Explain the following on the basis of the behavior of atoms and/or ions. a. Cooking with water is faster in a pressure cooker than in an open pan. b. Salt is used on icy roads. c. Melted sea ice from the Arctic Ocean produces fresh water. d. \(\mathrm{CO}_{2}(s)\) (dry ice) does not have a normal boiling point under normal atmospheric conditions, even though \(\mathrm{CO}_{2}\) is a liquid in fire extinguishers. e. Adding a solute to a solvent extends the liquid phase over a larger temperature range.

Boiling point elevation occurs when a non-volatile solute is dissolved in a solvent, resulting in an increase in the boiling point of the solution compared to the pure solvent. This can be explained through the colligative property known as 'Raoult's Law', which states that the presence of solute particles reduces the evaporation rate because fewer solvent molecules are at the surface, leading to a reduced vapor pressure at a given temperature.

As a result, to achieve vapor pressure equal to the external pressure, a higher temperature is required, which explains the elevation of the boiling point. This principle is what makes cooking in a pressure cooker faster, as the increased pressure inside the cooker raises the boiling point of water, allowing food to cook at a higher temperature more efficiently.

The mathematical equation to calculate the boiling point elevation is given by: \[\Delta T_b = i \cdot K_b \cdot m \] where \(\Delta T_b\) is the boiling point elevation, \(i\) is the van't Hoff factor (which represents the number of particles the solute splits into or forms in solution), \(K_b\) is the ebullioscopic constant of the solvent, and \(m\) is the molality of the solution.

Freezing point depression is another colligative property that describes the lowering of a solvent's freezing point when a solute is dissolved into it. This effect is commonly observed when salt is spread on icy roads. The salt particles disrupt the formation of the orderly ice crystal lattice, effectively requiring a colder temperature to achieve solidification.

This is due to the fact that the dissolving solute particles create a solute-solvent interaction, which lowers the chemical potential of the solvent and disrupts the freezing process. The extent of freezing point depression can be calculated by the equation: \[\Delta T_f = i \cdot K_f \cdot m \] where \(\Delta T_f\) represents the freezing point depression, \(K_f\) is the cryoscopic constant of the solvent, and the other symbols have the same meaning as in boiling point elevation.

This property is leveraged to our advantage in winter to melt ice on the roads, making them safer for travel.

Sublimation is the phase transition of a substance from the solid state directly to the gas state without first becoming liquid. This fascinating phenomenon is seen in substances like dry ice (solid carbon dioxide), which sublimates at standard atmospheric pressure and temperature.

The process is fundamentally different from the traditional phase changes of melting and evaporation because it does not involve a liquid phase at normal pressure. Instead, the solid gains enough energy to overcome not just the energy needed for melting, but also for vaporization in a single step.

Energy is absorbed by the solid's structure to break intermolecular forces, facilitating the transition directly to the gas phase. This process is used in various applications, such as in fire extinguishers, where pressurized liquid CO2 is released to quickly cool and quench fires.

Solution chemistry is a branch of chemistry that deals with the study of solutions, which are homogenous mixtures composed of two or more substances. In a typical solution, a solute (the substance being dissolved) is uniformly distributed within a solvent (the substance in which the solute dissolves).

Solution chemistry encompasses understanding how different substances interact within a solution, leading to various colligative properties such as boiling point elevation, freezing point depression, and others. The addition of a solute to a solvent affects the temperature range over which a substance remains in the liquid phase, as the solute disrupts the orderly solvent molecules from crystallizing or escaping into the vapor phase.

Solutions are crucial in many processes in daily life and industrial applications, including cooking, road maintenance, and the design of chemical products. Understanding how solutes affect the properties of solvents is key to controlling and optimizing these processes.