Question

Using the phase diagram for water and Raoult’s law, explain why salt is spread on the roads in winter (even when it is below freezing).

Short answer

When salt is added to water on roads in winter, it lowers the freezing point of water by decreasing the mole fraction of the solvent (water) and reducing the vapor pressure according to Raoult's Law (\(P = P^*_A \cdot x_A\)). This prevents the formation of ice and ensures safer driving conditions, even when temperatures are below 0°C.

Step-by-step solution

Understanding the Phase Diagram of Water

A phase diagram is a graphical representation of the equilibrium between different phases of a substance under varying conditions of temperature and pressure. For water, the phases it can exist in are solid (ice), liquid, and vapor. The phase diagram shows the boundaries where phase transitions happen. The diagram has three axes corresponding to the three phases; the horizontal axis corresponds to the temperature, and the vertical axis corresponds to pressure. At atmospheric pressure, we observe that the freezing point of water is 0°C. Below this temperature, water exists in its solid phase (ice), and above it, in its liquid phase.

Introducing Raoult's Law

Raoult's Law states that in a solution of a solvent and a non-volatile solute, the vapor pressure of the solvent over the solution is proportional to the mole fraction of the solvent. The law can be expressed mathematically as: \(P = P^*_A \cdot x_A\) Where: - \(P\) is the vapor pressure of the solution - \(P^*_A\) is the vapor pressure of the pure solvent - \(x_A\) is the mole fraction of the solvent in the solution

Explaining the Effects of Salt on Water's Freezing Point

When salt is added to water, it dissolves and forms a solution. According to Raoult's law, as the mole fraction of the solvent (water) decreases due to the presence of the solute (salt), the vapor pressure of the water over the solution decreases. To reach the same vapor pressure as in pure water, the solution (saltwater) must be at a lower temperature than the original freezing point of pure water (0°C). Thus, the introduction of salt lowers the freezing point of water, preventing it from turning into ice even when the temperature is below 0°C.

Applying the Effects to Road Safety in Winter

When salt is spread on roads in winter, it lowers the freezing point of any water or melting ice on the road surface. This prevents the formation of ice on the roads, which makes driving safer, as ice can create slippery and dangerous conditions. This is why salt is used during winter months to keep roads safe and free from ice, even when temperatures are below freezing.

Key concepts

Phase Diagram

A phase diagram is a useful tool that shows how a substance behaves under different temperatures and pressures. For water, it illustrates the equilibrium between its solid, liquid, and vapor phases.

The horizontal axis of the phase diagram represents temperature, while the vertical axis denotes pressure. This visual representation clearly shows that at standard atmospheric pressure, water freezes at 0°C. Below this temperature, water is a solid (ice), and above it, it transitions to a liquid.

Using the phase diagram of water helps us understand how the application of salt can modify the conditions under which water changes phases, especially in icy or snowy conditions.

Raoult's Law

Raoult's Law explains how the presence of a solute, like salt, affects the properties of a liquid, such as water. It states that the vapor pressure of a solvent over a solution decreases proportionally with the addition of a non-volatile solute.

This can be expressed with the equation: \[ P = P^*_A \cdot x_A \]Where:

• \(P\) is the vapor pressure of the solution
• \(P^*_A\) is the vapor pressure of pure solvent
• \(x_A\) is the mole fraction of the solvent in the solution

When salt is dissolved in water, the mole fraction of water decreases. As a result, its vapor pressure reduces. This decrease in vapor pressure leads to a decrease in the freezing point, a phenomenon known as "freezing point depression."

This principle plays a crucial role in preventing the formation of ice on roads during winter by allowing water to remain liquid at lower temperatures.

Vapor Pressure

Vapor pressure is the pressure exerted by the vapor of a liquid when it's in equilibrium with its liquid phase. This equilibrium is influenced by temperature and the presence of solutes.

In the case of saltwater, adding salt alters the vapor pressure by decreasing it. The lower vapor pressure requires that the temperature be further reduced to reach the equilibrium state typical of ice formation in pure water.

This interaction is why salt is so effective at lowering the freezing point. When added to icy roads, it makes it harder for the water to transition from a liquid to a solid state, reducing the likelihood of ice forming even as temperatures drop.

Road Safety in Winter

Spreading salt on roads during winter is a common practice to enhance safety. By understanding how salt affects the freezing point of water, we can appreciate its importance in road safety.

When salt is applied to roads, it dissolves into any moisture present, creating a saltwater solution. This lowers the freezing point of the water on the road surface, preventing it from freezing into ice. Even when temperatures fall below 0°C, the water remains liquid, significantly reducing slippery conditions that can lead to accidents.

This preventive measure is crucial in maintaining safe driving conditions during the cold winter months, ensuring vehicle traction and control by keeping roads free from hazardous ice patches.