Question

Predict the sign of \(\Delta S_{\text { system for each of the following changes. }}\) a. \(C I F(g)+F_{2}(g) \rightarrow C | F_{3}(g)\) c. \(C H_{3} O H(1) \rightarrow C H_{3} O H(a q)\) b. \(N H_{3}(g) \rightarrow N H_{3}(a q)\) d. \(C_{10} H_{8}(1) \rightarrow C_{10} H_{8}(s)\)

Short answer

a. \(\Delta S_{\text{system}} \approx 0\) (no substantial change in disorder) b. \(\Delta S_{\text{system}} < 0\) (system becomes less disordered) c. \(\Delta S_{\text{system}} > 0\) (system becomes more disordered) d. \(\Delta S_{\text{system}} < 0\) (system becomes less disordered)

Step-by-step solution

Compare the number of moles of the reactants and products

In this reaction, \(C I F(g)\) and \(F_{2}(g)\) are combining to form \(C I F_{3}(g)\), which means one mole of gas is reacting with another mole of gas to form one mole of gas.

Determine the entropy change

Since the number of moles of gas on both sides of the reaction is the same, there is no substantial increase or decrease in disorder. Thus, the change in entropy, \(\Delta S_{\text{system}}\), is close to zero for this reaction. #b. Predicting sign for \(N H_{3}(g) \rightarrow N H_{3}(a q)\)#

Compare the phases of the reactants and products

In this reaction, \(N H_{3}(g)\) is changing its phase from a gas to an aqueous solution (\(N H_{3}(a q)\)).

Determine the entropy change

In general, when a substance changes from a gas to a liquid or solution, the system becomes less disordered. Therefore, the change in entropy, \(\Delta S_{\text{system}}\), will be negative for this reaction. #c. Predicting sign for \(C H_{3} O H(1) \rightarrow C H_{3} O H(a q)\)#

Compare the phases of the reactants and products

In this reaction, \(C H_{3} O H(1)\), which is a liquid, is changing phase to an aqueous solution (\(C H_{3} O H(a q)\)).

Determine the entropy change

When a substance changes from a liquid to a solution, the system generally becomes more disordered, as the solute particles spread out in the solvent. Therefore, the change in entropy, \(\Delta S_{\text{system}}\), will be positive for this reaction. #d. Predicting sign for \(C_{10} H_{8}(1) \rightarrow C_{10} H_{8}(s)\)#

Compare the phases of the reactants and products

In this reaction, \(C_{10} H_{8}(1)\), which is a liquid, is changing phase to a solid (\(C_{10} H_{8}(s)\)).

Determine the entropy change

When a substance changes from a liquid to a solid, the system becomes less disordered, as the particles are now more tightly packed together. Therefore, the change in entropy, \(\Delta S_{\text{system}}\), will be negative for this reaction.

Key concepts

Phase Changes

Phase changes are transitions between different states of matter, such as solid, liquid, and gas. They're often associated with the gain or loss of energy by the substance undergoing the transition. During a phase change, the energy input or release does not change the temperature, but it changes the arrangement and movement of particles.
For example:

• *Melting:* Transition from solid to liquid, where particles start moving more freely.
• *Freezing:* Transition from liquid to solid, where particles move less and form a fixed arrangement.
• *Condensation:* Transition from gas to liquid, reducing the freedom of particle movement.
• *Evaporation:* Transition from liquid to gas, increasing particle movement.

Understanding these changes helps predict changes in the system's disorder or entropy.

Entropy Prediction

Entropy is a measure of disorder or randomness in a system. In chemical reactions, predicting whether the entropy will increase or decrease helps understand the spontaneity of the process. The sign of entropy change, \(\Delta S_{system}\), can be determined quickly by considering the phase and number of particles involved.
Some basic rules help us anticipate the nature of entropy change:

• When a system moves from a more ordered state (like solid) to a less ordered state (like gas), \(\Delta S_{system}\) tends to be positive, indicating an increase in disorder.
• In contrast, moving from less ordered to more ordered states usually results in a negative \(\Delta S_{system}\), showing a decrease in disorder.

Making these predictions gives deep insights into the behavior of a chemical reaction or physical process.

Gas to Liquid Transition

The transition from gas to liquid is often referred to as condensation. During this process, gas molecules lose energy, resulting in decreased movement and forming closer, more structured arrangements characteristic of liquids. This change leads to a more ordered state where molecules have less freedom to move than in a gaseous state.
As a result, the entropy change, \(\Delta S_{system}\), during gas to liquid transitions is generally negative. This means the disorder within the system decreases. Understanding this transition is crucial, for example, when predicting weather patterns like dew formation or looking at industrial processes involving gas liquification.

Liquid to Solid Transition

Changing from a liquid to a solid is known as freezing or solidification. In this process, the particles in a liquid lose energy, moving slower, and becoming fixed in place. This results in an orderly arrangement, characteristic of solids.
As a liquid solidifies, the entropy, or disorder, decreases, leading to a negative \(\Delta S_{system}\). This is because particles can no longer move freely, and they are arranged in an organized lattice structure. This concept is essential in understanding natural phenomena like the formation of ice from water or how metals solidify after melting in manufacturing.