Problem 12 - Chemistry in 30 days

Question

Among the following, the solution which shows the highest osmotic pressure is (a) \(0.05 \mathrm{M} \mathrm{Al}\left(\mathrm{NO}_{3}\right)_{3}\) (a) \(0.05 \mathrm{M} \mathrm{Al}\left(\mathrm{NO}_{3}\right)_{3}\) (c) \(0.05 \mathrm{M} \mathrm{K}_{3}\left[\mathrm{Cu}(\mathrm{CN})_{4}\right]\) (d) \(0.04 \mathrm{M} \mathrm{FeSO}_{4} \cdot\left(\mathrm{NH}_{4}\right)_{2} \mathrm{SO}_{4} \cdot 6 \mathrm{H}_{2} \mathrm{O}\)

Step-by-Step Solution

Answer

The solutions \( 0.05 \mathrm{M} \mathrm{Al}(\mathrm{NO}_3)_3 \) and \( 0.05 \mathrm{M} \mathrm{K}_3[\mathrm{Cu}(\mathrm{CN})_4] \) exhibit the highest osmotic pressure.

Step 1: Understand Osmotic Pressure Formula

The osmotic pressure \( \pi \) of a solution can be calculated using the formula \( \pi = iCRT \), where \( i \) is the van 't Hoff factor, \( C \) is the molarity of the solution, \( R \) is the gas constant, and \( T \) is the temperature in Kelvin. The higher the value of \( i \times C \), the higher the osmotic pressure.

Step 2: Determine Van 't Hoff Factor (i)

The van 't Hoff factor \( i \) is the number of ions a compound dissociates into when dissolved in water: - For \( \mathrm{Al}(\mathrm{NO}_3)_3 \), \( i = 4 \) (1 Al and 3 NO₃⁻ ions)- For \( \mathrm{K}_3[\mathrm{Cu}(\mathrm{CN})_4] \), \( i = 4 \) (3 K⁺ ions and 1 complex ion)- For \( \mathrm{FeSO}_4 \cdot (\mathrm{NH}_4)_2 \mathrm{SO}_4 \cdot 6\mathrm{H}_2\mathrm{O} \), \( i = 4 \) (1 Fe²⁺, 2 NH₄⁺, and 2 SO₄²⁻ ions)

Step 3: Calculate \( i \times C \)

Calculate the product \( i \times C \) for each solution:- \( \mathrm{Al}(\mathrm{NO}_3)_3 \): \( i \times C = 4 \times 0.05 = 0.20 \)- \( \mathrm{K}_3[\mathrm{Cu}(\mathrm{CN})_4] \): \( i \times C = 4 \times 0.05 = 0.20 \)- \( \mathrm{FeSO}_4 \cdot (\mathrm{NH}_4)_2 \mathrm{SO}_4 \cdot 6\mathrm{H}_2\mathrm{O} \): \( i \times C = 4 \times 0.04 = 0.16 \)

Step 4: Compare and Identify the Highest Value

Compare the \( i \times C \) values for each solution. The solutions with the highest value of \( i \times C \) are \( 0.05 \mathrm{M} \mathrm{Al}(\mathrm{NO}_3)_3 \) and \( 0.05 \mathrm{M} \mathrm{K}_3[\mathrm{Cu}(\mathrm{CN})_4] \), both equal to 0.20, which indicates they have the highest osmotic pressure. Both solutions are equivalent in terms of osmotic pressure.

Key Concepts

van 't Hoff factor

The van 't Hoff factor is a critical concept in understanding how substances behave in solutions. It essentially tells us how many particles a compound dissociates into when it's dissolved in water. This is significant because the number of particles in a solution influences properties such as osmotic pressure, boiling point elevation, and freezing point depression.

For example, consider a simple ionic compound like Al(NO\( \textsubscript{3}\))\( \textsubscript{3} \). When it dissolves in water, one formula unit dissociates into one aluminum ion (Al\( \textsuperscript{3+} \)) and three nitrate ions (NO\( \textsubscript{3}\))\( \textsuperscript{−} \). Thus, the total number of particles formed is four. Therefore, the van 't Hoff factor, denoted as \( i \), is 4.

Understanding the van 't Hoff factor helps us calculate important physical properties through equations such as \( \pi = iCRT \), where \( \pi \) is osmotic pressure, \( C \) is molarity, \( R \) is the ideal gas constant, and \( T \) is temperature in Kelvin. The van 't Hoff factor hence plays a vital role in predicting how the addition of a solute affects a solution.

molarity of solutions

Molarity is a way to express the concentration of a solution and is denoted by the letter \( M \). It tells us the number of moles of a solute present in one liter of solution. Molarity is a crucial factor when calculating the osmotic pressure because it directly influences the amount of solute present, which in turn affects properties like osmosis and diffusion.

For instance, if we have a solution of 0.05 M Al(NO\( \textsubscript{3}\))\( \textsubscript{3} \), this means there are 0.05 moles of aluminum nitrate per liter of solution. Similarly, for a 0.04 M solution of FeSO\( \textsubscript{4} \), it contains 0.04 moles of ferrous ammonium sulfate per liter.

• Molarity = moles of solute / liters of solution
• Molarity helps predict how chemical reactions will proceed in solution by indicating how many moles of reactants are available.
• Knowing molarity allows for the calculation of osmotic pressure using the formula \( \pi = iCRT \).

Thus, a solution's molarity, combined with its van 't Hoff factor, tells us a lot about its behavior in various chemical processes.

ionic dissociation in solutions

Ionic dissociation refers to the process where ionic compounds dissolve in water and separate into their respective ions. This process is essential in determining several solution properties, including osmotic pressure.

When ionic compounds dissolve, they break apart due to the attraction of the ions by water molecules, which surround and stabilize them. For example, when aluminum nitrate, Al(NO\( \textsubscript{3} \))\( \textsubscript{3} \), is dissolved in water, it dissociates into Al\( \textsuperscript{3+} \) ions and NO\( \textsubscript{3} \)\( \textsuperscript{−} \) ions. This leads to an increase in the number of particles in the solution, impacting colligative properties such as vapor pressure lowering, boiling point elevation, and osmotic pressure.

A few key points about ionic dissociation:

• Allows solutions to conduct electricity due to free ions.
• The extent of dissociation depends on the solubility of the compound.
• Helps in calculating the van 't Hoff factor for use in osmotic pressure and other property calculations.

Understanding ionic dissociation is vital in analyzing how ionic compounds contribute to various chemical properties and reactions in a solution.