Aqueous solutions \(\mathrm{A}\) and \(\mathrm{B}\) both contain urea at different concentrations. On standing while exposed to air, the vapor pressure of A remains constant while that of B gradually decreases. (a) Which solution has a higher boiling point? (b) Eventually the two solutions have the same vapor pressure. Explain.

Vapor pressure is a critical factor in the study of boiling point elevation. It is the pressure exerted by a vapor in equilibrium with its liquid (or solid) at a given temperature in a closed system. When a solute such as urea is dissolved in water, it disrupts the ability of water molecules to escape into a vapor state. This effect lowers the vapor pressure of the solution compared to that of the pure solvent.

If the vapor pressure of a solution remains constant, it indicates that there is no net loss or gain of solvent molecules in the solution. However, if the vapor pressure of a solution gradually decreases, it implies that the solvent (water) is evaporating, and consequently, the solute concentration is increasing.

Impact on Boiling Point

The concentration of a solute in a solution plays a pivotal role in determining the boiling point. Boiling point elevation occurs when a non-volatile solute is added to a solvent, like water, and the boiling point of the resulting solution is higher than that of the pure solvent. This happens because the solute particles interfere with the formation of vapor above the liquid, requiring a higher temperature to achieve the same vapor pressure necessary for boiling.

In the case of the exercise, solution B's decreasing vapor pressure indicates that its solute concentration is increasing due to solvent evaporation. Thus, solution B will have a higher boiling point compared to solution A with constant vapor pressure and stable solute concentration.

Aqueous solutions are water-based solutions where water is the solvent and substances dissolved in it are solutes. Water's ability to dissolve a wide range of substances is due to its polar nature. In an aqueous solution, the solute can be an electrolyte or a non-electrolyte like urea. Electrolytes will dissociate into ions, affecting the solution’s boiling point and other colligative properties significantly. However, even non-electrolytes like urea can influence the properties of the solvent due to the fact they create more particles in solution, and this change is directly related to the number of solute particles rather than their nature.

Colligative properties, such as boiling point elevation, are properties of solutions that depend only on the number of solute particles, not the identity of the solute. Other colligative properties include freezing point depression, vapor pressure lowering, and osmotic pressure.

These properties are foundational in understanding why solutions behave differently from their pure solvents. In the context of the textbook exercise, the colligative property in focus is the boiling point elevation. As the solute concentration in solution B increases (due to the evaporation of the solvent), the boiling point elevates, which explains why solution B will have a higher boiling point than solution A. When the solute concentration is equalized between the two solutions, they exhibit the same vapor pressure, indicating they now share the same colligative effects.