Question

Arrange the following aqueous solutions, each \(10 \%\) by mass in solute, in order of increasing boiling point: glucose \(\left(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\right)\), sucrose \(\left(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\right)\), sodium nitrate \(\left(\mathrm{NaNO}_{3}\right)\)

Short answer

The order of increasing boiling point for the given 10% by mass aqueous solutions is: \( C_6H_{12}O_6 \) (Glucose) ≈ \( C_{12}H_{22}O_{11} \) (Sucrose) < \( \mathrm{NaNO}_{3} \) (Sodium Nitrate). This is based on the number of particles produced by each solute, with glucose and sucrose producing one particle per molecule and sodium nitrate producing two particles per molecule.

Step-by-step solution

Define the Boiling Point Elevation Concept

The boiling point elevation is a colligative property, which means that it depends on the number of solute particles present in the solution and not on the nature of the solute particles. Therefore, the more solute particles in a solution, the higher the boiling point.

Identify the Number of Particles Released by Each Solute

We have to check the number of particles that will be released by each solute in the aqueous solution. 1. Glucose (\(C_6H_{12}O_6\)): It is a non-electrolyte and will not ionize in water. So, it will produce only one particle per molecule. 2. Sucrose (\(C_{12}H_{22}O_{11}\)): It is also a non-electrolyte and will not ionize in water. So, it will produce one particle per molecule. 3. Sodium Nitrate (\(\mathrm{NaNO}_{3}\)): It is an electrolyte and will ionize in water to produce its ions. The dissociation reaction for sodium nitrate is: \( \mathrm{NaNO_3} \longrightarrow \mathrm{Na^{+}} + \mathrm{NO_3^{-}} \) So, sodium nitrate will produce two particles (Na+ and NO3-) per molecule.

Arrange the Aqueous Solutions in Order of Increasing Boiling Point

Now that we know the number of particles produced by each solute, we can arrange the aqueous solutions in order of their increasing boiling point: 1. Glucose and Sucrose both produce one particle per molecule. Therefore, their effect on the boiling point elevation will be the same and will have a lower boiling point compared to sodium nitrate. 2. Sodium Nitrate produces two particles per molecule which will have more effect on the boiling point elevation. So, sodium nitrate solution will have the highest boiling point among all three solutions. Thus, the order of increasing boiling point for the given aqueous solutions is: \( C_6H_{12}O_6 \) (Glucose) ≈ \( C_{12}H_{22}O_{11} \) (Sucrose) < \( \mathrm{NaNO}_{3} \) (Sodium Nitrate).

Key concepts

Colligative Properties

Colligative properties are fascinating because they depend on the total number of solute particles in a solution, rather than the type or identity of those particles. This means that attributes like the boiling point elevation, freezing point depression, vapor pressure lowering, and osmotic pressure are influenced solely by how much solute is present.
The more solute particles dissolved in the solvent, the more significant the effect on these properties. This is why sugar and salt, despite being different chemically, can both raise the boiling point of water. But the key difference lies in how they exist in a solution. Colligative properties help us understand fundamental concepts in chemistry and are crucial in industries like food preservation and pharmaceuticals.

Number of Particles

The number of particles a solute releases into a solution directly impacts collorative properties like boiling point elevation. In our case, we see this effect clearly. Glucose and sucrose, which are non-electrolytes, dissolve in water but do not dissociate into ions. Each molecule of glucose or sucrose counts as a single particle in solution.
Sodium nitrate, an electrolyte, tells a different story. When dissolved in water, it dissociates into two ions: sodium (Na⁺) and nitrate (NO₃^-). This dissociation means that each molecule of sodium nitrate actually counts as two particles in the solution. More particles from a solute like sodium nitrate mean a more significant elevation of the solution's boiling point. Understanding how many particles a solute produces is crucial in predicting how it will affect a solution's properties.

Non-electrolyte and Electrolyte Behavior

Non-electrolytes, like glucose and sucrose, are compounds that, when dissolved, do not dissociate into ions. In solutions containing non-electrolytes, molecules remain intact, behaving uniformly without separating. This straightforward behavior results in fewer particles per solute molecule, affecting colligative properties less significantly.
Electrolytes, such as sodium nitrate, break into ions when dissolved in water. This ionization greatly increases the number of particles in the solution. For example, ionic compounds like sodium nitrate split into two ions, effectively doubling the number of particles compared to a non-electrolyte with the same molar concentration. The more particles present, the more pronounced the effects on boiling point elevation, freezing point depression, and other colligative properties. This distinction between non-electrolyte and electrolyte behavior is essential for predicting and controlling solution behavior in various scientific and practical applications.