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Chapter 13: Problem 85

The gas arsine, \(\mathrm{AsH}_{3},\) decomposes as follows: $$2 \mathrm{AsH}_{3}(g) \rightleftharpoons 2 \mathrm{As}(s)+3 \mathrm{H}_{2}(g)$$ In an experiment at a certain temperature, pure \(\mathrm{AsH}_{3}(g)\) was placed in an empty, rigid, sealed flask at a pressure of 392.0 torr. After 48 hours the pressure in the flask was observed to be constant at 488.0 torr. a. Calculate the equilibrium pressure of \(\mathrm{H}_{2}(g)\) b. Calculate \(K_{\mathrm{p}}\) for this reaction.

Short Answer

Expert verified
The equilibrium pressure of \(\mathrm{H}_{2}(g)\) is 96.0 Torr and the equilibrium constant \(K_{\mathrm{p}}\) for this reaction is approximately 0.189.

Step by step solution

01

1. Set up the ICE table.

We will start by setting up an ICE table (Initial, Change, and Equilibrium) to keep track of the changes in pressure for each substance in the reaction. $$ \begin{array}{l||ccc} & 2 \mathrm{AsH}_{3}(g) & \rightleftharpoons & 2 \mathrm{As}(s) & + & 3 \mathrm{H}_{2}(g) \\ \hline \hline I & 392.0 & & 0 & & 0 \\ C & -2x & & +2x & & +3x \\ E & 392.0-2x & & 2x & & 3x \\ \end{array} $$ where x refers to the change in pressure.
02

2. Calculate change in pressure.

We know that the total pressure at equilibrium is 488.0 torr. We can express the change in pressure (\(x\)) in terms of the equilibrium pressures of the reactant and product gases: $$ (392.0 - 2x) + 3x = 488.0 $$ Solve for \(x\): $$ x = 32.0\,\text{Torr} $$
03

3. Calculate equilibrium pressure of \(\mathrm{H}_{2}(g)\).

Now that we know the value of \(x\), we can find the equilibrium pressure of the hydrogen gas by using the equilibrium row of our ICE table: $$ P_{\mathrm{H}_{2}} = 3x = 3(32.0) = 96.0\,\text{Torr} $$ So, the equilibrium pressure of \(\mathrm{H}_{2}(g)\) is 96.0 Torr.
04

4. Calculate equilibrium constant \(K_{\mathrm{p}}\).

We can now calculate the equilibrium constant \(K_{\mathrm{p}}\) using the equilibrium pressures of \(\mathrm{AsH}_{3}\) and \(\mathrm{H}_{2}\): $$ K_{\mathrm{p}} = \dfrac{P_{\mathrm{H}_{2}^3}}{(P_{\mathrm{AsH}_{3}})^2} = \dfrac{(96.0)^3}{(392.0 - 2 \times 32.0)^2} $$ Calculate \(K_{\mathrm{p}}\): $$ K_{\mathrm{p}} \approx 0.189 $$ So, the equilibrium constant \(K_{\mathrm{p}}\) for this reaction is approximately 0.189. In conclusion, the equilibrium pressure of \(\mathrm{H}_{2}(g)\) is 96.0 Torr and the equilibrium constant \(K_{\mathrm{p}}\) for this reaction is approximately 0.189.

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Most popular questions from this chapter

Le Chatelier's principle is stated (Section 13.7\()\) as follows: "If a change is imposed on a system at equilibrium, the position of the equilibrium will shift in a direction that tends to reduce that change." The system $\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \rightleftharpoons 2 \mathrm{NH}_{3}(g)$ is used as an example in which the addition of nitrogen gas at equilibrium results in a decrease in \(\mathrm{H}_{2}\) concentration and an increase in \(\mathrm{NH}_{3}\) concentration. In the experiment the volume is assumed to be constant. On the other hand, if \(\mathrm{N}_{2}\) is added to the reaction system in a container with a piston so that the pressure can be held constant, the amount of \(\mathrm{NH}_{3}\) actually could decrease and the concentration of \(\mathrm{H}_{2}\) would increase as equilibrium is reestablished. Explain how this can happen. Also, if you consider this same system at equilibrium, the addition of an inert gas, holding the pressure constant, does affect the equilibrium position. Explain why the addition of an inert gas to this system in a rigid container does not affect the equilibrium position.

For the reaction $$\mathrm{C}(s)+\mathrm{CO}_{2}(g) \leftrightharpoons 2 \mathrm{CO}(g)$$ \(K_{\mathrm{p}}=2.00\) at some temperature. If this reaction at equilibrium has a total pressure of 6.00 \(\mathrm{atm}\) , determine the partial pressures of \(\mathrm{CO}_{2}\) and \(\mathrm{CO}\) in the reaction container.

Explain the difference between \(K, K_{\mathrm{p}},\) and \(Q\)

Consider the following reaction: $$\mathrm{H}_{2} \mathrm{O}(g)+\mathrm{CO}(g) \rightleftharpoons \mathrm{H}_{2}(g)+\mathrm{CO}_{2}(g)$$ Amounts of \(\mathrm{H}_{2} \mathrm{O}, \mathrm{CO}, \mathrm{H}_{2},\) and \(\mathrm{CO}_{2}\) are put into a flask so that the composition corresponds to an equilibrium position. If the CO placed in the flask is labeled with radioactive \(^{14} \mathrm{C}\) will \(^{14} \mathrm{C}\) be found only in \(\mathrm{CO}\) molecules for an indefinite period of time? Explain.

A sample of iron(II) sulfate was heated in an evacuated container to 920 K, where the following reactions occurred: $$\begin{array}{c}{2 \mathrm{FeSO}_{4}(s) \Longrightarrow \mathrm{Fe}_{2} \mathrm{O}_{3}(s)+\mathrm{SO}_{3}(g)+\mathrm{SO}_{2}(g)} \\\ {\mathrm{SO}_{3}(g) \rightleftharpoons \mathrm{SO}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g)}\end{array}$$ After equilibrium was reached, the total pressure was 0.836 atm and the partial pressure of oxygen was 0.0275 atm. Calculate \(K_{\mathrm{p}}\) for each of these reactions.
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