 \mathrm{HCl}(g)\) (b) \(\mathrm{PCl}_{3}(g)+\mathrm{PBr}_{3}(g) \rightleftharpoons \mathrm{PCl}_{2} \operatorname{Br}(g)+\mathrm{PClBr}_{2}(g)\) (c) \(\mathrm{NO}(g)+\mathrm{NO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons 2 \mathrm{HNO}_{2}(g)\) (d) \(\mathrm{H}_{2} \mathrm{O}(g)+\mathrm{Cl}_{2} \mathrm{O}(g) \rightleftharpoons 2 \mathrm{HOCl}(g)\) (e) \(\mathrm{Br}_{2}(g)+5 \mathrm{~F}_{2}(g) \rightleftharpoons 2 \mathrm{BrF}_{5}(g)\)

Write the equilibrium law for the following reactions in aqueous solution. (a) \(\mathrm{Ag}^{+}(a q)+2 \mathrm{NH}_{3}(a q) \rightleftharpoons \mathrm{Ag}\left(\mathrm{NH}_{3}\right)_{2}^{+}(a q)\) (b) \(\mathrm{Cd}^{2+}(a q)+4 \mathrm{SCN}^{-}(a q) \rightleftharpoons \mathrm{Cd}(\mathrm{SCN})_{4}^{2-}(a q)\)

Write the equilibrium law for the following reactions in aqueous solution. $$ \begin{array}{l} \text { (a) } \mathrm{HClO}(a q)+\mathrm{H}_{2} \mathrm{O} \rightleftharpoons \mathrm{H}_{3} \mathrm{O}+(a q)^{+} \mathrm{ClO}^{-}(a q) \\ \text { (b) } \mathrm{CO}_{3}^{2-}(a q)+\mathrm{HSO}^{-}(a q) \rightleftharpoons \\ \mathrm{HCO}_{3}^{-}(a q)+\mathrm{SO}_{4}^{2-}(a q) \end{array} $$

Use the following equilibria $$ \begin{aligned} 2 \mathrm{CH}_{4}(g) & \rightleftharpoons \mathrm{C}_{2} \mathrm{H}_{6}(g)+\mathrm{H}_{2}(g) & K_{\mathrm{c}} &=9.5 \times 10^{-13} \\ \mathrm{CH}_{4}(g)+\mathrm{H}_{2} \mathrm{O}(g) & \rightleftharpoons \mathrm{CH}_{3} \mathrm{OH}(g)+\mathrm{H}_{2}(g) K_{\mathrm{c}} &=2.8 \times 10^{-21} \end{aligned} $$ to calculate \(K_{\mathrm{c}}\) for the reaction $$ 2 \mathrm{CH}_{3} \mathrm{OH}(g)+\mathrm{H}_{2}(g) \rightleftharpoons \mathrm{C}_{2} \mathrm{H}_{6}(g)+2 \mathrm{H}_{2} \mathrm{O}(g) $$

Write the equilibrium law for each of the following reactions in terms of molar concentrations: (a) \(\mathrm{H}_{2}(g)+\mathrm{Cl}_{2}(g) \rightleftharpoons 2 \mathrm{HCl}(g)\) (b) \(\frac{1}{2} \mathrm{H}_{2}(g)+\frac{1}{2} \mathrm{Cl}_{2}(g) \rightleftharpoons \mathrm{HCl}(g)\) How does \(K_{\mathrm{c}}\) for reaction (a) compare with \(K_{\mathrm{c}}\) for reaction (b)?

A \(345 \mathrm{~mL}\) vessel contains \(\mathrm{NH}_{3}\) at a pressure of 745 torr and a temperature of \(45^{\circ} \mathrm{C}\). What is the molar concentration of ammonia in the container?

For which of the following reactions does \(K_{\mathrm{P}}=K_{\mathrm{c}}\) ? (a) \(2 \mathrm{H}_{2}(g)+\mathrm{C}_{2} \mathrm{H}_{2}(g) \rightleftharpoons \mathrm{C}_{2} \mathrm{H}_{6}(g)\) (b) \(\mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{NO}(g)\) (c) \(2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{NO}_{2}(g)\)

Calculate the molar concentration of water in (a) \(18.0 \mathrm{~mL}\) of \(\mathrm{H}_{2} \mathrm{O}(l),\) (b) \(100.0 \mathrm{~mL}\) of \(\mathrm{H}_{2} \mathrm{O}(l),\) and \(\mathbf{( c )} 1.00 \mathrm{~L}\) of \(\mathrm{H}_{2} \mathrm{O}(l)\). Assume that the density of water is \(1.00 \mathrm{~g} / \mathrm{mL}\)

The density of sodium chloride is \(2.164 \mathrm{~g} \mathrm{~cm}^{-3}\). What is the molar concentration of \(\mathrm{NaCl}\) in a \(12.0 \mathrm{~cm}^{3}\) sample of pure \(\mathrm{NaCl}\) ? What is the molar concentration of \(\mathrm{NaCl}\) in a \(25.0 \mathrm{~g}\) sample of pure \(\mathrm{NaCl}\) ?

Write the equilibrium law corresponding to \(K_{c}\) for each of the following heterogeneous reactions. (a) \(2 \mathrm{C}(s)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{CO}(g)\) (b) \(2 \mathrm{NaHSO}_{3}(s) \rightleftharpoons \mathrm{Na}_{2} \mathrm{SO}_{3}(s)+\mathrm{H}_{2} \mathrm{O}(g)+\mathrm{SO}_{2}(g)\) (c) \(2 \mathrm{C}(s)+2 \mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons \mathrm{CH}_{4}(g)+\mathrm{CO}_{2}(g)\) (d) \(\mathrm{CaCO}_{3}(s)+2 \mathrm{HF}(g) \rightleftharpoons \mathrm{C}_{2}(g)+\mathrm{CaF}_{2}(s)+\mathrm{H}_{2} \mathrm{O}(g)\) (e) \(\mathrm{CuSO}_{4} \cdot 5 \mathrm{H}_{2} \mathrm{O}(s) \rightleftharpoons \mathrm{CuSO}_{4}(s)+5 \mathrm{H}_{2} \mathrm{O}(g)\)

Write the equilibrium law corresponding to \(K_{c}\) for each of the following heterogeneous reactions. (a) \(\mathrm{CaCO}_{3}(s)+\mathrm{SO}_{2}(g) \rightleftharpoons \mathrm{CaSO}_{3}(s)+\mathrm{CO}_{2}(g)\) (b) \(\mathrm{AgCl}(s)+\mathrm{Br}^{-}(a q) \rightleftharpoons \mathrm{AgBr}(s)+\mathrm{Cl}^{-}(a q)\) (c) \(\mathrm{Cu}(\mathrm{OH})_{2}(s) \rightleftharpoons \mathrm{Cu}^{2+}(a q)+2 \mathrm{OH}^{-}(a q)\) (d) \(\mathrm{Mg}(\mathrm{OH})_{2}(s) \rightleftharpoons \mathrm{MgO}(s)+\mathrm{H}_{2} \mathrm{O}(g)\) (e) \(3 \mathrm{CuO}(s)+2 \mathrm{NH}_{3}(g) \rightleftharpoons\) \(3 \mathrm{Cu}(s)+\mathrm{N}_{2}(g)+3 \mathrm{H}_{2} \mathrm{O}(g)\)

The heterogeneous reaction \(2 \mathrm{HCl}(g)+\mathrm{I}_{2}(s) \rightleftharpoons\) \(2 \mathrm{HI}(g)+\mathrm{Cl}_{2}(g)\) has \(K_{\mathrm{c}}=1.6 \times 10^{-34}\) at \(25^{\circ} \mathrm{C}\). Suppose \(0.100 \mathrm{~mol}\) of \(\mathrm{HCl}\) and solid \(\mathrm{I}_{2}\) are placed in a \(1.00 \mathrm{~L}\) container. What will be the equilibrium concentrations of HI and \(\mathrm{Cl}_{2}\) in the container?

The reaction $$ \mathrm{CO}(g)+2 \mathrm{H}_{2}(g) \rightleftharpoons \mathrm{CH}_{3} \mathrm{OH}(g) $$ has \(\Delta H^{\circ}=-18 \mathrm{~kJ} .\) How will the amount of \(\mathrm{CH}_{3} \mathrm{OH}\) present at equilibrium be affected by the following changes? (a) Adding \(\mathrm{CO}(g)\) (b) Removing \(\mathrm{H}_{2}(g)\) (c) Decreasing the volume of the container (d) Adding a catalyst (e) Increasing the temperature

How will the position of equilibrium in the reaction $$ \text { heat }+\mathrm{CH}_{4}(g)+2 \mathrm{H}_{2} \mathrm{~S}(g) \rightleftharpoons \mathrm{CS}_{2}(g)+4 \mathrm{H}_{2}(g) $$ be affected by the following changes? (a) Adding \(\mathrm{CH}_{4}(g)\) (b) Adding \(\mathrm{H}_{2}(g)\) (c) Removing \(\mathrm{CS}_{2}(g)\) (d) Decreasing in the volume of the container (e) Increasing the temperature

Consider the equilibrium \(\mathrm{N}_{2} \mathrm{O}(g)+\mathrm{NO}_{2}(g) \rightleftharpoons 3 \mathrm{NO}(g) \quad \Delta H^{\circ}=+155.7 \mathrm{~kJ}\) In which direction will this equilibrium be shifted by the following changes? (a) Adding \(\mathrm{N}_{2} \mathrm{O}\) (b) Removing \(\mathrm{NO}_{2}\) (c) Adding NO (d) Increasing the temperature of the reaction mixture (e) Adding helium gas to the reaction mixture at constant volume (f) Decreasing the volume of the container at constant temperature

Consider the equilibrium $$ 2 \mathrm{NO}(g)+\mathrm{Cl}_{2}(g) \rightleftharpoons 2 \mathrm{NOCl}(g) $$ for which \(\Delta H^{\circ}=-77.07 \mathrm{~kJ} .\) How will the amount of \(\mathrm{Cl}_{2}\) at equilibrium be affected by the following changes? (a) Removing \(\mathrm{NO}(g)\) (b) Adding \(\mathrm{NOCl}(g)\) (c) Raising the temperature (d) Decreasing the volume of the container at constant temperature

At \(773^{\circ} \mathrm{C}\), a mixture of \(\mathrm{CO}(g), \mathrm{H}_{2}(g)\), and \(\mathrm{CH}_{3} \mathrm{OH}(g)\) was allowed to come to equilibrium. The concentrations were determined to be: \([\mathrm{CO}]=0.105 \mathrm{M},\left[\mathrm{H}_{2}\right]=0.250 \mathrm{M}\) \(\left[\mathrm{CH}_{3} \mathrm{OH}\right]=0.00261 M .\) Calculate \(K_{\mathrm{c}}\) for the reaction $$ \mathrm{CO}(g)+2 \mathrm{H}_{2}(g) \rightleftharpoons \mathrm{CH}_{3} \mathrm{OH}(g) $$

Ethylene, \(\mathrm{C}_{2} \mathrm{H}_{4}\), and water react under appropriate conditions to give ethanol. The reaction is: $$ \mathrm{C}_{2} \mathrm{H}_{4}(g)+\mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(g) $$ An equilibrium mixture of these gases at a certain temperature had the following partial pressures: \(P_{\mathrm{C}_{2} \mathrm{H}_{4}}=\) $$ 0.575 \mathrm{~atm}, P_{\mathrm{H}_{2} \mathrm{O}}=1.30 \mathrm{~atm}, \text { and } P_{\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}}=6.99 \mathrm{~atm} $$ What is the value of \(K_{\mathrm{P}}\) ?

At high temperature, \(2.00 \mathrm{~mol}\) of \(\mathrm{HBr}\) was placed in a 4.00 L container where it decomposed in the reaction: $$ 2 \mathrm{HBr}(g) \rightleftharpoons \mathrm{H}_{2}(g)+\mathrm{Br}_{2}(g) $$ At equilibrium the concentration of \(\mathrm{Br}_{2}\) was measured to be \(0.0955 \mathrm{M}\). What is \(K_{\mathrm{c}}\) for this reaction at this temperature?

A 0.050 mol sample of formaldehyde vapor, \(\mathrm{CH}_{2} \mathrm{O}\), was placed in a heated \(500 \mathrm{~mL}\) vessel and some of it decomposed. The reaction is $$ \mathrm{CH}_{2} \mathrm{O}(g) \rightleftharpoons \mathrm{H}_{2}(g)+\mathrm{CO}(g) $$ At equilibrium, the \(\mathrm{CH}_{2} \mathrm{O}(g)\) concentration was \(0.066 \mathrm{~mol} \mathrm{~L}^{-1}\). Calculate the value of \(K_{\mathrm{c}}\) for this reaction.

The reaction \(\mathrm{NO}_{2}(g)+\mathrm{NO}(g) \rightleftharpoons \mathrm{N}_{2} \mathrm{O}(g)+\mathrm{O}_{2}(g)\) reached equilibrium at a certain high temperature. Originally, the reaction vessel contained the following initial concentrations: \(\left[\mathrm{N}_{2} \mathrm{O}\right]=0.184 \mathrm{M},\left[\mathrm{O}_{2}\right]=0.377 M\) \(\left[\mathrm{NO}_{2}\right]=0.0560 M,\) and \([\mathrm{NO}]=0.294 M .\) The concentration of the \(\mathrm{NO}_{2}\), the only colored gas in the mixture, was monitored by following the intensity of the color. At equilibrium, the \(\mathrm{NO}_{2}\) concentration had become \(0.118 \mathrm{M}\). What is the value of \(K_{c}\) for this reaction at this temperature?

At a certain temperature, \(K_{\mathrm{c}}=0.18\) for the equilibrium \(\mathrm{PCl}_{3}(g)+\mathrm{Cl}_{2}(g) \rightleftharpoons \mathrm{PCl}_{5}(g)\) Suppose a reaction vessel at this temperature contained these three gases at the following concentrations: \(\left[\mathrm{PCl}_{3}\right]=\) \(0.0420 \mathrm{M},\left[\mathrm{Cl}_{2}\right]=0.0240 \mathrm{M},\left[\mathrm{PCl}_{5}\right]=0.00500 \mathrm{M}\) (a) Compute the reaction quotient and use it to determine whether the system is in a state of equilibrium. (b) If the system is not at equilibrium, in which direction will the reaction proceed to get to equilibrium?

At \(460^{\circ} \mathrm{C},\) the reaction $$ \mathrm{SO}_{2}(g)+\mathrm{NO}_{2}(g) \rightleftharpoons \mathrm{NO}(g)+\mathrm{SO}_{3}(g) $$ has \(K_{\mathrm{c}}=85.0\). A reaction flask at \(460^{\circ} \mathrm{C}\) contains these gases at the following concentrations: \(\left[\mathrm{SO}_{2}\right]=0.00250 \mathrm{M}\), \(\left[\mathrm{NO}_{2}\right]=0.00350 \quad M,[\mathrm{NO}]=0.0250 \quad M,\) and \(\left[\mathrm{SO}_{3}\right]=0.0400 \mathrm{M}\) (a) Is the reaction at equilibrium? (b) If not, in which direction will the reaction proceed to arrive at equilibrium?

At \(25^{\circ} \mathrm{C}, K_{\mathrm{c}}=0.145\) for the following reaction in the solvent \(\mathrm{CCl}_{4}\) $$ 2 \mathrm{BrCl} \rightleftharpoons \mathrm{Br}_{2}+\mathrm{Cl}_{2} $$ If the initial concentration of \(\mathrm{BrCl}\) in the solution is \(0.050 M,\) what will the equilibrium concentrations of \(\mathrm{Br}_{2}\) and \(\mathrm{Cl}_{2}\) be?

The reaction \(2 \mathrm{HCl}(g) \rightleftharpoons \mathrm{H}_{2}(g)+\mathrm{Cl}_{2}(g)\) has \(K_{\mathrm{c}}=\) \(3.2 \times 10^{-34}\) at \(25^{\circ} \mathrm{C}\). If a reaction vessel contains initially \(0.0500 \mathrm{~mol} \mathrm{~L}^{-1}\) of \(\mathrm{HCl}\) and then reacts to reach equilibrium, what will be the concentrations of \(\mathrm{H}_{2}\) and \(\mathrm{Cl}_{2}\) ?

At \(200^{\circ} \mathrm{C}, K_{\mathrm{c}}=1.4 \times 10^{-10}\) for the reaction $$ \mathrm{N}_{2} \mathrm{O}(g)+\mathrm{NO}_{2}(g) \rightleftharpoons 3 \mathrm{NO}(g) $$ If \(0.200 \mathrm{~mol}\) of \(\mathrm{N}_{2} \mathrm{O}\) and \(0.400 \mathrm{~mol} \mathrm{NO}_{2}\) are placed in a 4.00 L container, what would the NO concentration be if this equilibrium were established?

At a certain temperature, \(K_{\mathrm{c}}=0.18\) for the equilibrium $$ \mathrm{PCl}_{3}(g)+\mathrm{Cl}_{2}(g) \rightleftharpoons \mathrm{PCl}_{5}(g) $$ If \(0.026 \mathrm{~mol}\) of \(\mathrm{PCl}_{5}\) is placed in a \(2.00 \mathrm{~L}\) vessel at this temperature, what will the concentration of \(\mathrm{PCl}_{3}\) be at equilibrium?

At a certain temperature, \(K_{\mathrm{c}}=4.3 \times 10^{5}\) for the reaction $$ \mathrm{HCO}_{2} \mathrm{H}(g) \rightleftharpoons \mathrm{CO}(g)+\mathrm{H}_{2} \mathrm{O}(g) $$ If \(0.200 \mathrm{~mol}\) of \(\mathrm{HCO}_{2} \mathrm{H}\) is placed in a \(1.00 \mathrm{~L}\) vessel, what will be the concentrations of \(\mathrm{CO}\) and \(\mathrm{H}_{2} \mathrm{O}\) when the system reaches equilibrium? (Hint: Where does the position of equilibrium lie when \(K\) is very large?)

The reaction \(\mathrm{H}_{2}(g)+\mathrm{Br}_{2}(g) \rightleftharpoons 2 \mathrm{HBr}(g)\) has a \(K_{\mathrm{c}}=\) \(2.0 \times 10^{9}\) at \(25^{\circ} \mathrm{C}\). If \(0.100 \mathrm{~mol}\) of \(\mathrm{H}_{2}\) and \(0.200 \mathrm{~mol}\) of \(\mathrm{Br}_{2}\) are placed in a \(10.0 \mathrm{~L}\) container, what will all the equilibrium concentrations be at \(25^{\circ} \mathrm{C}\) ? (Hint: Where does the position of equilibrium lie when \(K\) is very large?)

The reaction \(\mathrm{N}_{2} \mathrm{O}_{4}(g) \rightleftharpoons 2 \mathrm{NO}_{2}(g)\) has \(K_{\mathrm{P}}=0.140\) at \(25^{\circ} \mathrm{C}\). In a reaction vessel containing these gases in equilibrium at this temperature, the partial pressure of \(\mathrm{N}_{2} \mathrm{O}_{4}\) was 0.250 atm. (a) What was the partial pressure of the \(\mathrm{NO}_{2}\) in the reaction mixture? (b) What was the total pressure of the mixture of gases?