Question

You drop an ice cube (made from pure water) into a saltwater solution at \(0^{\circ} \mathrm{C}\). Explain what happens and why.

Short answer

When a pure water ice cube is dropped into a saltwater solution at \(0^{\circ}\mathrm{C}\), it melts due to the difference in freezing points between pure water and saltwater. The melting process dilutes the saltwater solution, causing the localized freezing point to rise slightly and allowing more ice to melt. Eventually, the ice cube melts completely, and the mixture reaches a new equilibrium with a slightly lower salt concentration and a temperature near \(0^{\circ}\mathrm{C}\).

Step-by-step solution

Understand the initial conditions

Before mixing, we have a pure water ice cube at \(0^{\circ}\mathrm{C}\) and a saltwater solution at the same temperature. Pure water has a lower freezing point than saltwater due to the presence of dissolved salts. Thus, the saltwater remains liquid at this temperature, while the water is frozen. Step 2:

Observe the process that takes place

When the ice cube is dropped into the saltwater solution, it starts to melt because of the difference in freezing points between pure water and saltwater. The ice cube gradually turns into water, and at the same time, the solution cools down due to the heat exchange between the melting ice and the saltwater. Step 3:

Understand the effects of dissolving the ice cube

As the ice cube melts, the concentration of salt in the solution around the ice cube decreases because the melting process dilutes the saltwater solution. This localized decrease in salt concentration causes the freezing point of the water in the area around the ice cube to rise slightly, allowing more ice to melt. Step 4:

Describe the final equilibrium

Eventually, the ice cube will melt completely, and the resulting mixture of water and saltwater will reach a new equilibrium. The final concentration of salt in the solution will be slightly lower than the initial concentration, and the temperature of the mixture will still be near \(0^{\circ}\mathrm{C}\). In conclusion, when a pure water ice cube is dropped into a saltwater solution at \(0^{\circ}\mathrm{C}\), it melts due to the difference in freezing points between pure water and saltwater. The melting process dilutes the saltwater solution, leading to a new equilibrium with a lower salt concentration and a temperature near \(0^{\circ}\mathrm{C}\).

Key concepts

Colligative Properties

Understanding colligative properties is key to explaining why an ice cube melts when placed in a saltwater solution at freezing temperature. Colligative properties are characteristics of solutions that depend on the number of particles dissolved in the solvent and not on the nature of the chemical species themselves. Freezing point depression is one such property, which explains why the addition of salt to water lowers the freezing point of the solution.

In simpler terms, the more solute particles (like salt) you have in a solvent (like water), the lower the freezing point will be. This is because the solute particles disrupt the formation of the ordered structure necessary for the solvent to freeze. As a result, more energy (lower temperature) is required to arrange the solvent molecules into a solid state. When a substance like salt is dissolved in water, it separates into ions, effectively increasing the number of particles in the solution and magnifying the freezing point depression.

Solution Equilibrium

Solution equilibrium is another cornerstone concept necessary to describe the melting of an ice cube in saltwater. Equilibrium refers to a state of balance between opposing processes. In this case, the opposing processes are the melting of the ice and the freezing of the water. Initially, the pure water ice cube begins to melt in the saltwater because of the lower freezing point of the saltwater.

As the ice cube melts, it dilutes the saltwater solution, reducing the salt concentration around the ice. This dilution raises the local freezing point, allowing more ice to melt. Ultimately, the system reaches a new equilibrium where the rate of ice melting equals the rate of water freezing, and the solution's temperature stabilizes. This equilibrium is dynamic, meaning that melting and freezing processes continue to occur, but they balance each other, so there is no net change in the amount of ice or liquid water.

Phase Change

A phase change is the transformation of a substance from one state of matter to another, such as from solid to liquid or vice versa. When discussing the melting ice cube in the saltwater, we're focusing on the phase change of water from the solid phase (the ice cube) to the liquid phase (the water).

The phase change occurs because of the energy transfer between the saltwater solution and the ice cube. As the ice cube absorbs heat from the warmer solution, it gains enough energy for the water molecules to overcome the forces holding them in the solid state. This absorption of heat during melting is an endothermic process – it takes in energy from the surroundings.

Conversely, freezing is an exothermic process where the liquid releases heat as it transitions to a solid state. Normally, at the freezing point, these phase changes would be in equilibrium, but in our scenario with the saltwater, the presence of salt upsets this balance, leading to the complete melting of the ice cube.