Problem 79 - Chemistry

Question

The following compounds, listed with their boiling points, are liquid at \(-10^{\circ} \mathrm{C}:\) butane, \(-0.5^{\circ} \mathrm{C} ;\) ethanol, \(78.3^{\circ} \mathrm{C} ;\) toluene, \(110.6^{\circ} \mathrm{C}\). At \(-10^{\circ} \mathrm{C},\) which of these liquids would you expect to have the highest vapor pressure? Which the lowest? Explain.

Step-by-Step Solution

Answer

At -10°C, one can expect that butane will exert the highest vapor pressure as it has the lowest boiling point (-0.5°C). Conversely, toluene will have the lowest vapor pressure because it has the highest boiling point (110.6°C).

Step 1: Identify the liquid with the highest boiling point

From the provided boiling points for the four compounds, it can be seen that toluene has the highest boiling point at 110.6°C. Therefore, this is the compound that will have the lowest vapor pressure at -10°C.

Step 2: Identify the liquid with the lowest boiling point

Similarly, it can be noted that butane has the lowest boiling point from the given compounds at -0.5°C. This implies that butane will have the highest vapor pressure at -10°C.

Step 3: Logic behind the solution

The logic behind this solution is based on the principal that at a specific temperature, liquids with higher boiling points need more energy for their molecules to leave the liquid phase and become gas. Therefore, fewer will become gas, and their vapor pressure is lower. Conversely, liquids with lower boiling points need less energy for their molecules to become gas, so more will become gas, and their vapor pressure is higher.

Key Concepts

Boiling Point

The boiling point of a liquid is the temperature at which its vapor pressure equals the atmospheric pressure. At this point, the liquid turns into a gas. Different substances have distinct boiling points based on molecular structure and intermolecular forces.
- **Higher Boiling Point**: Substances like toluene, having a higher boiling point, need more energy for the molecules to escape into the gaseous phase.
- **Lower Boiling Point**: Substances like butane, with a lower boiling point, require less energy to vaporize.
Understanding boiling points helps determine how easily a liquid can evaporate or boil under specific conditions.

Molecular Energy

Molecular energy refers to the energy within molecules related to their movement and interactions. Atoms and molecules vibrate, rotate, and move around, contributing to kinetic energy.
- **Impact on Boiling**: For a liquid to boil, molecules must gain enough energy to overcome intermolecular forces and transition into a gas.
- **Factors Influencing Molecular Energy**:

• Temperature: Higher temperatures increase molecular energy.
• Intermolecular Forces: Stronger forces require more energy to overcome.

Molecular energy plays a crucial role in deciding how readily a substance turns from a liquid to a gas.

Phase Change

A phase change is a transition between different states of matter: solid, liquid, and gas. The most common phase changes related to vapor pressure include evaporation and boiling.
- **Evaporation vs. Boiling**:

• Evaporation: Occurs at the surface and can happen below boiling point.
• Boiling: Involves the entire liquid and happens at the boiling point.

- **Energy Requirement**: Phase changes require energy to break and reform molecular bonds.
Understanding phase changes explains why substances with different boiling points behave differently under the same temperature conditions.

Liquid-Gas Equilibrium

Liquid-gas equilibrium is a dynamic state where the rate of evaporation of a liquid equals the rate of condensation of its gas. This balance affects the vapor pressure of a liquid.
- **Vapor Pressure**: The pressure exerted by a vapor in equilibrium with its liquid is called vapor pressure.
- **Factors Affecting Equilibrium**:

• Temperature: Higher temperatures generally increase vapor pressure.
• Boiling Point: Substances with lower boiling points have higher vapor pressures at the same temperature.

When understanding liquid-gas equilibrium, one must consider the balance of molecular exchange between liquid and gas, crucial for predicting behavior at various temperatures.