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Chapter 12: Problem 109

An \(8.00-\mathrm{g}\) sample of \(\mathrm{SO}_{3}\) was placed in an evacuated container, where it decomposed at \(600^{\circ} \mathrm{C}\) according to the following reaction: $$\mathrm{SO}_{3}(g) \rightleftharpoons \mathrm{SO}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g)$$ At equilibrium the total pressure and the density of the gaseous mixtures were 1.80 atm and \(1.60 \mathrm{g} / \mathrm{L},\) respectively. Calculate \(K_{\mathrm{p}}\) for this reaction.

Short Answer

Expert verified
The short answer to this question is: To calculate the equilibrium constant \(K_p\) for the given reaction, follow these steps: 1. Calculate the initial moles of SO3 2. Calculate the moles of SO3, SO2, and O2 at equilibrium 3. Calculate the total moles of gases at equilibrium 4. Calculate the volume of the container 5. Calculate the partial pressures of the gases at equilibrium 6. Calculate the total pressure at equilibrium 7. Solve for x (the moles of SO3 decomposed) 8. Calculate the equilibrium constant \(K_p\) By following these steps, you can find the equilibrium constant Kp for this reaction.

Step by step solution

01

1. Calculate the Initial Moles of SO3

To find the initial moles of SO3, we will calculate it using the provided mass by dividing it by the molar mass of SO3: \(n_{SO3(initial)} = \frac{8.00g}{(32.07g/mol + 3(16g/mol))}\)
02

2. Calculate the Moles of SO3 at Equilibrium

Let's assume x moles of SO3 have decomposed at equilibrium. Then, the final moles of SO3 would be: \(n_{SO3(final)} = n_{SO3(initial)} - x\)
03

3. Calculate the Moles of SO2 and O2 at Equilibrium

As x moles of SO3 have decomposed, the final moles of SO2 and O2 would be: \(n_{SO2} = x\) \(n_{O2} = \frac{1}{2}x\)
04

4. Calculate the Total Moles of Gases at Equilibrium

Adding the moles of all three gases gives: \(n_{total} = n_{SO_3(final)} + n_{SO_2} + n_{O_2} = (n_{SO_3(initial)} - x) + x + \frac{1}{2}x\)
05

5. Calculate the Volume of the Container

Using the density, we can calculate the volume of the container: \(V = \frac{mass_{total}}{density} = \frac{8.00 g}{1.60 g/L}\)
06

6. Calculate the Partial Pressures at Equilibrium

Dividing the moles of each gas by the volume and then multiplying by the gas constant R and the temperature T, we can find the partial pressures of the gases at equilibrium: \(P_{SO3} = \frac{n_{SO3(final)}RT}{V}\) \(P_{SO2} = \frac{n_{SO2}RT}{V}\) \(P_{O2} = \frac{n_{O2}RT}{V}\)
07

7. Calculate the Total Pressure at Equilibrium

Using the partial pressures, we can find the total pressure at equilibrium: \(P_{total} = P_{SO3} + P_{SO2} + P_{O2}\)
08

8. Solve for x

Plug in the given total pressure (1.80 atm) into the total pressure equation obtained in step 7 and solve for x.
09

9. Calculate Kp

Now that we have calculated the partial pressures at equilibrium, we can determine the equilibrium constant Kp: \(K_p = \frac{P_{SO2}P_{O2}^{1/2}}{P_{SO3}}\) By calculating each step of the solution and inputting the values, we'll find the equilibrium constant, Kp, for this reaction.

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Most popular questions from this chapter

A sample of iron(II) sulfate was heated in an evacuated container to \(920 \mathrm{K},\) where the following reactions occurred:$$\begin{array}{c}2 \mathrm{FeSO}_{4}(s) \rightleftharpoons \mathrm{Fe}_{2} \mathrm{O}_{3}(s)+\mathrm{SO}_{3}(g)+\mathrm{SO}_{2}(g) \\ \mathrm{SO}_{3}(g) \rightleftharpoons \mathrm{SO}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \end{array}$$.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.

The equilibrium constant \(K_{\mathrm{p}}\) for the reaction $$\mathrm{CCl}_{4}(g) \rightleftharpoons \mathrm{C}(s)+2 \mathrm{Cl}_{2}(g)$$ at \(700^{\circ} \mathrm{C}\) is \(0.76 .\) Determine the initial pressure of carbon tetrachloride that will produce a total equilibrium pressure of 1.20 atm at \(700^{\circ} \mathrm{C}\).

Suppose a reaction has the equilibrium constant \(K=1.7 \times 10^{-8}\) at a particular temperature. Will there be a large or small amount of unreacted starting material present when this reaction reaches equilibrium? Is this reaction likely to be a good source of products at this temperature?

Which of the following statements is(are) true? Correct the false statement(s). a. When a reactant is added to a system at equilibrium at a given temperature, the reaction will shift right to reestablish equilibrium. b. When a product is added to a system at equilibrium at a given temperature, the value of \(K\) for the reaction will increase when equilibrium is reestablished. c. When temperature is increased for a reaction at equilibrium, the value of \(K\) for the reaction will increase. d. When the volume of a reaction container is increased for a system at equilibrium at a given temperature, the reaction will shift left to reestablish equilibrium. e. Addition of a catalyst (a substance that increases the speed of the reaction) has no effect on the equilibrium position.

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.)
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