Problem 11 - Chemistry in 30 days

Question

Among the following, the solution which shows the highest osmotic pressure is (a) \(0.05 \mathrm{M} \mathrm{NaCl}\) (b) \(0.10 \mathrm{M} \mathrm{BaCl}_{2}\) (c) \(0.05 \mathrm{M} \mathrm{FeCl}_{3}\) (d) \(0.05 \mathrm{M} \mathrm{Na}_{2} \mathrm{SO}_{4}\)

Step-by-Step Solution

Answer

The solution with the highest osmotic pressure is 0.10 M BaCl\(_2\).

Step 1: Understanding Osmotic Pressure Formula

Osmotic pressure (C0) is given by the formula \( \pi = iMRT \), where \( i \) is the van't Hoff factor, \( M \) is the molarity, \( R \) is the gas constant, and \( T \) is the temperature in Kelvin. Here, only \( i \) and \( M \) affect the relative values since \( R \) and \( T \) are constant.

Step 2: Calculate van't Hoff Factor

The van't Hoff factor \( i \) is the number of particles the compound dissociates into in solution. For NaCl, \( i = 2 \); for BaCl\(_2\), \( i = 3 \); for FeCl\(_3\), \( i = 4 \); and for Na\(_2\)SO\(_4\), \( i = 3 \).

Step 3: Determine Effective Concentration

The effective concentration for each solution can be determined by multiplying \( M \) and \( i \). Thus, for NaCl it is \( 0.05 \, M \times 2 = 0.10 \, M \), for BaCl\(_2\) it is \( 0.10 \, M \times 3 = 0.30 \, M \), for FeCl\(_3\) it is \( 0.05 \, M \times 4 = 0.20 \, M \), and for Na\(_2\)SO\(_4\) it is \( 0.05 \, M \times 3 = 0.15 \, M \).

Step 4: Compare Effective Concentrations

The compound with the highest effective concentration will have the highest osmotic pressure, as \( \pi \propto iM \). Among \( 0.10 \, M \), \( 0.30 \, M \), \( 0.20 \, M \), and \( 0.15 \, M \), \( 0.30 \, M \) is the greatest.

Step 5: Conclusion

Since 0.10 M BaCl\(_2\) has the highest effective concentration of 0.30 M, it will have the highest osmotic pressure among the options provided.

Key Concepts

van't Hoff factor

The van't Hoff factor, denoted as \( i \), plays an essential role in determining the properties of solutions, particularly their colligative properties such as osmotic pressure. The van't Hoff factor indicates the number of particles into which a solute dissociates in a solution.

For instance, when NaCl dissolves in water, it separates into two ions: \( \text{Na}^+ \) and \( \text{Cl}^- \). Consequently, the van't Hoff factor for NaCl is 2. Similarly, for other ionic compounds, the factor would depend on the total ions produced from dissociation.

Understanding the van't Hoff factor is crucial because it affects how we calculate the effective concentration of solute particles in a solution, which in turn influences properties like osmotic pressure, boiling point elevation, and freezing point depression.

molarity

Molarity, commonly represented by \( M \), is a measure of the concentration of a solute in a solution. It is defined as the number of moles of solute per liter of solution. The formula to calculate molarity is: \[ M = \frac{\text{moles of solute}}{\text{liters of solution}} \]

Molarity is a critical factor in determining the outcome of chemical reactions and the calculation of other properties, such as colligative properties like osmotic pressure.

• High molarity indicates a more concentrated solution with more solute particles.
• Low molarity means a less concentrated solution with fewer solute particles.

By understanding molarity, students can predict how changing the amount of solute or the volume of solution can affect the solution's overall behavior in a chemical context.

solution concentration

Solution concentration refers to the amount of solute present in a given quantity of solvent or solution. It is a broad concept encompassing different types of concentration measurements, including molarity, molality, and mass percent, among others.

In the context of osmotic pressure, we focus on molarity, which tells us how many moles of solute are present in one liter of solution.

The concentration of solute particles is vital because colligative properties like osmotic pressure depend on the concentration of solute particles, rather than the identity of the solute particles themselves.

In exercises such as the one given, students learn to differentiate between solutions based on their concentration, multiplying molarity by the van't Hoff factor to get the effective concentration impacting osmotic pressure.

ionic dissociation

Ionic dissociation is the process by which an ionic compound, when dissolved in water, separates into its constituent ions.

For example, when BaCl\(_2\) dissolves in water, it dissociates into one Ba\(^{2+}\) ion and two Cl\(^-\) ions, making a total of three ions. This gives BaCl\(_2\) a van't Hoff factor of 3.

Understanding ionic dissociation is essential because it determines the number of particles in the solution, affecting the van't Hoff factor and subsequently the calculation of colligative properties like osmotic pressure.

Different ionic compounds dissociate into a different number of particles in a solution, and this directly influences the solution's behavior, as seen in the context of calculating which solution has the highest osmotic pressure.