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Chapter 14: Problem 123

Iodine, \(\mathrm{I}_{2}\), is a blue-black solid, but it easily vaporizes to give a violet vapor. At high temperatures, this molecular substance dissociates to atoms: $$ \mathrm{I}_{2}(g) \rightleftharpoons 2 \mathrm{I}(g) $$ An absent-minded professor measured equilibrium constants for this dissociation at two temperatures, \(700^{\circ} \mathrm{C}\) and \(800^{\circ} \mathrm{C}\). He obtained the \(K_{p}\) values 0.01106 and \(0.001745,\) but he couldn't remember which value went with what temperature. Can you please help him assign temperatures to the equilibrium constants? State your argument carefully.

Short Answer

Expert verified
0.01106 is for 800掳C, and 0.001745 is for 700掳C.

Step by step solution

01

Write the Reaction

The reaction in question is the dissociation of iodine molecules to iodine atoms: \[ \mathrm{I}_{2}(g) \rightleftharpoons 2 \mathrm{I}(g) \]This equilibrium can be described by the equilibrium constant \(K_p\), which depends on the temperature.
02

Understand the Nature of the Reaction

Dissociation of \(\mathrm{I}_2\) into \(\mathrm{I}\) atoms is an endothermic process. Endothermic reactions absorb heat, leading to higher dissociation at higher temperatures, which increases the equilibrium constant \(K_p\).
03

Analyze the Relation Between Temperature and \(K_p\)

According to the principle of increased molecular motion at higher temperatures, endothermic reactions favor product formation more at higher temperatures, which means the value of \(K_p\) will be higher at higher temperatures.
04

Assign Equilibrium Constants to Temperatures

Since the dissociation of \(\mathrm{I}_2\) is endothermic and requires energy, the higher \(K_p\) value (0.01106) should correspond to the higher temperature (800掳C), while the lower \(K_p\) value (0.001745) should correspond to 700掳C.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Endothermic Reaction
In chemistry, an endothermic reaction is one that absorbs energy from its surroundings, usually in the form of heat. This kind of reaction requires energy input to proceed, unlike exothermic reactions that release energy. When iodine molecules (\(\mathrm{I}_2\)) dissociate into iodine atoms (\(\mathrm{I}\)), it is an endothermic process. This means that energy is absorbed to break the bonds between the iodine atoms in the molecule.

Key characteristics of endothermic reactions include:
  • Heat absorption makes the surroundings cooler.
  • Products have higher energy than reactants.
  • Reactions may require constant heating to proceed.
Understanding that the dissociation of iodine is endothermic helps in predicting how the reaction behaves with temperature changes.
Equilibrium Constant
In a chemical equilibrium, the equilibrium constant (\(K_p\)) quantitatively describes the ratio of concentrations of products to reactants at equilibrium. For any given chemical reaction, the equilibrium constant is a crucial measure that tells us how far the reaction proceeds before reaching equilibrium.

For the dissociation of \(\mathrm{I}_2(g)\rightleftharpoons 2\mathrm{I}(g)\), the equilibrium constant can be represented as: \[K_p = \frac{\text{[products]}}{\text{[reactants]}}\], which in this scenario translates to:\[K_p = \frac{[\mathrm{I}]^{2}}{[\mathrm{I}_{2}]}\].

When we talk about equilibrium, it's a state where the forward and reverse reactions occur at equal rates, meaning there is no net change in concentrations of reactants and products. A higher \(K_p\) value suggests products are favored, while a lower value suggests reactants are favored.
Temperature Dependence
Chemical equilibrium is sensitive to temperature, especially for endothermic reactions like the dissociation of iodine. When temperature increases, it directly influences the equilibrium constant.

For endothermic reactions, as temperature rises:
  • The added energy allows more reactant molecules to convert to products.
  • The equilibrium position shifts to favor products, thereby increasing \(K_p\).
  • This behavior aligns with Le Chatelier's Principle, which predicts that increasing the temperature of an endothermic reaction shifts the equilibrium towards the products.
In the iodine dissociation case, the higher \(K_p\) value at a higher temperature (800掳C) confirms that product formation (more iodine atoms) is favored when energy in the form of heat is supplied.

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Most popular questions from this chapter

When 0.0322 mol of \(\mathrm{NO}\) and \(1.52 \mathrm{~g}\) of bromine are placed in a 1.00 - \(\mathrm{L}\) reaction vessel and sealed, the mixture reacts and the following equilibrium is established: $$ 2 \mathrm{NO}(g)+\mathrm{Br}_{2}(g) \rightleftharpoons 2 \mathrm{NOBr}(g) $$ At \(25^{\circ} \mathrm{C}\) the equilibrium pressure of nitrosyl bromide is \(0.438 \mathrm{~atm} .\) What is \(K_{p} ?\)

Nitrogen monoxide, NO, reacts with bromine, \(\mathrm{Br}_{2}\), to give nitrosyl bromide, \(\mathrm{NOBr}\). $$ 2 \mathrm{NO}(g)+\mathrm{Br}_{2}(g) \rightleftharpoons 2 \mathrm{NOBr}(g) $$ A sample of 0.0524 mol NO with 0.0262 mol \(\mathrm{Br}_{2}\) gives an equilibrium mixture containing \(0.0311 \mathrm{~mol} \mathrm{NOBr}\). What is the composition of the equilibrium mixture?

The equilibrium constant \(K_{c}\) equals 0.0952 for the following reaction at \(227^{\circ} \mathrm{C}\). $$ \mathrm{CH}_{3} \mathrm{OH}(g) \rightleftharpoons \mathrm{CO}(g)+2 \mathrm{H}_{2}(g) $$ What is the value of \(K_{p}\) at this temperature?

Suppose sulfur dioxide reacts with oxygen at \(25^{\circ} \mathrm{C}\). $$ 2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{SO}_{3}(g) $$ The equilibrium constant \(K_{c}\) equals \(8.0 \times 10^{35}\) at this temperature. From the magnitude of \(K_{c}\), do you think this reaction occurs to any great extent when equilibrium is reached at room temperature? If an equilibrium mixture is \(1.0 \mathrm{M}\) \(\mathrm{SO}_{3}\) and has equal concentrations of \(\mathrm{SO}_{2}\) and \(\mathrm{O}_{2}\), what is the concentration of \(\mathrm{SO}_{2}\) in the mixture? Does this result agree with what you expect from the magnitude of \(K_{c} ?\)

Write the expression for the equilibrium constant \(K_{c}\) for each of the following equations: $$ \begin{array}{l} \text { a } \mathrm{C}(s)+\mathrm{CO}_{2}(g) \rightleftharpoons 2 \mathrm{CO}(g) \\ \text { b } \mathrm{FeO}(s)+\mathrm{CO}(g) \rightleftharpoons \mathrm{Fe}(s)+\mathrm{CO}_{2}(g) \\ \text { c } \mathrm{Na}_{2} \mathrm{CO}_{3}(s)+\mathrm{SO}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \rightleftharpoons \mathrm{Na}_{2} \mathrm{SO}_{4}(s)+\mathrm{CO}_{2}(g) \\ \text { d } \mathrm{PbI}_{2}(s) \rightleftharpoons \mathrm{Pb}^{2+}(a q)+2 \mathrm{I}^{-(a q)} \end{array} $$
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