At 25°C, the osmotic pressure of each 0.01 M solutions of AB2 and sucrose (C12H220 11 ) are 0.38 atm and 0.16 atm respectively. The van't Hoff factor for AB2 will be

• 4.25
• 2.37
• 3.72
• 2.89

To determine the van't Hoff factor (i) for the compound AB2, we can use the concept of osmotic pressure, which is directly related to the concentration of solute particles in solution. The van't Hoff factor is a measure of how many particles a solute produces in solution compared to the number of formula units dissolved. In this case, we know the osmotic pressures of both AB2 and sucrose solutions and can derive the van't Hoff factor from this information.

The Relationship Between Osmotic Pressure and Concentration

The osmotic pressure (\(\Pi\)) of a solution is given by the formula:

\(\Pi = i \cdot C \cdot R \cdot T\)

Where:

• \(\Pi\) = osmotic pressure
• i = van't Hoff factor
• C = molarity of the solution
• R = universal gas constant (0.0821 L·atm/(K·mol))
• T = temperature in Kelvin

Calculating the Van't Hoff Factor for AB2

First, let's convert the temperature from Celsius to Kelvin. At 25°C, the temperature in Kelvin is:

T = 25 + 273.15 = 298.15 K

Now, we can rearrange the osmotic pressure formula to solve for the van't Hoff factor:

i = \(\frac{\Pi}{C \cdot R \cdot T}\)

Now, we can substitute the known values for the AB2 solution:

• \(\Pi\) = 0.38 atm
• C = 0.01 M
• R = 0.0821 L·atm/(K·mol)
• T = 298.15 K

Plugging these values into the equation gives us:

i = \(\frac{0.38}{0.01 \cdot 0.0821 \cdot 298.15}\)

Calculating the Result

Let's calculate the denominator first:

0.01 M \(\cdot\) 0.0821 L·atm/(K·mol) \(\cdot\) 298.15 K = 0.2452 atm

Now we can continue with the calculation:

i = \(\frac{0.38}{0.2452} \approx 1.55\)

Now let's clarify the nature of AB2. Since it is presumed to dissociate into three particles (1 AB2 molecule yields 1 A and 2 B ions), we expect a theoretical van't Hoff factor of 3. However, our calculated value of approximately 1.55 suggests incomplete dissociation, possibly due to ion pairing or other interactions in solution.

Comparative Analysis

Now, let’s compare this with the sucrose solution. Sucrose does not dissociate in solution, meaning its van't Hoff factor is 1. The osmotic pressure of the sucrose solution, which is 0.16 atm, could also be calculated similarly, confirming that it behaves as a non-electrolyte.

Final Thoughts

In conclusion, while the theoretical van't Hoff factor for AB2, if it fully dissociates, would be close to 3, the actual calculated value shows it is lower, likely due to some interactions preventing complete dissociation. Therefore, if you were to choose from the provided options close to our findings, you would opt for a value that reflects the observed behavior in solution.