Question

List the following aqueous solutions in order of increasing boiling point: \(0.120 \mathrm{~m}\) glucose, \(0.050 \mathrm{~m} \mathrm{LiBr}, 0.050 \mathrm{~m}\) \(\mathrm{Zn}\left(\mathrm{NO}_{3}\right)_{2}\)

Short answer

The order of increasing boiling point for the given aqueous solutions is: LiBr < Glucose < Zn(NO3)2.

Step-by-step solution

Find the van't Hoff factor (i) for each solute

For this step, we need to determine how many particles each solute dissociates into in solution. Glucose is a non-electrolyte and does not dissociate in solution, thus having an i value of 1. For LiBr and Zn(NO3)2, they are both electrolytes and dissociate into ions, so we need to calculate the van't Hoff factor for each as follows: - Glucose: \(i = 1\) (as it does not dissociate) - LiBr: \(i = 1 + 1 = 2\) (1 Li+ and 1 Br- ions) - Zn(NO3)2: \(i = 1 + 2 \times 1 = 3\) (1 Zn2+ ion and 2 NO3- ions)

Calculate the boiling point elevation for each solution

To calculate the boiling point elevation, we use the formula: \[\Delta T_b = k_b \cdot i \cdot m\] where \(\Delta T_b\) is the boiling point elevation, \(k_b\) is the ebullioscopic constant (typically the same for all solutes in the same solvent), i is the van't Hoff factor, and m is the molality of the solution. We plug in the values for each solution and determine the boiling point elevation: - Glucose: \(\Delta T_{b1} = k_b \cdot 1 \cdot 0.120\) - LiBr: \(\Delta T_{b2} = k_b \cdot 2 \cdot 0.050\) - Zn(NO3)2: \(\Delta T_{b3} = k_b \cdot 3 \cdot 0.050\) Divide each equation by \(k_b\) and we get: - Glucose: \(\frac{\Delta T_{b1}}{k_b} = 0.120 \) - LiBr: \(\frac{\Delta T_{b2}}{k_b} = 0.100 \) - Zn(NO3)2: \(\frac{\Delta T_{b3}}{k_b} = 0.150 \)

Arrange the solutions in order of increasing boiling point

Based on the calculated values, we can now arrange the solutions in the order of increasing boiling point: 1. LiBr (\(\Delta T_b = 0.100\)) 2. Glucose (\(\Delta T_b = 0.120\)) 3. Zn(NO3)2 (\(\Delta T_b = 0.150\)) So the final order of increasing boiling point for the given aqueous solutions is: LiBr < Glucose < Zn(NO3)2.

Key concepts

van't Hoff factor

The van't Hoff factor, denoted as "i," is a term used in chemistry to indicate the number of particles a solute yields when dissolved in a solution. It's crucial when determining colligative properties, like boiling point elevation and freezing point depression.
\[\Delta T_b = k_b \cdot i \cdot m\]
Here's how the van't Hoff factor affects boiling point elevation:

• Non-electrolytes: These substances do not dissociate into ions in a solution. Glucose is a non-electrolyte, which means its van't Hoff factor is 1.
• Electrolytes: These substances dissociate fully or partially into ions. For example, LiBr dissociates into Li⁺ and Br^-, providing a van't Hoff factor of 2. Zn(NO₃)₂ dissociates into one Zn²⁺ ion and two NO₃^- ions, resulting in an "i" value of 3.

Understanding and calculating the van't Hoff factor correctly is essential for predicting how a solute will affect the boiling point and other properties of a solvent.

aqueous solutions

Aqueous solutions are formed when a solute dissolves in water, the solvent. They are vital in both laboratory experiments and industrial applications.
What makes water such a good solvent? Here are a few reasons:

• Polarity: Water molecules are polar, with a positive and negative end, allowing them to dissolve many different solutes.
• Hydrogen Bonding: Water can form hydrogen bonds with solutes that have compatible polar groups, facilitating dissolution.

Aqueous solutions are diverse, varying significantly depending on the solute added. When electrolytes like LiBr or Zn(NO₃)₂ are added to water, they dissociate into ions, affecting the solution's boiling and freezing points. In contrast, non-electrolytes like glucose do not form ions and influence these properties differently. Understanding the nature of aqueous solutions is critical for applications involving solubility, chemical reactions, and changes in physical properties.

molarity

Molarity is a basic concept in chemistry that measures the concentration of a solute in a solution. It is defined as the number of moles of solute per liter of solution and is expressed in units of moles per liter (M or mol/L).
Why is molarity important? Here are a few reasons:

• Measures Concentration: Molarity indicates how concentrated a solution is, which is crucial for understanding reaction dynamics and rates.
• Helps Standardize Solutions: By knowing the molarity, we can prepare precise solutions needed for accurate chemical analyses and experiments.

In the context of boiling point elevation, molarity is part of the formula \[\Delta T_b = k_b \cdot i \cdot m\]where "m" is the molality of the solution, which relates to molarity for dilute aqueous solutions. Understanding molarity helps chemists calculate how solute concentration affects the properties of a solution, like its boiling point.

boiling point

The boiling point is a critical physical property of any liquid. It is the temperature at which a liquid turns into vapor, indicating the energy required for molecules in the liquid to overcome atmospheric pressure.
How does boiling point affect solutions?

• Pure vs. Solution: Pure solvents have a set boiling point. Adding a solute, like in aqueous solutions, increases the boiling point due to the presence of dissolved particles. This is known as boiling point elevation.
• Colligative Properties: Boiling point elevation is a colligative property, meaning it depends on the number of solute particles, not their identity.

By understanding the boiling point of solutions, scientists can predict how solutions will behave under heat. For example, a higher van't Hoff factor results in a more significant increase in the boiling point, as seen with Zn(NO₃)_{2> compared to glucose in an aqueous solution.}