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 (\textrm{NaNO} _ { 3 } ) .

Short answer

The boiling point of a solution depends on the number of solute particles present. Glucose and sucrose contribute one particle each, while sodium nitrate contributes two particles. As a result, the order of increasing boiling points for the given 10% aqueous solutions is: glucose and sucrose (equal) < sodium nitrate.

Step-by-step solution

Understand the concept of boiling point elevation.

Boiling point elevation is a colligative property, which means it depends only on the number of solute particles and not their identity. When a non-volatile solute is added to a solvent, it decreases the vapor pressure of the solution, and hence, a higher temperature is required to reach the vapor pressure equal to the atmospheric pressure, causing an increase in the boiling point of the solution.

Determine the number of particles for each solute.

The boiling point elevation is proportional to the number of solute particles in the solution. Therefore, we need to find the number of particles (molecules or ions) contributed by each solute. For glucose, we have \(1\) molecule of \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\) per glucose unit, for sucrose, we have \(1\) molecule of \(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\) per sucrose unit, and for sodium nitrate, when it dissolves in water, it dissociates into \(2\) ions: \(1\) ion of \(\mathrm{Na}^{+}\) and \(1\) ion of \(\mathrm{NO}_{3}^{-}\).

Compare the boiling point elevations of the solutions.

Since all solutions have the same concentration, the one with more particles will have a higher boiling point elevation, and thus a higher boiling point. Glucose and sucrose contribute one particle each, while sodium nitrate contributes two particles. Therefore, the sodium nitrate solution will have the greatest boiling point elevation, and thus a higher boiling point than glucose and sucrose solutions.

Arrange the solutions in order of their boiling points.

With the comparative boiling point elevations in mind, we can now arrange the solutions in order of increasing boiling point. Since glucose and sucrose both have the same number of particles and the same boiling point elevation, they can be considered as having equal boiling points. Therefore, the order of increasing boiling points is: glucose and sucrose (equal) < sodium nitrate.

Key concepts

Colligative Properties

Colligative properties are a set of physical features of solutions that depend solely on the number of dissolved particles per unit of solvent, not on what those particles are. This fascinating aspect of chemistry explains how adding a substance to a solvent can change properties such as boiling point, freezing point, vapor pressure, and osmotic pressure.

For instance, when a solute is dissolved in a liquid solvent, the boiling point of the solution typically increases—a phenomenon known as boiling point elevation. Similarly, the freezing point goes down, in what's called freezing point depression. Another effect is the lowering of vapor pressure. It's essential to grasp that these changes occur irrespective of the solute's chemical identity; it's the quantity that matters. This principle allows scientists and engineers to predict how a solution will behave under different conditions.

Students studying this concept in the context of boiling point might see problems asking them to rank solutions by their boiling points, based on the amount of solute they contain.

Non-Volatile Solute

You may be wondering what a non-volatile solute is. In simple terms, it's a substance that does not readily evaporate into a gas under existing conditions. These solutes tend to have larger molecules and stronger intermolecular forces, keeping them from vaporizing easily.

When a non-volatile solute is dissolved in a solvent, it affects colligative properties such as boiling point elevation. By adding a non-volatile component to a liquid, you're effectively limiting the number of solvent molecules that can escape into the vapor phase. This restriction leads to a decrease in vapor pressure. Consequently, the solution needs a higher temperature to reach a vapor pressure that equals the atmospheric pressure. Hence, the boiling point goes up.

Larger amounts of a non-volatile solute will correspond to a higher increase in boiling point elevation. So, for homework problems or lab experiments requiring the calculation of boiling points, it's crucial to consider the nature of the solute used.

Dissociation of Electrolytes

Let's delve into the dissociation of electrolytes, a key factor in understanding boiling point elevation in solutions with ionic compounds. Electrolytes are substances that, when dissolved in water, break apart or dissociate into ions, which are charged particles. These ions are conductive and can carry an electric current through the solution.

Common salt \(NaCl\), for example, dissociates into \(Na^+\) and \(Cl^-\) ions. The important thing to remember here is that the dissociation process increases the number of particles in the solution, which in turn affects the colligative properties. Looking back at our textbook problem, we can see that sodium nitrate \(NaNO_3\) dissociates into two ions - \(Na^+\) and \(NO_3^-\) - which means it contributes double the number of particles compared to molecular compounds like glucose or sucrose that do not dissociate. This will lead to a greater boiling point elevation for the sodium nitrate solution.

Understanding the dissociation of electrolytes is essential for accurately predicting the changes in boiling point and other colligative properties. When working out problems or performing experiments, you should always take into account whether your solute is an electrolyte and how fully it dissociates in the solution.