Problem 58 - Chemistry: Principles and Reactions

Question

The freezing point of a \(0.21 m\) aqueous solution of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) is \(-0.796^{\circ} \mathrm{C}\) (a) What is \(i\) ? (b) Is the solution made up primarily of (i) \(\mathrm{H}_{2} \mathrm{SO}_{4}\) molecules only? (ii) \(\mathrm{H}^{+}\) and \(\mathrm{HSO}_{4}^{-}\) ions? (iii) \(2 \mathrm{H}^{+}\) and \(1 \mathrm{SO}_{4}^{2-}\) ions?

Step-by-Step Solution

Answer

Answer: The van't Hoff factor (i) is approximately 2, and the solution is made up primarily of H+ and HSO4- ions.

Step 1: Calculate the Freezing Point Depression

The freezing point of water is 0°C. The freezing point depression (ΔTf) is the difference between the freezing point of the pure solvent (water) and the freezing point of the solution. So, ΔTf = Freezing point of water - Freezing point of solution ΔTf = 0 - (-0.796) ΔTf = 0.796°C

Step 2: Use the Freezing Point Depression Formula to Find i

The freezing point depression formula is: ΔTf = i * Kf * m where: ΔTf = Freezing point depression (0.796°C, already calculated in Step 1) Kf = The cryoscopic constant for water (1.86°C·kg/mol) m = Molality of the solution (0.21 mol/kg) i = Van't Hoff factor (this is what we need to find) Substituting the known values, we get: 0.796 = i * 1.86 * 0.21 Now we will solve for i: i = 0.796 / (1.86 * 0.21) i ≈ 2

Step 3: Determine the Primary Ions in the Solution

Since the calculated van't Hoff factor (i) is close to 2, we can conclude that the solution is made up primarily of H+ and HSO4- ions. Therefore, the solution is primarily composed of the ions mentioned in option (ii). #Answer#: (a) The van't Hoff factor (i) is approximately 2. (b) The solution is made up primarily of H+ and HSO4- ions (option (ii)).

Key Concepts

Van't Hoff factor

The van't Hoff factor, often represented as \( i \), is a crucial concept in understanding the effect of solutes on colligative properties such as freezing point depression. It represents the number of particles a compound dissociates into when dissolved in a solvent. For non-electrolytes, like sugar, the van't Hoff factor is usually 1, since they do not dissociate into ions.
For electrolytes, like

• Acids: Strong acids, such as $url{www.heliosdfx.cominform/parated-alert-metroot/furl volutpat-conference-roduct/}HCl, completely dissociate into two ions (\( i = 2 \)), while weaker acids may have a van't Hoff factor slightly greater than 1.
• Bases: Strong bases like NaOH dissociate fully into two ions, leading to \( i = 2 \).
• Salts: Ionic compounds, like NaCl, also dissociate fully, each resulting in multiple particles.

In the case of sulfuric acid (\( \text{H}_{2} \text{SO}_{4} \)), it partially dissociates into \( \text{H}^+ \) ions and \( \text{HSO}_4^- \) ions, giving a van't Hoff factor close to 2. This helps explain the observed freezing point depression, as the presence of these ions lowers the temperature at which the solution freezes.

Cryoscopic constant

The cryoscopic constant, denoted as \( K_f \), is a property specific to a solvent which quantifies its ability to lower the freezing point when a solute is added. Every solvent has a different cryoscopic constant, determining how much the freezing point changes per molal concentration of the solute. For water, this constant is \( 1.86^{\circ} \text{C} \cdot \text{kg/mol} \).
This constant is utilized in the freezing point depression formula: \[ \Delta T_f = i \times K_f \times m \]Here:

• \( \Delta T_f \): The change in freezing point
• \( i \): van't Hoff factor
• \( K_f \): Cryoscopic constant
• \( m \): Molality of the solution

Understanding \( K_f \) is essential for accurately calculating the impact of different solutes on a solvent's freezing point. In practical applications, this constant allows scientists to predict and manipulate the freezing points of solutions by adjusting solutes and their concentrations. This is vital in industries such as automotive, where antifreeze application depends heavily on cryoscopic constants.

Molality

Molality, represented by \( m \), measures the concentration of a solute in a solution, specifically defined as the number of moles of solute per kilogram of solvent. Unlike molarity, molality does not change with temperature, as it is based on mass rather than volume.
This concentration measurement is crucial in calculations involving colligative properties like freezing point depression because it accounts for the amount of solvent directly. It helps standardize comparisons across different types of solutions.The formula for molality is:\[ m = \frac{\text{moles of solute}}{\text{kilograms of solvent}} \]Molality is a practical measure in scientific studies, especially when comparing solutions at different temperatures. For example:

• A common application is the study of how solutions behave under extreme temperature conditions.
• In this exercise, the \( 0.21 m \) molality indicates the concentration of \( \text{H}_{2} \text{SO}_{4} \) used to calculate the freezing point depression.

Using molality in experiments ensures that results are not skewed by temperature changes, making it a more reliable measure than molarity for such studies.

Aqueous solution chemistry

Aqueous solution chemistry focuses on substances dissolved in water, where water acts as the solvent. This field encompasses a wide range of reactions and properties since water is a universal solvent and interacts uniquely with various solutes, including acids, bases, and salts.
When dealing with an aqueous solution, several factors come into play:

• Dissolution: Water's polarity allows it to dissolve many ionic compounds into constituent ions.
• Reactivity: Water can participate in chemical reactions, such as hydrolysis, affecting the solubility and behavior of dissolved substances.
• Electric conductivity: Ionic compounds in water increase its ability to conduct electricity due to the presence of free ions.

Understanding aqueous solutions is crucial when exploring freezing point depression. For example, a solution of sulfuric acid (\( \text{H}_{2} \text{SO}_{4} \)) in water dissociates into ions which influence the freezing process.Through interactions in an aqueous solution, the characteristics of solute and solvent combine to alter physical properties, playing an essential role in fields like environmental science, medicine, and industrial chemistry.