Problem 79
Question
For each of these processes at \(25^{\circ} \mathrm{C}\), indicate whether the entropy effect, the energy effect, both, or neither favors the process. $$ \text { (a) } \begin{aligned} \mathrm{C}_{3} \mathrm{H}_{8}(\mathrm{~g})+5 \mathrm{O}_{2}(\mathrm{~g}) \rightleftharpoons 3 \mathrm{CO}_{2}(\mathrm{~g})+4 \mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \\ \Delta_{t} H^{\circ}=&-2045 \mathrm{~kJ} / \mathrm{mol} \end{aligned} $$ (b) \(\mathrm{Br}_{2}(\mathrm{~g}) \rightleftharpoons \mathrm{Br}_{2}(\ell)\) $$ \Delta_{r} H^{\circ}=-31 \mathrm{~kJ} / \mathrm{mol} $$ $$ \text { (c) } 2 \mathrm{Ag}(\mathrm{s})+3 \mathrm{~N}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{AgN}_{3}(\mathrm{~s}) \quad \Delta_{\mathrm{r}} H^{\circ}=618 \mathrm{~kJ} / \mathrm{mol} $$
Step-by-Step Solution
Verified Answer
(a) Both effects favor; (b) Only energy effect favors; (c) Neither effect favors.
1Step 1: Analyze Reaction (a)
For reaction \( \text{(a)} \), \( \Delta_{t} H^{\circ}=-2045 \text{ kJ/mol} \), indicating an exothermic process, so the energy effect favors the process. To determine the entropy effect, count the gas moles: 6 moles on the left, 7 moles on the right, indicating an increase in entropy. Thus, both energy and entropy effects favor the process.
2Step 2: Analyze Reaction (b)
For reaction \( \text{(b)} \), \( \Delta_{r} H^{\circ}=-31 \text{ kJ/mol} \), making it exothermic, so the energy effect favors the process. However, the process is a gas condensing to a liquid, indicating a decrease in entropy. Hence, only the energy effect favors the process.
3Step 3: Analyze Reaction (c)
For reaction \( \text{(c)} \), \( \Delta_{r} H^{\circ}=618 \text{ kJ/mol} \), implying an endothermic process, so the energy effect does not favor the process. The reaction results in a decrease in the number of gas moles from 3 to 0, leading to a decrease in entropy, which also does not favor the process. Therefore, neither energy nor entropy effects favor this process.
Key Concepts
EntropyEnergy effectExothermic and Endothermic reactions
Entropy
Entropy is a key concept in thermodynamics that measures the disorder or randomness of a system. In chemistry, when a reaction occurs, we often look at the change in entropy to determine whether the system is becoming more disordered.
For example, in reaction (a) from the exercise, the number of gas molecules increases from 6 to 7. This suggests an increase in disorder, meaning that the entropy effect favors the process because it tends to increase with more gas molecules. When gas molecules increase, the randomness also increases, thus favoring the reaction.
On the other hand, in reaction (b), a gas turns into a liquid, which significantly decreases the disorder. Hence, the entropy effect does not favor this process. Lastly, reaction (c) shows a decrease in the number of gas molecules from the reactants to the products, going from 3 moles of gas to a more ordered solid form. This results in decreased entropy, which does not favor the process either.
Understanding entropy helps us predict whether a reaction will naturally proceed based on the change in disorder.
For example, in reaction (a) from the exercise, the number of gas molecules increases from 6 to 7. This suggests an increase in disorder, meaning that the entropy effect favors the process because it tends to increase with more gas molecules. When gas molecules increase, the randomness also increases, thus favoring the reaction.
On the other hand, in reaction (b), a gas turns into a liquid, which significantly decreases the disorder. Hence, the entropy effect does not favor this process. Lastly, reaction (c) shows a decrease in the number of gas molecules from the reactants to the products, going from 3 moles of gas to a more ordered solid form. This results in decreased entropy, which does not favor the process either.
Understanding entropy helps us predict whether a reaction will naturally proceed based on the change in disorder.
Energy effect
In addition to entropy, the energy effect of a reaction is crucial in determining whether it is likely to occur. The energy effect is typically described in terms of enthalpy change (\( \Delta H \)), which tells us whether a reaction liberates or absorbs heat.
For reaction (a), the enthalpy change is highly negative (\( \Delta_{t} H^{\circ}=-2045 \text{ kJ/mol} \)), indicating that the reaction is exothermic. It releases energy, thus the energy effect favors the process.
Similarly, reaction (b) has an enthalpy change of \( \Delta_{r} H^{\circ}=-31 \text{ kJ/mol} \), which means it also releases heat, favoring the process through the energy effect.
Contrastingly, reaction (c) involves an endothermic process with \( \Delta_{r} H^{\circ}=618 \text{ kJ/mol} \), suggesting that energy is absorbed rather than released. Here, the energy effect does not favor the reaction, since input energy is needed for the reaction to proceed.
The energy effect helps us understand the feasibility of reactions in terms of heat exchange.
For reaction (a), the enthalpy change is highly negative (\( \Delta_{t} H^{\circ}=-2045 \text{ kJ/mol} \)), indicating that the reaction is exothermic. It releases energy, thus the energy effect favors the process.
Similarly, reaction (b) has an enthalpy change of \( \Delta_{r} H^{\circ}=-31 \text{ kJ/mol} \), which means it also releases heat, favoring the process through the energy effect.
Contrastingly, reaction (c) involves an endothermic process with \( \Delta_{r} H^{\circ}=618 \text{ kJ/mol} \), suggesting that energy is absorbed rather than released. Here, the energy effect does not favor the reaction, since input energy is needed for the reaction to proceed.
The energy effect helps us understand the feasibility of reactions in terms of heat exchange.
Exothermic and Endothermic reactions
Exothermic and endothermic reactions are terms used to describe whether energy is released or absorbed during a chemical reaction.
In an exothermic reaction, heat is released to the surroundings. For example, reactions (a) and (b) both show negative enthalpy changes, meaning they give off heat. This usually occurs when bonds forming in the products are stronger than those broken in the reactants.
Conversely, an endothermic reaction, like reaction (c), absorbs heat, indicated by a positive enthalpy change. During these reactions, the system requires heat to convert reactants into products.
In an exothermic reaction, heat is released to the surroundings. For example, reactions (a) and (b) both show negative enthalpy changes, meaning they give off heat. This usually occurs when bonds forming in the products are stronger than those broken in the reactants.
- Exothermic reactions often result in temperature increase of the system.
- They can proceed spontaneously if other conditions like entropy are also favorable.
Conversely, an endothermic reaction, like reaction (c), absorbs heat, indicated by a positive enthalpy change. During these reactions, the system requires heat to convert reactants into products.
- Endothermic reactions often lead to a temperature drop in the system.
- Such reactions are not spontaneous unless compensated by other factors, such as a large increase in entropy.
Other exercises in this chapter
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