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Chapter 15: Problem 35

A mixture of \(0.140 \mathrm{~mol}\) of \(\mathrm{NO}, 0.060 \mathrm{~mol}\) of \(\mathrm{H}_{2},\) and 0.260 mol of \(\mathrm{H}_{2} \mathrm{O}\) is placed in a \(2.0-\mathrm{L}\) vessel at \(330 \mathrm{~K}\). Assume that the following equilibrium is established: $$2 \mathrm{NO}(g)+2 \mathrm{H}_{2}(g) \rightleftharpoons \mathrm{N}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(g)$$ At equilibrium \(\left[\mathrm{H}_{2}\right]=0.010 \mathrm{M}\). (a) Calculate the equilibrium concentrations of \(\mathrm{NO}, \mathrm{N}_{2},\) and \(\mathrm{H}_{2} \mathrm{O} .\) (b) Calculate \(K_{c}\).

Short Answer

Expert verified
The equilibrium concentrations are \(NO:~0.030~M\), \(N_2:~0.020~M\), and \(H_2O:~0.170~M\). The equilibrium constant, \(K_c \approx 637\).

Step by step solution

01

Determine Change in Concentrations

: Let's define the change in concentrations for the species involved in the reaction as they reach equilibrium: - \(\Delta [NO] = -2x\) - \(\Delta [H_2] = -x\) - \(\Delta [N_2] = +x\) - \(\Delta [H_2O] = +2x\) The problem gives us that the \(equilibrium~concentration~of~H_2 = 0.010~M\) \[Initial~concentration~of~H_2 + \Delta [H_2] = Equilibrium~concentration~of~H_2\]
02

Calculate the Change (x)

: Now, solve for x: \(0.030 - x = 0.010\) \((x = 0.020~M)\)
03

Calculate Equilibrium Concentrations

: Using the value of x, we can now calculate the equilibrium concentrations of the other species: \[Equilibrium~concentration~of~NO = (0.070 - 2(0.020)) = 0.030~M\] \[Equilibrium~concentration~of~N_2 = (0 + 0.020) = 0.020~M\] \[Equilibrium~concentration~of~H_2O = (0.130 + 2(0.020)) = 0.170~M\]
04

Calculate Kc

: Now, we can calculate the equilibrium constant, Kc, using these equilibrium concentrations: \(K_c = \frac{[N_2][H_2O]^2}{[NO]^2[H_2]^2}\) \(K_c = \frac{(0.020)(0.170)^2}{(0.030)^2(0.010)^2}\) \(K_c \approx 637\) - The equilibrium concentrations are \(NO:~0.030~M\), \(N_2:~0.020~M\), and \(H_2O:~0.170~M\). - The equilibrium constant, \(K_c \approx 637\).

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Most popular questions from this chapter

A flask is charged with \(152.0 \mathrm{kPa}\) of $\mathrm{N}_{2} \mathrm{O}_{4}(g)\( and \)101.3 \mathrm{kPa}\( \)\mathrm{NO}_{2}(g)$ at \(25^{\circ} \mathrm{C},\) and the following equilibrium is achieved: $$\mathrm{N}_{2} \mathrm{O}_{4}(g) \rightleftharpoons 2 \mathrm{NO}_{2}(g)$$ After equilibrium is reached, the partial pressure of \(\mathrm{NO}_{2}\) is \(51.9 \mathrm{kPa}\). (a) What is the equilibrium partial pressure of \(\mathrm{N}_{2} \mathrm{O}_{4} ?(\mathbf{b})\) Calculate the value of \(K_{p}\) for the reaction. (c) Calculate \(K_{c}\) for the reaction.

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 \(\mathrm{K} .\) 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 \(450 \mathrm{~K}\).

At \(800 \mathrm{~K},\) the equilibrium constant for the reaction \(\mathrm{A}_{2}(g) \rightleftharpoons 2 \mathrm{~A}(g)\) is $K_{c}=3.1 \times 10^{-4}$. (a) Assuming both forward and reverse reactions are elementary reactions, which rate constant do you expect to be larger, \(k_{f}\) or \(k_{r} ?\) (b) If the value of $k_{f}=0.27 \mathrm{~s}^{-1}\(, what is the value of \)k_{r}\( at \)800 \mathrm{~K} ?$ (c) Based on the nature of the reaction, do you expect the forward reaction to be endothermic or exothermic? (d) If the temperature is raised to $1000 \mathrm{~K}\(, will the reverse rate constant \)k_{r}$ increase or decrease? Will the change in \(k_{r}\) be larger or smaller than the change in \(k_{f}\) ?

A 5.37 -g sample of \(\mathrm{SO}_{3}\) is placed in a 5.00-L container and heated to \(1000 \mathrm{~K}\). The \(\mathrm{SO}_{3}\) decomposes to \(\mathrm{SO}_{2}\) and \(\mathrm{O}_{2}\) : $$2 \mathrm{SO}_{3}(g) \rightleftharpoons 2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g)$$ At equilibrium, the total pressure in the container is 157 \(\mathrm{kPa}\). Find the values of \(K_{p}\) and \(K_{c}\) for this reaction at \(1100 \mathrm{~K}\).

Which of the following reactions lies to the right, favoring the formation of products, and which lies to the left, favoring formation of reactants? (a) $\mathrm{H}_{2} \mathrm{O}(g)+\mathrm{CO}(g) \rightleftharpoons \mathrm{CO}_{2}(g)+\mathrm{H}_{2}(g)\( at \)1300 \mathrm{~K} K_{c}=0.57$ (b) \(2 \mathrm{CO}(g) \rightleftharpoons \mathrm{CO}_{2}(g)+\mathrm{C}(s)\) at \(900 \mathrm{~K} K_{p}=0.0572\)
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