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Chapter 12: Problem 35

At a certain temperature, \(K\) is \(1.3 \times 10^{5}\) for the reaction $$2 \mathrm{H}_{2}(g)+\mathrm{S}_{2}(g) \rightleftharpoons 2 \mathrm{H}_{2} \mathrm{~S}(g)$$ What is the equilibrium pressure of hydrogen sulfide if those of hydrogen and sulfur gases are \(0.103\) atm and \(0.417\) atm, respectively?

Short Answer

Expert verified
Question: Given the reaction H2(g) + S2(g) ⇌ 2H2S(g) with an equilibrium constant K = 1.3 x 10^5, find the equilibrium pressure of H2S if the equilibrium pressures of H2 and S2 are 0.103 atm and 0.417 atm, respectively. Answer: The equilibrium pressure of hydrogen sulfide (H2S) is approximately 0.449 atm.

Step by step solution

01

Write down the expression for the equilibrium constant (K)

According to the given balanced chemical equation, the expression for the equilibrium constant (K) can be written as follows: $$K = \frac{P_{H_2S}^2}{P_{H_2}^2 \times P_{S_2}}$$ Here, \(P_{H_2S}\) is the equilibrium pressure of hydrogen sulfide, \(P_{H_2}\) is the equilibrium pressure of hydrogen, and \(P_{S_2}\) is the equilibrium pressure of sulfur.
02

Insert the given values into the expression for K

We have K = \(1.3 \times 10^{5}\), \(P_{H_2} = 0.103\) atm, and \(P_{S_2} = 0.417\) atm. Plugging these values into the expression for K, we get: $$1.3 \times 10^{5} = \frac{P_{H_2S}^2}{(0.103)^2 \times 0.417}$$
03

Solve for the equilibrium pressure of hydrogen sulfide (\(P_{H_2S}\))

Now, we just need to solve for \(P_{H_2S}\): $$P_{H_2S}^2 = 1.3 \times 10^{5} \times (0.103)^2 \times 0.417$$ $$P_{H_2S} = \sqrt{1.3 \times 10^{5} \times (0.103)^2 \times 0.417}$$ $$P_{H_2S} \approx 0.449 \text{ atm}$$ So, the equilibrium pressure of hydrogen sulfide is approximately 0.449 atm.

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Most popular questions from this chapter

Consider the following reaction at a certain temperature: $$2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{NO}_{2}(g)$$ A reaction mixture contains \(0.70 \mathrm{~atm}\) of \(\mathrm{O}_{2}\) and \(0.81\) atm of NO. When equilibrium is established, the total pressure in the reaction vessel is \(1.20 \mathrm{~atm}\). Find \(K\)

For the following reactions, predict whether the pressure of the reactants or products increases or remains the same when the volume of the reaction vessel is increased. (a) \(\mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons \mathrm{H}_{2} \mathrm{O}(g)\) (b) \(\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \rightleftharpoons 2 \mathrm{NH}_{3}(g)\) (c) \(\mathrm{C}_{2} \mathrm{H}_{4}(g)+\mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(g)\)

Isopropyl alcohol is the main ingredient in rubbing alcohol. It can decompose into acetone (the main ingredient in nail polish remover) and hydrogen gas according to the following reaction: $$\mathrm{C}_{3} \mathrm{H}_{7} \mathrm{OH}(g) \rightleftharpoons \mathrm{C}_{2} \mathrm{H}_{6} \mathrm{CO}(g)+\mathrm{H}_{2}(g)$$ At \(180^{\circ} \mathrm{C}\), the equilibrium constant for the decomposition is \(0.45\). If \(20.0 \mathrm{~mL}\) \((d=0.785 \mathrm{~g} / \mathrm{mL})\) of isopropyl alcohol is placed in a \(5.00\) -L vessel and heated to \(180^{\circ} \mathrm{C}\), what percentage remains undissociated at equilibrium?

. For the reaction $$\mathrm{C}(s)+\mathrm{CO}_{2}(g) \rightleftharpoons 2 \mathrm{CO}(g)$$ \(K=168\) at \(1273 \mathrm{~K}\). If one starts with \(0.3\) atm of \(\mathrm{CO}_{2}\) and \(12.0 \mathrm{~g}\) of \(\mathrm{C}\) at \(1273 \mathrm{~K}\), will the equilibrium mixture contain (a) mostly \(\mathrm{CO}_{2}\) ? (b) mostly CO? (c) roughly equal amounts of \(\mathrm{CO}_{2}\) and \(\mathrm{CO}\) ? (d) only C?

Benzaldehyde, a flavoring agent, is obtained by the dehydrogenation of benzyl alcohol. $$\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CH}_{2} \mathrm{OH}(g) \rightleftharpoons \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CHO}(g)+\mathrm{H}_{2}(g)$$ \(K\) for the reaction at \(250^{\circ} \mathrm{C}\) is \(0.56\). If \(1.50 \mathrm{~g}\) of benzyl alcohol is placed in a 2.0-L flask and heated to \(250^{\circ} \mathrm{C}\), (a) what is the partial pressure of the benzaldehyde when equilibrium is established? (b) how many grams of benzyl alcohol remain at equilibrium?
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