Problem 2 - Chemistry The Central Science In Si Units

Question

As shown here, one type of computer keyboard cleaner contains liquefied 1,1-difluoroethane \(\left(\mathrm{C}_{2} \mathrm{H}_{4} \mathrm{~F}_{2}\right),\) which is a gas at atmospheric pressure. When the nozzle is squeezed, the 1,1 -difluoroethane vaporizes out of the nozzle at high pressure, blowing dust out of objects. (a) Based on your experience, is the vaporization a spontaneous process at room temperature? (b) Defining the 1,1 -difluoroethane as the system, do you expect \(q_{\mathrm{sys}}\) for the process to be positive or negative? (c) Predict whether \(\Delta S\) is positive or negative for this process. (d) Given your answers to (a), (b), and (c), do you think the operation of this product depends more on enthalpy or entropy? [Sections 19.1 and 19.2 ]

Step-by-Step Solution

Answer

(a) Yes, it is spontaneous. (b) \(q_{\text{sys}}\) is positive. (c) \(\Delta S\) is positive. (d) The process depends more on entropy.

Step 1: Understand the Process

The process described involves the vaporization of 1,1-difluoroethane from a liquid to a gas, which takes place at room temperature. Vaporization increases the disorder of the system, as molecules move from an ordered liquid state to a more disordered gaseous state.

Step 2: Analyze Spontaneity (Part a)

Vaporization is generally a spontaneous process at room temperature for volatile substances like 1,1-difluoroethane. This is because the process results in a more disordered state (gas), which is favored at typical conditions.

Step 3: Determine Heat Exchange (Part b)

Since vaporization is an endothermic process, the system absorbs heat from the surroundings. Thus, the heat exchange for the system, \(q_{\text{sys}}\), is expected to be positive.

Step 4: Analyze Entropy Change (Part c)

During vaporization, entropy increases as the molecules transition from a liquid to a gaseous state, implying that \(\Delta S\) is positive.

Step 5: Evaluate Main Dependence (Part d)

Given that the process is spontaneous and accompanied by an increase in entropy and positive heat exchange (\(q_{\text{sys}}\)), the operation of the product likely depends more on the entropy change rather than enthalpy.

Key Concepts

Spontaneity

Spontaneity is a term used to describe processes that occur naturally without needing external influence under given conditions. A spontaneous process is one that naturally progresses towards equilibrium. In the context of vaporization, a volatile substance like 1,1-difluoroethane at room temperature can transition from a liquid to a gas spontaneously. This process increases the randomness or disorder, moving to a more favored gaseous state. Room temperature supports enough energy, resulting in substances like 1,1-difluoroethane readily vaporizing. Importantly, spontaneity is not directly about speed; it's about whether the process will occur unprompted.

• Vaporization increases disorder.
• Favorability at room temperature supports spontaneous behavior.

Endothermic Process

An endothermic process is one where the system absorbs heat from its surroundings. This involves a net intake of energy to facilitate the transition from one state to another. In this case, 1,1-difluoroethane vaporizes, requiring heat to change from liquid to gas. When the nozzle is squeezed, energy from the environment is absorbed by the system. This absorbed energy, seen as heat, helps break intermolecular forces, enabling the molecules to enter the gaseous phase. Consequently, the heat exchange ( \(q_{\text{sys}}\)) for the system becomes positive, indicating an input of energy.

• Heat is absorbed from surroundings.
• Positive heat exchange due to the endothermic nature.

Entropy Change

Entropy, a measure of disorder in a system, usually increases when a substance transitions from a liquid to a gas. For 1,1-difluoroethane undergoing vaporization, the increase in disorder is notable. The molecules, initially packed in a liquid state, gain freedom and spread out in the gaseous state. This transition results in a greater amount of microstates and configurations available to the molecules. Therefore, \(\Delta S\) is positive in this context. The increase in entropy is a significant driving force behind the spontaneous vaporization process.

• Transition from liquid to gas increases disorder.
• Entropy increases with greater molecular freedom.

Enthalpy vs Entropy

Understanding the balance between enthalpy (heat content) and entropy (disorder) is crucial in determining process favorability. The vaporization of 1,1-difluoroethane is spontaneous, indicating entropy plays a major role. Despite being endothermic (absorbing heat), the process relies heavily on the resultant increase in entropy to drive it forward. In this scenario, the entropy change overshadows the enthalpy aspect, indicating operations like this keyboard cleaner prioritize disorder increase. Entropy ensures the product functions effectively, compensating for any positive enthalpy change.

• Entropy increases favor spontaneity.
• Process relies more on entropy, less on enthalpy.