Question

Order these solutions in order of decreasing osmotic pressure, assuming an ideal van't Hoff factor: 0.1 \(\mathrm{M} \mathrm{HCl}, 0.1 \mathrm{M} \mathrm{CaCl}_{2}, 0.05 \mathrm{M} \mathrm{MgBr}_{2},\) and \(0.07 \mathrm{M} \mathrm{Ga}\left(\mathrm{C}_{2} \mathrm{H}_{3} \mathrm{O}_{2}\right)_{3}\).

Short answer

Order: CaCl2, Ga(C2H3O2)3, HCl, MgBr2.

Step-by-step solution

Understanding Osmotic Pressure and the Formula

Osmotic pressure (\( \Pi \)) is calculated using the formula \( \Pi = \imath \times M \times R \times T \), where \( \imath \) is the van't Hoff factor, \( M \) is molarity, \( R \) is the ideal gas constant, and \( T \) is the temperature in Kelvin. In this problem, we need to consider the van’t Hoff factor for each solution to determine the osmotic pressure.

Calculate the Van't Hoff Factor for Each Compound

1. \( \text{HCl} \) dissociates into \( \text{H}^+ \) and \( \text{Cl}^- \), providing \( \imath = 2 \).2. \( \text{CaCl}_2 \) dissociates into \( \text{Ca}^{2+} \) and 2 \( \text{Cl}^- \), giving \( \imath = 3 \).3. \( \text{MgBr}_2 \) dissociates into \( \text{Mg}^{2+} \) and 2 \( \text{Br}^- \), also resulting in \( \imath = 3 \).4. \( \text{Ga}( ext{C}_2 ext{H}_3 ext{O}_2)_3 \) dissociates into \( \text{Ga}^{3+} \) and 3 \( \text{C}_2 ext{H}_3 ext{O}_2^- \) ions, so \( \imath = 4 \).

Calculate the Osmotic Pressure for Each Solution

For each solution, calculate \( \Pi = \imath \times M \). Since \( R \) and \( T \) are constant for all calculations, we only compare \( \imath \times M \).1. \( \text{HCl} \): \( 2 \times 0.1 = 0.2 \)2. \( \text{CaCl}_2 \): \( 3 \times 0.1 = 0.3 \)3. \( \text{MgBr}_2 \): \( 3 \times 0.05 = 0.15 \)4. \( \text{Ga}( ext{C}_2 ext{H}_3 ext{O}_2)_3 \): \( 4 \times 0.07 = 0.28 \) Thus, the osmotic pressures in decreasing order are: CaCl2, Ga(C2H3O2)3, HCl, MgBr2.

Key concepts

van't Hoff factor

The van't Hoff factor, denoted as \( \imath \), plays a crucial role in determining osmotic pressure. It describes how many particles a compound dissociates into in a solution. This factor accounts for the number of ions formed from the dissociation of a solute.

For example, when hydrochloric acid (HCl) is dissolved, it breaks into one hydrogen ion (\( \text{H}^+ \)) and one chloride ion (\( \text{Cl}^- \)). Thus, its van't Hoff factor is 2.

• HCl: \( \text{HCl} \rightarrow \text{H}^+ + \text{Cl}^- \), \( \imath = 2 \)
• Calcium chloride (\( \text{CaCl}_2 \)): \( \text{CaCl}_2 \rightarrow \text{Ca}^{2+} + 2 \text{Cl}^- \), resulting in \( \imath = 3 \).
• Magnesium bromide (\( \text{MgBr}_2 \)): \( \text{MgBr}_2 \rightarrow \text{Mg}^{2+} + 2 \text{Br}^- \), also an \( \imath = 3 \).
• Gallium acetate \( \left(\text{Ga(C}_2 \text{H}_3 \text{O}_2\right)_3 \): \( \text{Ga(C}_2 \text{H}_3 \text{O}_2\right)_3 \rightarrow \text{Ga}^{3+} + 3 \text{C}_2 \text{H}_3 \text{O}_2^- \), thus, \( \imath = 4 \).

The van't Hoff factor is essential when calculating properties like osmotic pressure because it directly influences how a solute behaves in a solution.

dissociation

Dissociation is the process whereby a compound separates into ions when dissolved in a solvent like water. This process is significant in determining the van't Hoff factor, which, in turn, impacts the colligative properties of solutions, such as boiling point elevation, freezing point depression, and osmotic pressure.

Ionic compounds typically dissociate in water. For instance, HCl dissociates into its constituent ions, H+ and Cl-, as it interacts with water molecules. This separation increases the number of particles in the solution, impacting various properties.

• Complete Dissociation: Compounds like HCl and NaCl dissociate completely in water.
• Partial Dissociation: Weak acids and bases, like acetic acid (CH3COOH), only partially dissociate.

The degree of dissociation provides insight into the solute’s behavior and the solution's ionic strength. Understanding the dissociation process is crucial for predicting how solutes will affect the characteristics of a solution.

solution concentration

Solution concentration, often expressed in molarity (M), plays a pivotal role in determining the properties of a solution, such as osmotic pressure. Molarity is defined as the number of moles of solute per liter of solution. It provides a measure of how much solute is present in a given volume of solvent.

In osmotic pressure calculations, solution concentration directly affects the outcome. Specifically, osmotic pressure is calculated using the formula \( \Pi = \imath \times M \times R \times T \). For comparative purposes, since R and T are constants, the focus is primarily on \( \imath \times M \).

• Higher Molarity: A higher concentration of solute will contribute to a higher osmotic pressure.
• Comparative Analysis: To compare solutions, examining \( \imath \times M \) helps determine which solution exerts greater osmotic pressure.

Concentration helps gauge how different solutes, with their varying dissociation profiles and resulting van't Hoff factors, will influence the solution's osmotic attributes.