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Chapter 14: Problem 20

A reaction vessel contains \(\mathrm{NH}_{3}, \mathrm{~N}_{2},\) and \(\mathrm{H}_{2}\) at equilibrium at a certain temperature. The equilibrium concentrations are \(\left[\mathrm{NH}_{3}\right]=0.25 M,\left[\mathrm{~N}_{2}\right]=0.11 M\) and \(\left[\mathrm{H}_{2}\right]=1.91 \mathrm{M} .\) Calculate the equilibrium constant \(K_{\mathrm{c}}\) for the synthesis of ammonia if the reaction is represented as (a) \(\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \rightleftharpoons 2 \mathrm{NH}_{3}(g)\) (b) \(\frac{1}{2} \mathrm{~N}_{2}(g)+\frac{3}{2} \mathrm{H}_{2}(g) \rightleftharpoons \mathrm{NH}_{3}(g)\)

Short Answer

Expert verified
After substituting the given concentration values and performing the calculations, you would obtain the equilibrium constants \(K_c\) for the first and the second reaction respectively.

Step by step solution

01

Identify the given quantities

You are provided with equilibrium concentrations of the three substances involved in the reactions. These concentrations: \([NH_{3}]=0.25M\), \([N_{2}]=0.11M\), and \([H_{2}]=1.91M\), are all at a certain temperature.
02

Applying the equilibrium constant formula for reaction (a)

The expression for the equilibrium constant \(K_c\) for the reaction \(N_2(g)+3H_2(g) \leftrightarrows 2NH_3(g)\) is given by: \[K_c= \frac{[NH_{3}]^2}{[{N_{2}]\cdot({H_{2}})^3}}\]Now we can substitute the given concentration values into this formula: \[K_c= \frac{(0.25)^2}{0.11 \cdot (1.91)^3}\]. Upon calculating, you'll arrive at the equilibrium constant \(K_c\) for the first reaction.
03

Applying the equilibrium constant formula for reaction (b)

The expression for the equilibrium constant \(K_c\) for the reaction \(\frac{1}{2}N_{2}(g)+\frac{3}{2}H_{2}(g) \leftrightarrow NH_{3}(g)\) is given by: \[K_c= \frac{[NH_{3}]}{[N_{2}]^{1/2} \cdot [H_{2}]^{3/2}}\]Similarly, substitute the given concentration values in this formula:\[K_c= \frac{0.25}{(0.11)^{1/2} \cdot (1.91)^{3/2}}\]. Calculate this expression to obtain the equilibrium constant \(K_c\) for the second reaction.

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Most popular questions from this chapter

At \(25^{\circ} \mathrm{C},\) the equilibrium partial pressures of \(\mathrm{NO}_{2}\) and \(\mathrm{N}_{2} \mathrm{O}_{4}\) are 0.15 atm and 0.20 atm, respectively. If the volume is doubled at constant temperature, calculate the partial pressures of the gases when a new equilibrium is established.

A quantity of 1.0 mole of \(\mathrm{N}_{2} \mathrm{O}_{4}\) was introduced into an evacuated vessel and allowed to attain equilibrium at a certain temperature $$\mathrm{N}_{2} \mathrm{O}_{4}(g) \rightleftharpoons 2 \mathrm{NO}_{2}(g)$$ The average molar mass of the reacting mixture was \(70.6 \mathrm{~g} / \mathrm{mol} .\) (a) Calculate the mole fractions of the gases. (b) Calculate \(K_{P}\) for the reaction if the total pressure was 1.2 atm. (c) What would be the mole fractions if the pressure were increased to 4.0 atm by reducing the volume at the same temperature?

Consider the following reaction at equilibrium: $$\mathrm{A}(g) \rightleftharpoons 2 \mathrm{~B}(g)$$ From the data shown here, calculate the equilibrium constant (both \(K_{P}\) and \(K_{\mathrm{c}}\) ) at each temperature. Is the reaction endothermic or exothermic? $$ \begin{array}{clr} \text { Temperature }\left({ }^{\circ} \mathrm{C}\right) & {[\mathrm{A}](M)} & {[\mathrm{B}](M)} \\ 200 & 0.0125 & 0.843 \\ 300 & 0.171 & 0.764 \\ 400 & 0.250 & 0.724 \end{array} $$

Pure nitrosyl chloride (NOCl) gas was heated to \(240^{\circ} \mathrm{C}\) in a \(1.00-\mathrm{L}\) container. At equilibrium the total pressure was 1.00 atm and the \(\mathrm{NOCl}\) pressure was 0.64 atm. $$2 \mathrm{NOCl}(g) \rightleftharpoons 2 \mathrm{NO}(g)+\mathrm{Cl}_{2}(g)$$ (a) Calculate the partial pressures of \(\mathrm{NO}\) and \(\mathrm{Cl}_{2}\) in the system. (b) Calculate the equilibrium constant \(K_{P}\).

Consider the reaction $$2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{NO}_{2}(g)$$ At \(430^{\circ} \mathrm{C},\) an equilibrium mixture consists of 0.020 mole of \(\mathrm{O}_{2}, 0.040\) mole of \(\mathrm{NO},\) and 0.96 mole of \(\mathrm{NO}_{2}\). Calculate \(K_{P}\) for the reaction, given that the total pressure is 0.20 atm.
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