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Chapter 17: Problem 105

Which of the following reactions (or processes) are expected to have a negative value for \(\Delta S^{\circ} ?\) a. \(\mathrm{SiF}_{6}(a q)+\mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{HF}(g)+\mathrm{SiF}_{4}(g)\) b. \(4 \mathrm{Al}(s)+3 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{Al}_{2} \mathrm{O}_{3}(s)\) c. \(\mathrm{CO}(g)+\mathrm{Cl}_{2}(g) \longrightarrow \mathrm{COCl}_{2}(g)\) d. \(\mathrm{C}_{2} \mathrm{H}_{4}(g)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(l)\) e. \(\mathrm{H}_{2} \mathrm{O}(s) \longrightarrow \mathrm{H}_{2} \mathrm{O}(l)\)

Short Answer

Expert verified
The reactions with negative 螖S掳 are: - Reaction b: \(4 \mathrm{Al}(s) + 3 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{Al}_{2} \mathrm{O}_{3}(s)\) - Reaction c: \(\mathrm{CO}(g) + \mathrm{Cl}_{2}(g) \longrightarrow \mathrm{COCl}_{2}(g)\) - Reaction d: \(\mathrm{C}_{2} \mathrm{H}_{4}(g) + \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(l)\)

Step by step solution

01

Analyze each reaction

We will go through each of the given reactions and compare the particles and states in the reactants and products. a. SiF6(aq) + H2(g) 鈫� 2 HF(g) + SiF4(g) Reactants: 1 aqueous, 1 gas Products: 2 gases In this case, the number of gas particles increased, so the disorder increases. 螖S掳 will be positive. b. 4 Al(s) + 3 O2(g) 鈫� 2 Al2O3(s) Reactants: 4 solids, 3 gases Products: 2 solids Here, the number of gas particles decreased, and the number of solid particles also decreased. As a result, the disorder decreases, and 螖S掳 will be negative. c. CO(g) + Cl2(g) 鈫� COCl2(g) Reactants: 1 gas, 1 gas Products: 1 gas The number of gas particles decreased, so the disorder decreases. 螖S掳 will be negative. d. C2H4(g) + H2O(l) 鈫� C2H5OH(l) Reactants: 1 gas, 1 liquid Products: 1 liquid The number of gas particles decreased, so the disorder decreases. 螖S掳 will be negative. e. H2O(s) 鈫� H2O(l) Reactants: 1 solid Products: 1 liquid In this case, there is a transition from a solid state to a liquid state, which increases the disorder. 螖S掳 will be positive.
02

Answer the question

Based on our analysis of each reaction, the reactions with negative 螖S掳 are: - Reaction b: 4 Al(s) + 3 O2(g) 鈫� 2 Al2O3(s) - Reaction c: CO(g) + Cl2(g) 鈫� COCl2(g) - Reaction d: C2H4(g) + H2O(l) 鈫� C2H5OH(l)

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Key Concepts

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

Thermodynamics
Thermodynamics explores the energy changes involved in chemical reactions. One essential part is entropy, which measures system disorder. When we talk about a reaction having negative or positive entropy change (\( \Delta S ^{\circ} \)), it tells us if the disorder in the system decreases or increases. A positive \( \Delta S ^{\circ} \) indicates an increase in disorder, whereas a negative \( \Delta S ^{\circ} \) signifies a decrease. Understanding how energy is transferred and transformed during reactions is crucial to predicting if reactions occur spontaneously. Thermodynamics helps us grasp why certain chemical processes are favorable and others are not. It acts like a guide for chemists, indicating the direction that reactions should naturally proceed.
Chemical Reactions
Chemical reactions involve the transformation of reactants into products. They are central to chemistry and can exhibit different behaviors regarding entropy changes. Knowing the states of reactants and products allows us to predict whether reactions entail an increase or decrease in disorder. For instance, a reaction that forms gaseous products from solids often increases disorder and, thus, has a positive entropy change. Conversely, processes that condense gases into liquids or solids typically lower disorder, leading to negative entropy changes. In our exercises, reactions transforming multiple gases into fewer particles often result in decreased disorder, featuring a negative \( \Delta S ^{\circ} \). Understanding the nature of reactants and products gives clarity to how reactions will behave energetically.
States of Matter
The states of matter - solid, liquid, gas - are key in defining the entropy of a system. Gases, with highly disordered particles, usually possess more entropy compared to liquids and solids. In analyzing the entropy change of a reaction, acknowledging the states helps determine changes in disorder. For example, a solid to liquid transition generally increases disorder because liquid particles move more freely than solid ones. Oppositely, the formation of solids from gases usually results in decreased entropy. In a reaction, identifying how states of matter switch between reactants and products lets us predict \( \Delta S ^{\circ} \), whether it rises or falls. Thus, understanding states of matter provides insight into the impact on overall physical changes in reactions.
Disorder in Chemistry
Disorder, or entropy, is a crucial concept in chemistry, reflecting a system's randomness. More disorder signifies higher entropy, while ordered states have lower entropy. In chemistry, shifts in states of matter or reduced particle numbers typically lead to decreased disorder. This is what's seen in reactions that combine particles or transition materials to a more ordered solid state. On the other hand, reactions forming gases or breaking down solids into more dispersed particles increase disorder. Entropy, therefore, is a valuable indicator of energy dispersal within a reaction. It helps explain phenomena like why ice melts naturally (increased disorder). Familiarity with how reactions affect disorder allows chemists to better predict and control chemical processes, offering immense practical benefits.

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Most popular questions from this chapter

What information can be determined from \(\Delta G\) for a reaction? Does one get the same information from \(\Delta G^{\circ},\) the standard free energy change? \(\Delta G^{\circ}\) allows determination of the equilibrium constant \(K\) for a reaction. How? How can one estimate the value of \(K\) at temperatures other than \(25^{\circ} \mathrm{C}\) for a reaction? How can one estimate the temperature where \(K=1\) for a reaction? Do all reactions have a specific temperature where \(K=1 ?\)

Some water is placed in a coffee-cup calorimeter. When 1.0 \(\mathrm{g}\) of an ionic solid is added, the temperature of the solution increases from \(21.5^{\circ} \mathrm{C}\) to \(24.2^{\circ} \mathrm{C}\) as the solid dissolves. For the dissolving process, what are the signs for \(\Delta S_{\mathrm{sys}}, \Delta S_{\mathrm{surt}},\) and \(\Delta S_{\mathrm{univ}} ?\)

The melting point for carbon diselenide \(\left(\mathrm{CSe}_{2}\right)\) is \(-46^{\circ} \mathrm{C}\) . At a temperature of \(-75^{\circ} \mathrm{C},\) predict the signs for \(\Delta S_{\mathrm{surr}}\) and \(\Delta S_{\mathrm{univ}}\) for the following process: \(\operatorname{CSe}_{2}(l) \rightarrow \operatorname{CSe}_{2}(s)\)

Consider the following reaction at \(25.0^{\circ} \mathrm{C} :\) $$2 \mathrm{NO}_{2}(g) \rightleftharpoons \mathrm{N}_{2} \mathrm{O}_{4}(g)$$ The values of \(\Delta H^{\circ}\) and \(\Delta S^{\circ}\) are \(-58.03\) kJ/mol and \(-176.6 \mathrm{J} / \mathrm{K}\) . mol, respectively. Calculate the value of \(K\) at \(25.0^{\circ} \mathrm{C}\) . Assuming \(\Delta H^{\circ}\) and \(\Delta S^{\circ}\) are temperature independent, estimate the value of \(K\) at \(100.0^{\circ} \mathrm{C}\) .

At what temperatures will the following processes be spontaneous? a. \(\Delta H=-18 \mathrm{kJ}\) and \(\Delta S=-60 . \mathrm{J} / \mathrm{K}\) b. \(\Delta H=+18 \mathrm{kJ}\) and \(\Delta S=+60 . \mathrm{JK}\) c. \(\Delta H=+18 \mathrm{kJ}\) and \(\Delta S=-60 . \mathrm{J} / \mathrm{K}\) d. \(\Delta H=-18 \mathrm{kJ}\) and \(\Delta S=+60 . \mathrm{J} / \mathrm{K}\)
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