Problem 88 - Chemistry: The Central Science in SI Units, Global Edition

Question

For each of the following processes, indicate whether the signs of \(\Delta S\) and \(\Delta H\) are expected to be positive, negative, or about zero. (a) A solid sublimes. (b) The temperature of a sample of \(\mathrm{Co}(s)\) is lowered from \(60^{\circ} \mathrm{C}\) to \(25^{\circ} \mathrm{C} .\) (c) Ethyl alcohol evaporates from a beaker. (d) A diatomic molecule dissociates into atoms. (e) A piece of charcoal is combusted to form \(\mathrm{CO}_{2}(g)\) and \(\mathrm{H}_{2} \mathrm{O}(g)\).

Step-by-Step Solution

Answer

a) ΔS > 0, ΔH > 0 b) ΔS < 0, ΔH < 0 c) ΔS > 0, ΔH > 0 d) ΔS > 0, ΔH > 0 e) ΔS > 0, ΔH < 0

Step 1: a) A solid sublimes.

In sublimation, a solid changes directly into a gas without passing through a liquid state. This results in an increase in the disorder of the system, so the entropy (∆S) will be positive. Since this process is endothermic, meaning it requires energy input to break the bonds and change the solid into a gas, the enthalpy (∆H) is positive as well. Result: ΔS > 0, ΔH > 0

Step 2: b) The temperature of a sample of Co(s) is lowered from 60°C to 25°C

In this process, the temperature of the sample of cobalt(s) is decreasing. As the temperature decreases, the motion of the particles within the solid slows down. This results in a decrease in disorder, so the entropy (∆S) will be negative. The cooling process releases heat, making it an exothermic process, so the enthalpy (∆H) is negative as well. Result: ΔS < 0, ΔH < 0

Step 3: c) Ethyl alcohol evaporates from a beaker

When ethyl alcohol evaporates, its molecules go from a liquid state to a gaseous state. Gas molecules have more freedom of motion and are more disordered compared to liquid molecules. Therefore, the entropy (∆S) will be positive. This process is endothermic because it requires input of heat energy to break intermolecular forces, so the enthalpy (∆H) is positive as well. Result: ΔS > 0, ΔH > 0

Step 4: d) A diatomic molecule dissociates into atoms

When a diatomic molecule dissociates into individual atoms, the number of particles in the system increases and the particles have more freedom of motion. This results in an increase in disorder, so the entropy (∆S) will be positive. As bonds must be broken in order to separate the atoms, this process requires energy input, so the enthalpy (∆H) is also positive. Result: ΔS > 0, ΔH > 0

Step 5: e) A piece of charcoal is combusted to form CO2(g) and H2O(g)

Combustion of charcoal is an exothermic reaction, meaning it releases heat. Therefore, the enthalpy (∆H) will be negative. In the combustion process, the complex carbon structure of charcoal is broken down into smaller, simpler molecules (CO2 and H2O gases). This results in an increase in disorder, so the entropy (∆S) will be positive. Result: ΔS > 0, ΔH < 0

Key Concepts

Entropy

Entropy is a measure of the disorder or randomness in a system. When a system undergoes a change, the entropy can increase, decrease, or remain about the same.
In thermodynamics, we often express this change in entropy as ΔS.

• A positive ΔS means the system's disorder has increased. For example, when a solid sublimes, it changes directly into a gas. This transition increases molecular motion and disorder, so ΔS is positive.
• A negative ΔS indicates a decrease in disorder. For example, when the temperature of a solid sample like cobalt decreases, the motion of its particles lessens, making ΔS negative.
• If the system's state doesn't significantly change, ΔS might be around zero. However, this is less common in dynamic processes.

Understanding the concept of entropy helps us predict the spontaneity of a process. Generally, natural processes tend to favor increased entropy. But this tendency interacts with energy changes, mainly covered under the concept of enthalpy.

Enthalpy

Enthalpy is a measure of the total heat content in a system. In chemistry, it helps determine whether a reaction absorbs or releases heat, noted as ΔH.
When analyzing enthalpy, a few key points stand out:

• A positive ΔH means the process is endothermic. It absorbs heat from the surroundings, as seen in sublimation and evaporation. This energy input is crucial to break bonds or overcome intermolecular forces.
• A negative ΔH denotes an exothermic process. Such reactions release heat, like the cooling of cobalt or the combustion of charcoal.

Recognizing whether a process is endothermic or exothermic lets us better understand energy flow and its impact on surrounding environments.

Endothermic and Exothermic Processes

Endothermic and exothermic processes involve the absorption and release of heat respectively, fundamentally affecting the energy dynamics in chemical reactions.

• An endothermic process requires an input of energy from the surroundings, seen in reactions where bonds are broken, such as sublimation, evaporation, and dissociation of molecules. This energy is needed to overcome forces of attraction between molecules or atoms, resulting in a positive ΔH.
• Conversely, an exothermic process releases energy to the surroundings. This happens during the formation of stable bonds or simpler molecules from complex structures, like in the combustion of charcoal. Here, the heat release marks the reaction as exothermic, with a negative ΔH.

Both types of processes play a vital role in nature and industry. Endothermic processes are essential for storing energy, while exothermic ones are utilized for energy release, such as in heating systems or engines.