Question

Compare Which of the following solutions has the highest concentration? Rank the solutions from the greatest to the smallest boiling point depression. Explain your answer. a. 0.10 mol \(\mathrm{NaBr}\) in 100.0 \(\mathrm{mL}\) solution b. 2.1 \(\mathrm{mol} \mathrm{KOH}\) in 1.00 \(\mathrm{L}\) solution c. 1.2 \(\mathrm{mol} \mathrm{KMnO}_{4}\) in 3.00 \(\mathrm{L}\) solution

Short answer

The highest concentration and boiling point depression is for solution b (KOH) with a m*i value of 4.2, followed by solution a (NaBr) with a value of 2.0, and lastly solution c (KMnO$_{4}$) with the lowest concentration and boiling point depression value of 0.8. The ranking is as follows: b (KOH) > a (NaBr) > c (KMnO$_{4}$).

Step-by-step solution

Calculate the molality for each solution

Calculate the molality for each solution using the formula: Molality (m) = moles of solute / kg of solvent For solution a: 0.10 mol NaBr / (100.0 mL × 1 g/mL × 1 kg/1000 g) = 1.0 mol/kg (assuming the density of water is 1 g/mL) For solution b: 2.1 mol KOH / (1.00 L × 1000 g/L × 1 kg/1000 g) = 2.1 mol/kg (assuming the density of water is 1 g/mL) For solution c: 1.2 mol KMnO4 / (3.00 L × 1000 g/L × 1 kg/1000 g) = 0.4 mol/kg (assuming the density of water is 1 g/mL)

Calculate the van 't Hoff factor for each solute

Determine the van 't Hoff factor (i) for each solute based on the number of particles the solute will produce in the solution. For electrolytes, i will be equal to the number of ions produced by the solute. For NaBr: i = 1 (Na⁺) + 1 (Br⁻) = 2 For KOH: i = 1 (K⁺) + 1 (OH⁻) = 2 For KMnO4: i = 1 (K⁺) + 1 (MnO4⁻) = 2

Determine the boiling point depression for each solution

Use the boiling point depression formula: ΔT = K_b * m * i We don't need the values of K_b as the constant will be the same for all solutions since we are comparing their boiling points in the same solvent (water). We only need to rank the products m*i for each solute: Solution a (NaBr): m*i = 1.0 mol/kg * 2 = 2.0 Solution b (KOH): m*i = 2.1 mol/kg * 2 = 4.2 Solution c (KMnO4): m*i = 0.4 mol/kg * 2 = 0.8

Rank the solutions

Rank the solutions from the greatest to the smallest boiling point depression based on their calculated m*i values: 1. Solution b (KOH): 4.2 2. Solution a (NaBr): 2.0 3. Solution c (KMnO4): 0.8 The highest boiling point depression (and highest concentration) is for solution b (KOH), followed by solution a (NaBr) and lastly, the lowest boiling point depression (and lowest concentration) is for solution c (KMnO4).

Key concepts

Molality

Molality is a measure of the concentration of a solute in a solution expressed in terms of moles per kilogram of solvent. Unlike molarity, which is based on volume, molality is based on the mass of the solvent, making it independent of temperature.
Here is how you can calculate molality:

• Identify the number of moles of solute present.
• Determine the mass of the solvent in kilograms.
• Divide the moles of solute by kilograms of solvent to find molality.

This property is essential when considering colligative properties like boiling point elevation and freezing point depression, as changes in temperature do not affect molality. For example, if you have 0.10 moles of NaBr dissolved in 100 grams of water, the molality would be 1 mol/kg, assuming the density of water is 1 g/mL.
Knowing how to calculate and interpret molality is crucial for determining the effects solutes have on solutions.

Van 't Hoff Factor

The Van 't Hoff factor, often symbolized as "i," acts as a multiplier for colligative properties, indicating how many particles a solute forms in a solution. This factor is especially relevant for electrolytes, which dissociate into ions upon dissolution.
When calculating this factor, consider:

• A non-electrolyte, like glucose, does not dissociate. Therefore, it has a factor of 1.
• A strong electrolyte, such as NaBr, dissociates completely. Hence, it has a factor based on the total ions produced.
• In the case of NaBr, which dissociates into Na⁺ and Br⁻, the Van 't Hoff factor is 2.

This factor directly impacts properties like boiling point depression by modifying the effect of molality in the equation. A higher "i" value means more particles are present, leading to a greater impact on the boiling point.

Electrolytes

Electrolytes are compounds that dissolve in water to produce electrically conductive solutions. They dissociate into positive and negative ions, and their behavior in solutions plays a crucial role in thermodynamic properties.

• When dissolved, strong electrolytes disassemble completely into ions.
• E.g., KOH and NaBr are strong electrolytes that dissociate fully, forming multiple particles per formula unit, affecting the solution's concentration and properties.
• Weak electrolytes partially dissociate, forming fewer ions.

Understanding the nature of electrolytes helps predict how they will impact boiling and freezing points, as the number of particles in the solution contributes significantly to these changes. The greater the number of ions, the more pronounced the effects on colligative properties.

Concentration

Concentration is a broad concept that indicates how much solute is present in a given quantity of solvent or solution. It can be expressed in various ways, such as molarity, molality, and percentages.
Each type of concentration measurement has its applications:

• **Molarity** (M) is moles of solute per liter of solution.
• **Molality** (m), as discussed earlier, is moles of solute per kilogram of solvent.
• **Mass percent** involves grams of solute per 100 grams of solution.

In this exercise, concentration is vital for determining the boiling point depression of different solutions. Comparing concentrations reveals how the amount of solute impacts colligative properties, influencing solutions like KOH with a higher concentration resulting in a greater boiling point depression than others with lower concentrations.