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Chapter 13: Problem 36

At \(1100 \mathrm{K}, K_{\mathrm{p}}=0.25\) for the reaction $$2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{SO}_{3}(g)$$ What is the value of \(K\) at this temperature?

Short Answer

Expert verified
The value of K at 1100 K for the given reaction is approximately 22.58.

Step by step solution

01

Calculate the change in moles of gas (∆n) in the balanced equation

First, we need to determine the change in the number of moles of gas in the balanced equation: Reactants: 2 moles of SO2(g) + 1 mole of O2(g) = 3 moles Products: 2 moles of SO3(g) ∆n = moles of products - moles of reactants ∆n = 2 - 3 = -1
02

Use the relation between Kp and Kc to find Kc

Now we'll use the relationship between Kp and Kc, which is: \( K_{p} = K_{c}(RT)^{\Delta n} \) Where R is the universal gas constant (0.0821 L atm/mol K), T is the temperature in Kelvin, and ∆n is the change in the number of moles of gas. We have Kp = 0.25, T = 1100 K, and ∆n = -1. Substituting these values into the formula, we get: \( 0.25 = K_{c}(0.0821\times1100)^{-1} \)
03

Determine the value of K (Kc)

To find Kc, we'll now solve the equation for Kc: \( K_{c} = \frac{0.25}{(0.0821\times1100)^{-1}} \) \( K_{c} = 0.25\times(0.0821\times1100) \) \( K_{c} = 0.25\times90.31 \) Calculating the value, we get: \( K_{c} = 22.5775 \) Therefore, the value of K at 1100 K is approximately 22.58.

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Most popular questions from this chapter

At \(25^{\circ} \mathrm{C}, K_{\mathrm{p}}=5.3 \times 10^{5}\) for the reaction $$\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \rightleftharpoons 2 \mathrm{NH}_{3}(g)$$ When a certain partial pressure of \(\mathrm{NH}_{3}(g)\) is put into an otherwise empty rigid vessel at \(25^{\circ} \mathrm{C}\) , equilibrium is reached when 50.0\(\%\) of the original ammonia has decomposed. What was the original partial pressure of ammonia before any decomposition occurred?

At \(2200^{\circ} \mathrm{C}, K_{\mathrm{p}}=0.050\) for the reaction $$\mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{NO}(g)$$ What is the partial pressure of NO in equilibrium with \(\mathrm{N}_{2}\) and \(\mathrm{O}_{2}\) that were placed in a flask at initial pressures of 0.80 and \(0.20 \mathrm{atm},\) respectively?

What will happen to the number of moles of \(\mathrm{SO}_{3}\) in equilibrium with \(\mathrm{SO}_{2}\) and \(\mathrm{O}_{2}\) in the reaction $$2 \mathrm{SO}_{3}(g) \rightleftharpoons 2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g)$$ in each of the following cases? a. Oxygen gas is added. b. The pressure is increased by decreasing the volume of the reaction container. c. In a rigid reaction container, the pressure is increased by adding argon gas. d. The temperature is decreased (the reaction is endothermic). e. Gaseous sulfur dioxide is removed.

At \(25^{\circ} \mathrm{C}, K=0.090\) for the reaction $$\mathrm{H}_{2} \mathrm{O}(g)+\mathrm{Cl}_{2} \mathrm{O}(g) \rightleftharpoons 2 \mathrm{HOCl}(g)$$ Calculate the concentrations of all species at equilibrium for each of the following cases. a. 1.0 \(\mathrm{g} \mathrm{H}_{2} \mathrm{O}\) and 2.0 $\mathrm{g} \mathrm{Cl}_{2} \mathrm{O}$ are mixed in a 1.0 -L flask. b. 1.0 mole of pure HOCl is placed in a 2.0 \(\mathrm{L}\) flask.

At a particular temperature, a \(3.0-\mathrm{L}\) flask contains 2.4 moles of \(\mathrm{Cl}_{2}, 1.0\) mole of \(\mathrm{NOCl}\) , and \(4.5 \times 10^{-3}\) mole of NO. Calculate \(K\) at this temperature for the following reaction: $$2 \mathrm{NOCl}(g) \rightleftharpoons 2 \mathrm{NO}(g)+\mathrm{Cl}_{2}(g)$$
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