Question

Predict the sign of the entropy change of the system for each of the following reactions: (a) \(2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{SO}_{3}(g)\) (b) \(\mathrm{Ba}(\mathrm{OH})_{2}(s) \longrightarrow \mathrm{BaO}(s)+\mathrm{H}_{2} \mathrm{O}(g)\) (c) \(\mathrm{CO}(\mathrm{g})+2 \mathrm{H}_{2}(\mathrm{~g}) \longrightarrow \mathrm{CH}_{3} \mathrm{OH}(l)\) (d) \(\mathrm{FeCl}_{2}(s)+\mathrm{H}_{2}(g) \longrightarrow \mathrm{Fe}(s)+2 \mathrm{HCl}(g)\)

Short answer

(a) Entropy change is close to zero or slightly negative. (b) Entropy change is positive. (c) Entropy change is negative. (d) Entropy change is positive.

Step-by-step solution

(a) Analyzing moles and states of SO2 and O2

For the reaction \(2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{SO}_{3}(g)\), we can see that the number of moles of gas on both sides is the same (3 moles of gas in the reactants and 2 moles in the products). Therefore, the change in the number of moles does not help us determine the sign of entropy change.

(a) Conclusion for sign of entropy change

Since no physical states are changing and the number of moles of gas is remaining constant, the entropy change of the system is close to zero or slightly negative.

(b) Analyzing moles and states of Ba(OH)2

For the reaction \(\mathrm{Ba}(\mathrm{OH})_{2}(s) \longrightarrow \mathrm{BaO}(s)+\mathrm{H}_{2} \mathrm{O}(g)\), we see that one mole of solid reactant is producing one mole of solid product and one mole of gaseous product.

(b) Conclusion for sign of entropy change

Since we have a change from solid to gas, the entropy change of the system is positive.

(c) Analyzing moles and states of CO and H2

For the reaction \(\mathrm{CO}(\mathrm{g})+2 \mathrm{H}_{2}(\mathrm{~g}) \longrightarrow \mathrm{CH}_{3} \mathrm{OH}(l)\), we see that three moles of gas are combining to form one mole of liquid product.

(c) Conclusion for sign of entropy change

Since we have a decrease in the number of moles of gas and a change from gas to liquid, the entropy change of the system is negative.

(d) Analyzing moles and states of FeCl2 and H2

For the reaction \(\mathrm{FeCl}_{2}(s)+\mathrm{H}_{2}(g) \longrightarrow \mathrm{Fe}(s)+2 \mathrm{HCl}(g)\), we see that one mole of solid reactant and one mole of gas reactant form one mole of solid product and two moles of gas product.

(d) Conclusion for sign of entropy change

Since we have an increase in the number of moles of gas, the entropy change of the system is positive.

Key concepts

Chemical Reactions and Entropy Change

Understanding the direction of entropy change in chemical reactions is crucial for predicting the spontaneity of processes. Entropy, a measure of disorder or randomness in a system, tends to increase in a closed system over time. During chemical reactions, entropy can either increase or decrease, depending on the specifics of the reaction.

When predicting the sign of entropy change, we consider the number of moles of reactants and products, as well as their states of matter. For example, reaction (a) involves the same number of moles of gaseous reactants and products, which suggests minimal change in entropy. In contrast, reaction (b) produces a gas from a solid, leading to increased disorder and positive entropy change. Reaction (c) reduces the number of moles of gas as it forms a liquid, usually indicating a negative entropy change. Lastly, reaction (d) generates more moles of gas from a solid, again suggesting a rise in entropy.

However, entropy is not solely determined by changes in mole numbers and states of matter. Other factors such as molecular complexity and temperature also play significant roles in the overall entropy of a system. A well-crafted educational resource will convey these nuances to help students fully grasp the entropy changes accompanying chemical reactions.

States of Matter and Entropy

The state of matter is a fundamental concept when learning about entropy. Generally, gases have the highest entropy, followed by liquids, and then solids, which typically have the lowest entropy. This ranking arises from the amount of freedom particles have to move and mix within these states.

In reactions such as the ones presented, noticing the phase transitions can immediately give insights into the entropy change of the system. Transitioning from a solid to a gas, as seen in reaction (b), will lead to greater disorder as the molecules in the gas phase are much more spread out than in a solid. On the other hand, forming a liquid from gases, as in reaction (c), results in a decrease in entropy because the liquid state is more ordered than the gaseous state.

To enhance comprehension, visual aids illustrating particle movement in different states can help students imagine the microscopic view of entropy. Additionally, practical examples, like the entropy increase when ice melts into water or when water evaporates into steam, can make the concept more relatable.

Moles of Gas and Entropy

The concept of moles relates to the amount of substance and is particularly useful in chemistry for quantifying particles in a reaction. When discussing entropy in terms of moles of gas, a greater number of moles implies more particles, which typically means a higher entropy due to increased possibilities for particle arrangement.

For example, in reaction (d), the production of two moles of gas from one solid and one gas indicates an increase in the number of particles that can move freely, resulting in higher entropy. In contrast, when the number of moles of gas diminishes as gases turn into a liquid, as seen in reaction (c), the entropy decreases because the particles are more constrained.

Taking into account the impact of mole changes on entropy, educators can use stoichiometric calculations to illustrate how to predict and quantify entropy changes in chemical reactions. Clarifying that not all particle arrangements contribute equally to the entropy can deepen students' understanding of the probabilistic nature of entropy.