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Chapter 15: Problem 104

For the reaction \(2 \mathrm{NO}_{2}(\mathrm{g}) \rightleftharpoons 2 \mathrm{NO}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g})\) \(K_{\mathrm{c}}=1.8 \times 10^{-6}\) at \(184^{\circ} \mathrm{C} . \mathrm{At} 184^{\circ} \mathrm{C},\) the value of \(K_{\mathrm{c}}\) for the reaction \(\mathrm{NO}(\mathrm{g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{g}) \rightleftharpoons \mathrm{NO}_{2}(\mathrm{g})\) is (a) \(0.9 \times 10^{6}\) (b) \(7.5 \times 10^{2}\) (c) \(5.6 \times 10^{5}\) (d) \(2.8 \times 10^{5}\)

Short Answer

Expert verified
(b) \(7.5 \times 10^{2}\)

Step by step solution

01

Rearranging the given reaction

First, rearrange the provided reaction to match the reaction for which we need to find the equilibrium constant. The rearranged reaction will be \(NO_{2(g)} \rightleftharpoons NO_{(g)} + 1/2 O_{2(g)}\)
02

Determine the equilibrium constant for the rearranged reaction

In the rearranged reaction, notice that the stoichiometric coefficients are half of those in the original reaction. The equilibrium constant for the related reaction is the square root of the equilibrium constant for the original reaction. This is because the stoichiometric coefficients in the balanced chemical equation are exponents in the equation for the equilibrium constant. So, \(K_{c(new)}= \sqrt{K_{c(original)}} = \sqrt{1.8 \times 10^{-6}} = 1.34 \times 10^{-3}\).
03

Determine the equilibrium constant for the desired reaction

The desired reaction is the reverse of the rearranged reaction, so the equilibrium constant for the desired reaction is the reciprocal of the equilibrium constant for the rearranged reaction. Therefore, \(K_{c(desired)} = 1/K_{c(new)} = 1/(1.34 \times 10^{-3}) = 0.75 \times 10^{6}\)

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Most popular questions from this chapter

A mixture of \(1.00 \mathrm{mol} \mathrm{NaHCO}_{3}(\mathrm{s})\) and \(1.00 \mathrm{mol}\) \(\mathrm{Na}_{2} \mathrm{CO}_{3}(\mathrm{s})\) is introduced into a \(2.50 \mathrm{L}\) flask in which the partial pressure of \(\mathrm{CO}_{2}\) is 2.10 atm and that of \(\mathrm{H}_{2} \mathrm{O}(\mathrm{g})\) is \(715 \mathrm{mmHg} .\) When equilibrium is established at \(100^{\circ} \mathrm{C},\) will the partial pressures of \(\mathrm{CO}_{2}(\mathrm{g})\) and \(\mathrm{H}_{2} \mathrm{O}(\mathrm{g})\) be greater or less than their initial partial pressures? Explain. $$\begin{array}{r} 2 \mathrm{NaHCO}_{3}(\mathrm{s}) \rightleftharpoons \mathrm{Na}_{2} \mathrm{CO}_{3}(\mathrm{s})+\mathrm{CO}_{2}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \\ K_{\mathrm{p}}=0.23 \mathrm{at} 100^{\circ} \mathrm{C} \end{array}$$

\(1.00 \mathrm{mol}\) each of \(\mathrm{CO}\) and \(\mathrm{Cl}_{2}\) are introduced into an evacuated 1.75 L flask, and the following equilibrium is established at \(668 \mathrm{K}\). $$ \mathrm{CO}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{g}) \longrightarrow \mathrm{COCl}_{2}(\mathrm{g}) \quad K_{\mathrm{p}}=22.5 $$ For this equilibrium, calculate (a) the partial pressure of \(\mathrm{COCl}_{2}(\mathrm{g}) ;\) (b) the total gas pressure.

A 1.100 L flask at \(25^{\circ} \mathrm{C}\) and 1.00 atm pressure contains \(\mathrm{CO}_{2}(\mathrm{g})\) in contact with \(100.0 \mathrm{mL}\) of a saturated aqueous solution in which \(\left[\mathrm{CO}_{2}(\mathrm{aq})\right]=3.29 \times 10^{-2} \mathrm{M}\) (a) What is the value of \(K_{c}\) at \(25^{\circ} \mathrm{C}\) for the equilibrium \(\mathrm{CO}_{2}(\mathrm{g}) \rightleftharpoons \mathrm{CO}_{2}(\mathrm{aq}) ?\) (b) If 0.01000 mol of radioactive \(^{14} \mathrm{CO}_{2}\) is added to the flask, how many moles of the \(^{14} \mathrm{CO}_{2}\) will be found in the gas phase and in the aqueous solution when equilibrium is re-established? [Hint: The radioactive \(^{14} \mathrm{CO}_{2}\) distributes itself between the two phases in exactly the same manner as the nonradioactive \(\left.^{12} \mathrm{CO}_{2} .\right]\)

For the following reaction, \(K_{\mathrm{c}}=2.00\) at \(1000^{\circ} \mathrm{C}\) $$2 \operatorname{COF}_{2}(\mathrm{g}) \rightleftharpoons \mathrm{CO}_{2}(\mathrm{g})+\mathrm{CF}_{4}(\mathrm{g})$$ If a \(5.00 \mathrm{L}\) mixture contains \(0.145 \mathrm{mol} \mathrm{COF}_{2}, 0.262 \mathrm{mol}\) \(\mathrm{CO}_{2},\) and \(0.074 \mathrm{mol} \mathrm{CF}_{4}\) at a temperature of \(1000^{\circ} \mathrm{C}\) (a) Will the mixture be at equilibrium? (b) If the gases are not at equilibrium, in what direction will a net change occur? (c) How many moles of each gas will be present at equilibrium?

The volume of the reaction vessel containing an equilibrium mixture in the reaction \(\mathrm{SO}_{2} \mathrm{Cl}_{2}(\mathrm{g}) \rightleftharpoons\) \(\mathrm{SO}_{2}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{g})\) is increased. When equilibrium is re-established, (a) the amount of \(\mathrm{Cl}_{2}\) will have increased; (b) the amount of \(\mathrm{SO}_{2}\) will have decreased; (c) the amounts of \(\mathrm{SO}_{2}\) and \(\mathrm{Cl}_{2}\) will have remained the same; (d) the amount of \(\mathrm{SO}_{2} \mathrm{Cl}_{2}\) will have increased.
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