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(a) Which solution is expected to have the higher boiling point: \(0.20 \mathrm{m}\) KBr or \(0.30 \mathrm{m}\) sugar? (b) Which aqueous solution has the lower freezing point: \(0.12 \mathrm{m} \mathrm{NH}_{4} \mathrm{NO}_{3}\) or \(0.10 \mathrm{m} \mathrm{Na}_{2} \mathrm{CO}_{3} ?\)

Short Answer

Expert verified
(a) 0.20 m KBr has a higher boiling point. (b) 0.10 m Na鈧侰O鈧 has a lower freezing point.

Step by step solution

01

Understanding the Problem

We need to compare two different sets of solutions based on their boiling and freezing points. The boiling point and freezing point of a solution are affected by the number of solute particles present in the solution, a concept described as colligative properties.
02

Review Colligative Properties

Colligative properties such as boiling point elevation and freezing point depression depend on the molal concentration of particles. More particles mean more effect on boiling or freezing points. We need to account for the dissociation of ionic compounds into their constituent ions.
03

Calculate Effective Concentration for KBr and Sugar

For part (a), KBr dissociates into 2 ions: K鈦 and Br鈦. The effective molality for KBr is therefore approximately double the initial molality, i.e., \(0.20 \, \text{m} \times 2 = 0.40 \, \text{m}\). Sugar does not dissociate as it is a covalent compound, maintaining a molality of \(0.30 \, \text{m}\).
04

Determine Higher Boiling Point

The solution with a higher molal concentration of particles will have a higher boiling point. Since KBr has an effective molality of \(0.40 \, \text{m}\) compared to \(0.30 \, \text{m}\) for sugar, the 0.20 m KBr solution will have the higher boiling point.
05

Calculate Effective Concentration for NH鈧凬O鈧 and Na鈧侰O鈧

For part (b), NH鈧凬O鈧 dissociates into 2 ions: \(\text{NH}_4^+\) and \(\text{NO}_3^-\), hence its effective molality is \(0.12 \, \text{m} \times 2 = 0.24 \, \text{m}\). Na鈧侰O鈧 dissociates into 3 ions: 2 \(\text{Na}^+\) and 1 \(\text{CO}_3^{2-}\), hence its effective molality is \(0.10 \, \text{m} \times 3 = 0.30 \, \text{m}\).
06

Determine Lower Freezing Point

The solution with a higher effective molal concentration of particles leads to a greater depression of the freezing point. With \(0.30 \, \text{m}\) effective molality, Na鈧侰O鈧 has a lower freezing point than NH鈧凬O鈧 (\(0.24 \, \text{m}\) effective molality).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Boiling Point Elevation
Boiling point elevation refers to the phenomenon where the boiling point of a liquid (solvent) increases when a non-volatile solute is dissolved in it. This happens because the addition of solute particles disrupts the escape of solvent molecules into the vapor phase, requiring more energy (heat) to overcome this disturbance and boil. Simply put, the presence of solute particles makes it harder for the liquid to transition into gas, thereby elevating its boiling point.

Key points to remember:
  • Boiling point elevation depends solely on the number of solute particles, not their identity. This is a perfect example of a colligative property.
  • The formula for boiling point elevation is \[\Delta T_b = i \cdot K_b \cdot m\]
    where \( \Delta T_b \) is the boiling point elevation, \( i \) is the van 't Hoff factor (number of particles the solute splits into), \( K_b \) is the ebullioscopic constant, and \( m \) is the molality of the solution.
  • Electrolytes like salts which dissociate into ions cause more significant elevation compared to non-electrolytes because they increase the number of particles in the solution.
In the exercise, comparing KBr and sugar, KBr dissociates into ions, thus effectively doubling the amount of solute particles as compared to the non-dissociating sugar, leading to a higher boiling point elevation for the KBr solution.
Freezing Point Depression
Freezing point depression occurs when the addition of a solute to a solvent results in the lowering of the freezing point of the solution. This effect is due to the solute particles interfering with the orderly arrangement of the solvent molecules required to form a solid. In simpler terms, solute particles work like obstacles that prevent the solvent from crystallizing as easily, meaning more energy removal (lower temperatures) is needed to solidify the solution.

Some essential points:
  • Like boiling point elevation, freezing point depression is a colligative property, meaning it depends only on the number of solute particles in the solution.
  • The formula to compute the freezing point depression is\[\Delta T_f = i \cdot K_f \cdot m\]
    where \( \Delta T_f \) is the depression in freezing point, \( i \) is the van 't Hoff factor, \( K_f \) is the cryoscopic constant, and \( m \) is the molality.
  • Ionic compounds, which dissociate into multiple ions in solution, tend to have a larger effect on freezing point depression compared to covalent compounds that do not dissociate.
In the exercise, Na鈧侰O鈧, which dissociates into three ions, results in a more significant decrease in freezing point compared to NH鈧凬O鈧, which breaks into just two ions.
Ionic Dissociation
Ionic dissociation refers to when ionic compounds, typically salts, split into their constituent ions when dissolved in a solvent. This process is crucial for understanding colligative properties because the number of particles that result from dissociation directly affects properties that depend on particle concentration, like boiling point elevation and freezing point depression.

Important notes to consider:
  • Ionic dissociation increases the effective concentration of particles in a solution. For example, NaCl dissociates into two ions (Na鈦 and Cl鈦), effectively doubling the concentration of particles compared to its initial molality.
  • The extent of dissociation is expressed as the van 't Hoff factor \( i \), which tells us how many particles a compound forms in the solution. For instance, for Na鈧侰O鈧, \( i = 3 \) because it dissociates into 2 Na鈦 and 1 CO鈧兟测伝.
  • Solutions exhibiting ionic dissociation often demonstrate greater colligative effects due to the increased number of particles.
In the exercise, recognizing the extent of ionic dissociation is pivotal in determining the boiling and freezing points of solutions, as it directly influences the molality of the solution based on the number of particles formed through dissociation.

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Most popular questions from this chapter

Which of the following substances is/are likely to dissolve in water, and which is/are likely to dissolve in benzene \(\left(\mathrm{C}_{6} \mathrm{H}_{6}\right) ?\) (a) \(\mathrm{NaNO}_{3}\) (b) diethyl ether, \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OCH}_{2} \mathrm{CH}_{3}\) (c) naphthalene, \(\mathrm{C}_{10} \mathrm{H}_{8}\) (see page 454 for structure) (d) \(\mathrm{NH}_{4} \mathrm{Cl}\)

A 35.0 -g sample of ethylene glycol, \(\mathrm{HOCH}_{2} \mathrm{CH}_{2} \mathrm{OH}\), is dissolved in 500.0 g of water. The vapor pressure of water at \(32^{\circ} \mathrm{C}\) is \(35.7 \mathrm{mm}\) Hg. What is the vapor pressure of the water-ethylene glycol solution at \(32^{\circ} \mathrm{C} ?\) (Ethylene glycol is nonvolatile.)

A newly synthesized compound containing boron and fluorine is \(22.1 \%\) boron. Dissolving \(0.146 \mathrm{g}\) of the compound in \(10.0 \mathrm{g}\) of benzene gives a solution with a vapor pressure of \(94.16 \mathrm{mm}\) Hg at \(25^{\circ} \mathrm{C} .\) (The vapor pressure of pure benzene at this temperature is 95.26 mm Hg.) In a separate experiment, it is found that the compound does not have a dipole moment. (a) What is the molecular formula for the compound? (b) Draw a Lewis structure for the molecule, and suggest a possible molecular structure. Give the bond angles in the molecule and the hybridization of the boron atom.

You want to prepare a solution that is \(0.0512 m\) in \(\mathrm{NaNO}_{3}\) What mass of \(\mathrm{NaNO}_{3}\) must be added to \(500 .\) g of water? What is the mole fraction of \(\mathrm{NaNO}_{3}\) in the solution?

Which pairs of liquids will be miscible? (a) \(\mathrm{H}_{2} \mathrm{O}\) and \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{3}\) (b) \(\mathrm{C}_{6} \mathrm{H}_{6}\) (benzene) and \(\mathrm{CCl}_{4}\) (c) \(\mathrm{H}_{2} \mathrm{O}\) and \(\mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H}\)

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