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Chapter 13: Problem 24

For the reaction $$ \mathrm{H}_{2}(g)+\mathrm{Br}_{2}(g) \rightleftharpoons 2 \mathrm{HBr}(g) $$ \(K_{\mathrm{p}}=3.5 \times 10^{4}\) at \(1495 \mathrm{~K}\). What is the value of \(K_{\mathrm{p}}\) for the following reactions at \(1495 \mathrm{~K}\) ? a. \(\mathrm{HBr}(g) \rightleftharpoons \frac{1}{2} \mathrm{H}_{2}(g)+\frac{1}{2} \mathrm{Br}_{2}(g)\) b. \(2 \mathrm{HBr}(g) \rightleftharpoons \mathrm{H}_{2}(g)+\mathrm{Br}_{2}(g)\) c. \(\frac{1}{2} \mathrm{H}_{2}(g)+\frac{1}{2} \mathrm{Br}_{2}(g) \rightleftharpoons \mathrm{HBr}(g)\)

Short Answer

Expert verified
The values of \(K_p\) for the following reactions at \(1495\) K are: a. \(K_{p(a)} = \left(\frac{1}{3.5 \times 10^4}\right)^{\frac{1}{2}} \approx 5.67 \times 10^{-3}\) b. \(K_{p(b)} = \frac{1}{3.5 \times 10^4} \approx 2.86 \times 10^{-5}\) c. \(K_{p(c)} = \left(3.5 \times 10^4\right)^{\frac{1}{2}} \approx 187\)

Step by step solution

01

Recall Equilibrium Constant Manipulation Rules

When manipulating a balanced chemical equation, we need to remember two main rules concerning the equilibrium constant: - If the reaction is reversed, the new equilibrium constant is the reciprocal of the original one. - If the balanced equation is multiplied or divided by a scalar (n), then the new equilibrium constant is raised to the power of (n). 2. Find the value of \(K_p\) for Reaction a
02

Calculate K_p for Reaction a

In reaction a, the given reaction is reversed and divided by 2. This means we need to take the reciprocal of the given \(K_p\) and raise it to the power of (1/2). \[ K_{p(a)} = \left(\frac{1}{K_p}\right)^{\frac{1}{2}} \] Substitute the given \(K_{p}\) value: \[ K_{p(a)} = \left(\frac{1}{3.5 \times 10^4}\right)^{\frac{1}{2}} \] Now calculate the value for \(K_{p(a)}\). 3. Find the value of \(K_p\) for Reaction b
03

Calculate K_p for Reaction b

Reaction b is simply the reverse of the given reaction. This means we need to take the reciprocal of the given \(K_p\). \[ K_{p(b)} = \frac{1}{K_p} \] Substitute the given \(K_{p}\) value: \[ K_{p(b)} = \frac{1}{3.5 \times 10^4} \] Now calculate the value for \(K_{p(b)}\). 4. Find the value of \(K_p\) for Reaction c
04

Calculate K_p for Reaction c

In reaction c, the given reaction is divided by 2. This means we need to raise the given \(K_p\) to the power of (1/2). \[ K_{p(c)} = \left(K_p\right)^{\frac{1}{2}} \] Substitute the given \(K_{p}\) value: \[ K_{p(c)} = \left(3.5 \times 10^4\right)^{\frac{1}{2}} \] Now calculate the value for \(K_{p(c)}\).

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Most popular questions from this chapter

Suppose a reaction has the equilibrium constant \(K=1.3 \times 10^{8}\). What does the magnitude of this constant tell you about the relative concentrations of products and reactants that will be present once equilibrium is reached? Is this reaction likely to be a good source of the products?

A \(1.604-\mathrm{g}\) sample of methane \(\left(\mathrm{CH}_{4}\right)\) gas and \(6.400 \mathrm{~g}\) oxygen gas are sealed into a 2.50-L vessel at \(411^{\circ} \mathrm{C}\) and are allowed to reach equilibrium. Methane can react with oxygen to form gaseous carbon dioxide and water vapor, or methane can react with oxygen to form gaseous carbon monoxide and water vapor. At equilibrium, the pressure of oxygen is \(0.326 \mathrm{~atm}\), and the pressure of water vapor is \(4.45\) atm. Calculate the pressures of carbon monoxide and carbon dioxide present at equilibrium.

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 mixture were \(1.80 \mathrm{~atm}\) and \(1.60 \mathrm{~g} / \mathrm{L}\), respectively. Calculate \(K_{\mathrm{p}}\) for this reaction.

Consider the reaction \(\mathrm{A}(g)+2 \mathrm{~B}(g) \rightleftharpoons \mathrm{C}(g)+\mathrm{D}(g)\) in a 1.0-L rigid flask. Answer the following questions for each situation \((\mathrm{a}-\mathrm{d})\) : i. Estimate a range (as small as possible) for the requested substance. For example, [A] could be between \(95 M\) and \(100 M\) ii. Explain how you decided on the limits for the estimated range. iii. Indicate what other information would enable you to narrow your estimated range. iv. Compare the estimated concentrations for a through d, and explain any differences. a. If at equilibrium \([\mathrm{A}]=1 M\), and then \(1 \mathrm{~mol} \mathrm{C}\) is added, estimate the value for \([\mathrm{A}]\) once equilibrium is reestablished. b. If at equilibrium \([\mathrm{B}]=1 M\), and then \(1 \mathrm{~mol} \mathrm{C}\) is added, estimate the value for [B] once equilibrium is reestablished. c. If at equilibrium \([\mathrm{C}]=1 M\), and then \(1 \mathrm{~mol} \mathrm{C}\) is added, estimate the value for \([\mathrm{C}]\) once equilibrium is reestablished. d. If at equilibrium \([\mathrm{D}]=1 M\), and then \(1 \mathrm{~mol} \mathrm{C}\) is added, estimate the value for [D] once equilibrium is reestablished.

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