Question

Explain the cooling effect experienced when ethanol is rubbed on your skin, given that \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(l) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(g) \quad \Delta H^{\circ}=42.2 \mathrm{~kJ} / \mathrm{mol}\)

Short answer

Ethanol evaporates, absorbing heat from the skin for the endothermic process, causing cooling.

Step-by-step solution

Understanding the Evaporation Process

Ethanol, when applied to the skin, transitions from a liquid phase to a gaseous phase (evaporation). This is represented by the process \( \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(l) \rightarrow \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(g) \). Evaporation occurs when molecules at the surface gain enough energy to overcome intermolecular forces and enter the gaseous state.

Analyze the Enthalpy Change

The given thermochemical equation states that the enthalpy change (\( \Delta H^{\circ} \)) for the evaporation of ethanol is \( 42.2 \mathrm{~kJ/mol} \). This positive value indicates that the process requires energy input, as it is an endothermic process.

Connect Energy Absorption to Cooling Effect

As ethanol evaporates from your skin, it absorbs heat energy from the skin in order to overcome the enthalpy change (\( 42.2 \mathrm{~kJ/mol} \)). This absorption of heat energy from the skin results in a decrease in skin temperature, leading to the sensation of cooling.

Key concepts

Ethanol

Ethanol is a chemical compound with the formula \( C_2H_5OH \), commonly known as alcohol. It is widely used in industrial and consumer products, from fuel to antiseptic hand sanitizers. One of its notable properties is its ability to evaporate quickly. When you apply ethanol to your skin, its molecules transition from a liquid state to a gaseous state. This process is called evaporation. Ethanol's high volatility—meaning it easily transforms into vapor at room temperature—makes it effective in applications where quick drying is needed.
Ethanol has relatively weak intermolecular forces—specifically, hydrogen bonds—compared to heavier alcohols, which allows it to evaporate quickly.
This evaporation process on the skin brings about the cooling sensation we experience.
Understanding ethanol's characteristics is essential for recognizing its broad applications and effects on temperature changes during its evaporation.

Enthalpy Change

Enthalpy change, represented by \( \Delta H^{\circ} \), refers to the heat absorbed or released in a chemical reaction at constant pressure. When ethanol evaporates, the enthalpy change is positive, specifically \( \Delta H^{\circ} = 42.2 \text{ kJ/mol} \).
This value tells us that the process requires an input of energy.

• Positive \( \Delta H^{\circ} \): Indicates an endothermic process where energy is absorbed.
• The magnitude of \( 42.2 \text{ kJ/mol} \): Describes the energy required to convert 1 mole of liquid ethanol to its gaseous state.

During the evaporation process, ethanol absorbs this energy from the surrounding environment, like your skin, which ultimately results in a cooling effect. In reactions, the concept of enthalpy change is pivotal in determining whether heat is absorbed or released, and how that affects the surrounding environment.

Endothermic Process

An endothermic process is defined by the absorption of heat. In the context of ethanol on the skin, this process is what causes the cooling effect.
When ethanol evaporates:

• Heat is absorbed from your skin to provide the necessary energy for molecular separation.
• This energy absorption corresponds to the enthalpy change \( \Delta H^{\circ} = 42.2 \text{ kJ/mol} \).

In simpler terms, the heat from your skin is utilized to break the bonds between ethanol molecules, allowing them to transition into the vapor phase. As a result, the skin loses heat, which you feel as a cooling sensation. Recognizing the nature of endothermic processes helps us understand phenomena such as sweating and how other evaporative effects also result in cooling.