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Chapter 13: Problem 33

The following equilibrium pressures at a certain temperature were observed for the reaction $$\begin{aligned} 2 \mathrm{NO}_{2}(g) & \rightleftharpoons 2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \\ P_{\mathrm{NO}_{2}} &=0.55 \mathrm{atm} \\\ P_{\mathrm{NO}} &=6.5 \times 10^{-5} \mathrm{atm} \\ P_{\mathrm{O}_{2}} &=4.5 \times 10^{-5} \mathrm{atm} \end{aligned}$$ Calculate the value for the equilibrium constant \(K_{\mathrm{p}}\) at this temperature.

Short Answer

Expert verified
The value for the equilibrium constant, \(K_p\), at this temperature is approximately \(1.184 \times 10^{-9}\).

Step by step solution

01

Write the balanced chemical equation

The balanced chemical equation for the reaction is: \(2NO_2(g) \rightleftharpoons 2NO(g) + O_2(g) \) #Step 2: Write the expression for Kp#
02

Write the expression for Kp

The general expression for Kp for a reaction is given by the ratio of the product of the partial pressures of the products raised to their stoichiometric coefficients to the product of the partial pressures of the reactants raised to their stoichiometric coefficients. For this reaction, the expression for Kp is: \(K_p = \frac{[NO]^2 \times [O_2]}{[NO_2]^2} \) #Step 3: Substitute the given partial pressures into the Kp expression#
03

Substitute the given partial pressures into the Kp expression

We are given the partial pressures at equilibrium as follows: \(P_{NO_2} = 0.55 \, atm\) \(P_{NO} = 6.5 \times 10^{-5} \, atm\) \(P_{O_2} = 4.5 \times 10^{-5} \, atm\) Substitute these values into the Kp expression: \(K_p = \frac{(6.5 \times 10^{-5})^2 \times (4.5 \times 10^{-5})}{(0.55)^2} \) #Step 4: Calculate the value of Kp#
04

Calculate the value of Kp

Using a calculator, we can compute the value of Kp: \(K_p = \frac{(6.5 \times 10^{-5})^2 \times (4.5 \times 10^{-5})}{(0.55)^2} \approx 1.184 \times 10^{-9} \) The value for the equilibrium constant, Kp, at this temperature is approximately \(1.184 \times 10^{-9}\).

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Most popular questions from this chapter

The creation of shells by mollusk species is a fascinating process. By utilizing the \(\mathrm{Ca}^{2+}\) in their food and aqueous environment, as well as some complex equilibrium processes, a hard calcium carbonate shell can be produced. One important equilibrium reaction in this complex process is $$\mathrm{HCO}_{3}^{-}(a q) \leftrightharpoons \mathrm{H}^{+}(a q)+\mathrm{CO}_{3}^{2-}(a q) K=5.6 \times 10^{-11}$$ If 0.16 mole of \(\mathrm{HCO}_{3}^{-}\) is placed into 1.00 \(\mathrm{L}\) of solution, what will be the equilibrium concentration of \(\mathrm{CO}_{3}^{2-2}\) ?

Consider the reaction $$\mathrm{P}_{4}(g) \rightleftharpoons 2 \mathrm{P}_{2}(g)$$ where \(K_{\mathrm{p}}=1.00 \times 10^{-1}\) at 1325 \(\mathrm{K}\) . In an experiment where \(\mathrm{P}_{4}(g)\) is placed into a container at 1325 \(\mathrm{K}\) , the equilibrium mixture of \(\mathrm{P}_{4}(g)\) and \(\mathrm{P}_{2}(g)\) has a total pressure of 1.00 atm. Calculate the equilibrium pressures of \(\mathrm{P}_{4}(g)\) and \(\mathrm{P}_{2}(g) .\) Calculate the fraction (by moles) of \(\mathrm{P}_{4}(g)\) that has dissociated to reach equilibrium.

In a study of the reaction $$3 \mathrm{Fe}(s)+4 \mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons \mathrm{Fe}_{3} \mathrm{O}_{4}(s)+4 \mathrm{H}_{2}(g)$$ at 1200 \(\mathrm{K}\) it was observed that when the equilibrium partial pressure of water vapor is 15.0 torr, the total pressure at equilibrium is 36.3 torr. Calculate the value of \(K_{\mathrm{p}}\) for this reaction at 1200 \(\mathrm{K}\) . Hint: Apply Dalton's law of partial pressures.)

For the reaction $$\mathrm{PCl}_{5}(g) \rightleftharpoons \mathrm{PCl}_{3}(g)+\mathrm{Cl}_{2}(g)$$ at \(600 . \mathrm{K}\) , the equilibrium constant, \(K_{\mathrm{p}},\) is \(11.5 .\) Suppose that 2.450 \(\mathrm{g} \mathrm{PCl}_{5}\) is placed in an evacuated 500 -mL bulb, which is then heated to \(600 . \mathrm{K}\) . a. What would be the pressure of \(\mathrm{PCl}_{5}\) if it did not dissociate? b. What is the partial pressure of \(\mathrm{PCl}_{5}\) at equilibrium? c. What is the total pressure in the bulb at equilibrium? d. What is the percent dissociation of PCl_ at equilibrium?

For a typical equilibrium problem, the value of \(K\) and the initial reaction conditions are given for a specific reaction, and you are asked to calculate the equilibrium concentrations. Many of these calculations involve solving a quadratic or cubic equation. What can you do to avoid solving a quadratic or cubic equation and still come up with reasonable equilibrium concentrations?
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