Question

Arrange the following aqueous solutions in order of (i) increasing vapor pressure of water and (ii) increasing boiling point. (a) \(0.35 \mathrm{m} \mathrm{HOCH}_{2} \mathrm{CH}_{2} \mathrm{OH}\) (a nonvolatile solute) (b) \(0.50 \mathrm{m}\) sugar (c) \(0.20 \mathrm{m} \mathrm{KBr}\) (a strong electrolyte) (d) \(0.20 m \mathrm{Na}_{2} \mathrm{SO}_{4}\) (a strong electrolyte)

Short answer

(i) Increasing vapor pressure: (a), (c), (b), (d); (ii) Increasing boiling point: (a), (c), (b), (d).

Step-by-step solution

Understanding the Concept of Vapor Pressure

Vapor pressure of a solution depends on the presence of nonvolatile solutes. It decreases as the concentration of solute particles increases. The more solute particles present in the solution, the lower the vapor pressure compared to pure solvent.

Calculate the Total Particle Concentration

For solutions with nonvolatile solutes or electrolytes, calculate the total number of solute particles that affect vapor pressure. - For non-electrolytes like (a) and (b), the concentration of particles is the same as the molality: - Solution (a): 0.35 m - Solution (b): 0.50 m - For strong electrolytes, the concentration of particles is the sum of ions produced: - Solution (c) KBr dissociates into K⁺ and Br⁻ (i = 2), so the concentration is 0.20 m × 2 = 0.40 m. - Solution (d) Na₂SO₄ dissociates into 2Na⁺ and SO₄²⁻ (i = 3), so the concentration is 0.20 m × 3 = 0.60 m.

Arrange in Order of Increasing Vapor Pressure

The solution with the lowest concentration of solute particles has the highest vapor pressure. Arranging according to particle concentration gives: 1. (a) 0.35 m HOCH₂CH₂OH 2. (c) 0.40 m KBr 3. (b) 0.50 m sugar 4. (d) 0.60 m Na₂SO₄.

Understanding Boiling Point Elevation

The boiling point of a solution increases with the concentration of solute particles because a higher concentration lowers the vapor pressure, requiring a higher temperature to reach atmospheric pressure. Thus, boiling point elevation increases with the concentration of solute particles.

Arrange in Order of Increasing Boiling Point

The order of increasing boiling point is the same as that for increasing solute particle concentration. Thus, the order is: 1. (a) 0.35 m HOCH₂CH₂OH 2. (c) 0.40 m KBr 3. (b) 0.50 m sugar 4. (d) 0.60 m Na₂SO₄.

Key concepts

Vapor Pressure

Vapor pressure is a key concept in understanding colligative properties of solutions. It refers to the pressure exerted by a vapor in equilibrium with its liquid or solid form in a closed system. When nonvolatile solutes are added to a solvent, they disrupt the natural equilibrium between the liquid phase and its vapor. This leads to a decrease in the vapor pressure compared to the pure solvent. The more solute particles present in a solution, the greater the decrease in vapor pressure.

- The presence of solute molecules or ions reduces the number of solvent molecules available to escape into the vapor phase.
- This concept is crucial in applications where vapor pressure needs to be controlled or predicted, such as in predicting weather patterns or in designing chemical processes.

For instance, in the given exercise, solutions with higher particle concentrations, such as the one with Na₂SO₄, have lower vapor pressures because they contain more solute particles, which further lower the number of solvent molecules transitioning into vapor.

Boiling Point Elevation

Boiling point elevation is another critical colligative property alteration arising when solutes are added to solvents. This effect occurs because introducing solute particles reduces the solvent's vapor pressure. Consequently, a higher temperature is required to raise the vapor pressure to match the external atmospheric pressure, leading to an elevated boiling point.

- The degree of boiling point elevation is directly proportional to the number of dissolved solute particles in the solution.
- It's important in many real-world applications, such as cooking and chemical engineering, where precise control of boiling points is necessary.

In our exercise, solutions like the one containing Na₂SO₄, due to having the greatest concentration of solute particles, would exhibit the highest boiling point increase compared to those with fewer solute particles.

Molality

Molality is a measure of the concentration of a solution expressed in moles of solute per kilogram of solvent. It's a particularly useful way to express concentration because it remains constant with changes in temperature and pressure, as opposed to molarity which can vary under different conditions.

- Molality is used frequently in the calculations of colligative properties because these properties depend on the concentration of solute particles and not on the volume of the solution.
- It is calculated by taking the moles of solute and dividing it by the kilograms of solvent.

In context with the given exercise, molality directly affects both vapor pressure depression and boiling point elevation, as solutions with higher molalities have greater effects.

Electrolytes

Electrolytes are substances that dissociate into ions when dissolved in water, conducting an electrical current. Strong electrolytes dissociate completely into their constituent ions. This feature distinguishes them from non-electrolytes, which do not produce ions in solution.

- The presence of electrolytes significantly affects colligative properties because each electrolyte molecule disassembles into multiple particles, effectively multiplying the effect on both vapor pressure and boiling point of the solution.
- For example, in the exercise, Na₂SO₄ dissociates into three ions per formula unit, thus tripling its effect compared to a non-electrolyte at the same molality.

This property of electrolytes makes them highly crucial in applications requiring precise control of solution properties, such as in medicinal formulation and battery technology.